STS/phplot.php

<?php
/**
 * PHPlot - A class for creating scientific and business graphs, charts, plots
 *
 * This file contains two PHP classes which are used to create graphs,
 * charts, and plots. The PHPlot class is the basic class which creates
 * indexed-color images, and the extended PHPlot_truecolor class creates
 * full-color (24-bit) images.
 * PHPlot currently requires PHP 5.3 or later.
 *
 * $Id: phplot.php 1774 2015-11-03 00:18:50Z lbayuk $
 *
 * @version 6.2.0
 * @copyright 1998-2015 Afan Ottenheimer
 * @license GNU Lesser General Public License, version 2.1
 * @link http://sourceforge.net/projects/phplot/ PHPlot Web Site with downloads, tracker, discussion
 * @link http://phplot.sourceforge.net PHPlot Project Web Site with links to documentation
 * @author lbayuk (2006-present) <lbayuk@users.sourceforge.net>
 * @author Miguel de Benito Delgado (co-author and maintainer, 2003-2005)
 * @author Afan Ottenheimer (original author)
 */

/*
 * This is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation;
 * version 2.1 of the License.
 *
 * This software is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this software; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
 * ---------------------------------------------------------------------
 */

/**
 * Class for creating a plot
 *
 * The PHPlot class represents a plot (chart, graph) with all associated
 * parameters. This creates a palette (indexed) color image which is limited
 * to 256 total colors. For truecolor images (24 bit R, G, B), see the
 * PHPlot_truecolor class.
 *
 * In most cases, methods of PHPlot just change the internal properties, and
 * nothing actually happens until the DrawGraph() method is used. Therefore
 * methods can be used in any order up until DrawGraph(); the order should not
 * affect the results.
 *
 * Note: Without a background image, the PHPlot class creates a palette
 * (indexed) color image, and the PHPlot_truecolor class creates a truecolor
 * image. If a background image is used with the constructor of either class,
 * the type of image produced matches the type of the background image.
 *
 */
class PHPlot
{
    /** PHPlot version constant as a string */
    const version = '6.2.0';
    /** PHPlot version constant as a number = major * 10000 + minor * 100 + patch */
    const version_id = 60200;

    // All class variables are declared here, and initialized (if applicable).
    // Starting with PHPlot-6.0, most variables have 'protected' visibility
    // For more information on these variables, see the Reference Manual, Developer's Guide, List
    // of Member Variables. The list below is in alphabetical order, matching the manual.

    /** Calculated width of bars for bar charts */
    protected $actual_bar_width;
    /** Calculated bar gap */
    protected $bar_adjust_gap;
    /** Extra space between groups of bars */
    public $bar_extra_space = 0.5;
    /** Width of bar relative to space for one bar */
    public $bar_width_adjust = 1;
    /** Color (R,G,B,A) for image background */
    protected $bg_color;
    /** Background image filename */
    protected $bgimg;
    /** Background image tiling mode */
    protected $bgmode;
    /** Scale factor for box widths in box plots */
    public $boxes_frac_width = 0.3;
    /** Maximum half-width for boxes in box plots */
    public $boxes_max_width = 8;
    /** Minimum half-width for boxes in box plots */
    public $boxes_min_width = 2;
    /** Ratio of the width of the 'T' ends of box plot whiskers to the width of the boxes */
    public $boxes_t_width = 0.6;
    /** Flag: Don't send cache suppression headers */
    protected $browser_cache = FALSE;
    /** Max bubble size for bubbles plots */
    public $bubbles_max_size;
    /** Min bubbles size for bubble plots */
    public $bubbles_min_size = 6;
    /** Callback (hook) function information, indexed by callback reason */
    protected $callbacks = array(
        'data_points' => NULL,
        'draw_setup' => NULL,
        'draw_image_background' => NULL,
        'draw_plotarea_background' => NULL,
        'draw_titles' => NULL,
        'draw_axes' => NULL,
        'draw_graph' => NULL,
        'draw_border' => NULL,
        'draw_legend' => NULL,
        'draw_all' => NULL,
        'data_color' => NULL,
        'debug_textbox' => NULL,
        'debug_scale' => NULL,
    );
    /** Flag: Draw dashed or solid grid lines? */
    protected $dashed_grid = TRUE;
    /** Initial dashed pattern code */
    protected $dashed_style = '2-4';
    /** The (converted) data array */
    protected $data;
    /** Array of colors (R,G,B,A) for data borders available with some plot types */
    protected $data_border_colors;
    /** Array of colors (R,G,B,A) for data lines/marks/bars/etc. */
    protected $data_colors;
    /** Maximum number of dependent variable values */
    protected $data_columns;
    /** Array: Per row maximum Y value */
    protected $data_max;
    /** Array: Per row minimum Y value */
    protected $data_min;
    /** Format of the data array */
    protected $data_type = 'text-data';
    /** Obsolete - suffix for 'data'-formatted labels */
    public $data_units_text = '';
    /** Angle (in degrees) for data value labels */
    public $data_value_label_angle = 90;
    /** Distance (in pixels) for data value labels */
    public $data_value_label_distance = 5;
    /** Color (R,G,B,A) to use for axis data labels */
    protected $datalabel_color;
    /** Flag: data type has error bars */
    protected $datatype_error_bars;
    /** Flag: data type has implied X or Y */
    protected $datatype_implied;
    /** Flag: data type is one-column data for pie chart */
    protected $datatype_pie_single;
    /** Flag: data type has swapped X and Y values (horizontal plot) */
    protected $datatype_swapped_xy;
    /** Flag: data type includes Y and Z value pairs */
    protected $datatype_yz;
    /** Static array of data type information */
    static protected $datatypes = array(   // See DecodeDataType() and $datatype_* flags
        'text-data'          => array('implied' => TRUE),
        'text-data-single'   => array('implied' => TRUE, 'pie_single' => TRUE),
        'data-data'          => array(),
        'data-data-error'    => array('error_bars' => TRUE),
        'data-data-yx'       => array('swapped_xy' => TRUE),
        'text-data-yx'       => array('implied' => TRUE, 'swapped_xy' => TRUE),
        'data-data-xyz'      => array('yz' => TRUE),
        'data-data-yx-error' => array('swapped_xy' => TRUE, 'error_bars' => TRUE),
    );
    /** Static array of data type aliases => primary name */
    static protected $datatypes_map = array(
        'text-linear' => 'text-data',
        'linear-linear' => 'data-data',
        'linear-linear-error' => 'data-data-error',
        'text-data-pie' => 'text-data-single',
        'data-data-error-yx' => 'data-data-yx-error',
    );
    /** Character to use for decimal point in formatted numbers */
    protected $decimal_point;
    /** The default color array, used to initialize data_colors and error_bar_colors */
    protected $default_colors = array(
        'SkyBlue', 'green', 'orange', 'blue', 'red', 'DarkGreen', 'purple', 'peru',
        'cyan', 'salmon', 'SlateBlue', 'YellowGreen', 'magenta', 'aquamarine1', 'gold', 'violet'
    );
    /** Dashed-line template, as a string of space-separated markers (see SetDefaultDashedStyle) */
    protected $default_dashed_style;
    /** Default TrueType font file */
    protected $default_ttfont;
    /** Array of flags for elements that must be drawn at most once */
    protected $done = array();
    /** Flag: How to handle missing Y values */
    protected $draw_broken_lines = FALSE;
    /** Flag: Draw data borders, available with some plot types */
    protected $draw_data_borders;
    /** Flag: Draw borders on pie chart segments */
    protected $draw_pie_borders;
    /** Flag: Draw the background of the plot area */
    protected $draw_plot_area_background = FALSE;
    /** Flag: Draw X data label lines */
    protected $draw_x_data_label_lines = FALSE;
    /** Flag: Draw X grid lines? */
    protected $draw_x_grid;
    /** Flag: Draw Y data label lines */
    protected $draw_y_data_label_lines = FALSE;
    /** Flag: Draw Y grid lines? */
    protected $draw_y_grid;
    /** Color (R,G,B,A) to use for data value labels */
    protected $dvlabel_color;
    /** Array of colors (R,G,B,A) for error bars */
    protected $error_bar_colors;
    /** Thickness of error bar lines */
    protected $error_bar_line_width = 1;
    /** Shape (style) of error bars: line or tee */
    protected $error_bar_shape = 'tee';
    /** Size of error bars */
    protected $error_bar_size = 5;
    /** Image format: png, gif, jpg, wbmp */
    protected $file_format = 'png';
    /** Array of font information (should be protected, but public for possible callback use) */
    public $fonts;
    /** Flag: Draw grid on top of or behind the plot */
    public $grid_at_foreground = FALSE;
    /** Color (R,G,B,A) to use for axes, plot area border, legend border, pie chart lines and text */
    protected $grid_color;
    /** Controls fraction of bar group space used for bar */
    public $group_frac_width = 0.7;
    /** Color (R,G,B,A) for image border, if drawn */
    protected $i_border;
    /** Image border type */
    protected $image_border_type = 'none';
    /** Width of image border in pixels */
    protected $image_border_width;
    /** Image height */
    protected $image_height;
    /** Image width */
    protected $image_width;
    /** Image resource (should be protected, but public to reduce breakage) */
    public $img;
    /** Prevent recursion in error message image production */
    protected $in_error;
    /** Flag: don't send headers */
    protected $is_inline = FALSE;
    /** Label format info */
    protected $label_format = array('x' => array(), 'xd' => array(), 'y' => array(), 'yd' => array());
    /** Pie chart label position factor */
    protected $label_scale_position = 0.5;
    /** Legend text array */
    protected $legend;
    /** Color (R,G,B,A) for the legend background */
    protected $legend_bg_color;
    /** Alignment of color boxes or shape markers in the legend: left, right, or none */
    protected $legend_colorbox_align = 'right';
    /** Color control for colorbox borders in legend  */
    protected $legend_colorbox_borders = 'textcolor';
    /** Adjusts width of color boxes in the legend */
    public $legend_colorbox_width = 1;
    /** Array holding legend position information */
    protected $legend_pos;
    /** Flag: reverse the order of lines in the legend box, bottom to top  */
    protected $legend_reverse_order = FALSE;
    /** Legend style setting, left or right */
    protected $legend_text_align = 'right';
    /** Color (R,G,B,A) for the legend text  */
    protected $legend_text_color;
    /** Draw color boxes (if false or unset) or shape markers (if true) in the legend  */
    protected $legend_use_shapes = FALSE;
    /** Color (R,G,B,A) for grid lines and X data lines */
    protected $light_grid_color;
    /** Controls inter-line spacing of text */
    protected $line_spacing = 4;
    /** Plot line style(s) */
    protected $line_styles = array('solid', 'solid', 'dashed');
    /** Plot line width(s) */
    protected $line_widths = 1;
    /** Flag to avoid importing locale info */
    public $locale_override = FALSE;
    /** Overall max X value in the data array */
    protected $max_x;
    /** Overall max Y value in the data array */
    protected $max_y;
    /** Overall max Z value in the data array (for X/Y/Z data type only)  */
    protected $max_z;
    /** Overall min X value in the data array */
    protected $min_x;
    /** Overall min Y value in the data array */
    protected $min_y;
    /** Overall min Z value in the data array (for X/Y/Z data type only)  */
    protected $min_z;
    /** Color index of image background */
    protected $ndx_bg_color;
    /** Color index array for data borders */
    protected $ndx_data_border_colors;
    /** Color index array for plot data lines/marks/bars/etc. */
    protected $ndx_data_colors;
    /** Color index array for plot data, darker shade */
    protected $ndx_data_dark_colors;
    /** Color index for axis data labels  */
    protected $ndx_datalabel_color;
    /** Color index for data value labels  */
    protected $ndx_dvlabel_color;
    /** Color index array for error bars */
    protected $ndx_error_bar_colors;
    /** Color index for axes, plot area border, legend border, pie chart lines and text */
    protected $ndx_grid_color;
    /** Color index for image border lines */
    protected $ndx_i_border;
    /** Color index for image border lines, darker shade */
    protected $ndx_i_border_dark;
    /** Color index for the legend background  */
    protected $ndx_legend_bg_color;
    /** Color index for the legend text  */
    protected $ndx_legend_text_color;
    /** Color index for grid lines and X data lines */
    protected $ndx_light_grid_color;
    /** Color index for unshaded pie chart segment borders  */
    protected $ndx_pieborder_color;
    /** Color index for pie chart data labels  */
    protected $ndx_pielabel_color;
    /** Color index of plot area background */
    protected $ndx_plot_bg_color;
    /** Color index for labels and legend text */
    protected $ndx_text_color;
    /** Color index for tick marks */
    protected $ndx_tick_color;
    /** Color index for tick labels  */
    protected $ndx_ticklabel_color;
    /** Color index for main title */
    protected $ndx_title_color;
    /** Color index for X title  */
    protected $ndx_x_title_color;
    /** Color index for Y title  */
    protected $ndx_y_title_color;
    /** Number of rows in the data array (number of points along X, or number of bar groups, for example) */
    protected $num_data_rows;
    /** Array with number of entries in each data row (including label and X if present) */
    protected $num_recs;
    /** Forced number of X tick marks */
    protected $num_x_ticks = '';
    /** Forced number of Y tick marks */
    protected $num_y_ticks = '';
    /** Scale factor for element widths in OHLC plots. */
    public $ohlc_frac_width = 0.3;
    /** Maximum half-width for elements in OHLC plots */
    public $ohlc_max_width = 8;
    /** Minimum half-width for elements in OHLC plots */
    public $ohlc_min_width = 2;
    /** Redirect to output file */
    protected $output_file;
    /** Aspect ratio for shaded pie charts */
    public $pie_diam_factor = 0.5;
    /** Flag: True to draw pie chart segments clockwise, false or unset for counter-clockwise.  */
    protected $pie_direction_cw = FALSE;
    /** Flag: If true, do not include label sizes when calculating pie size.  */
    protected $pie_full_size = FALSE;
    /** Source of label text for pie charts (percent, value, label, or index)  */
    protected $pie_label_source;
    /** Minimum amount of the plot area that will be reserved for the pie */
    public $pie_min_size_factor = 0.5;
    /** Starting angle in degrees for the first segment in a pie chart */
    protected $pie_start_angle = 0;
    /** Color (R,G,B,A) to use for unshaded pie chart segment borders */
    protected $pieborder_color;
    /** Color (R,G,B,A) to use for pie chart data labels */
    protected $pielabel_color;
    /** Calculated plot area array: ([0],[1]) is top left, ([2],[3]) is bottom right */
    protected $plot_area;
    /** Height of the plot area */
    protected $plot_area_height;
    /** Width of the plot area */
    protected $plot_area_width;
    /** Color (R,G,B,A) for plot area background */
    protected $plot_bg_color;
    /** Where to draw plot borders. Can be scalar or array of choices. */
    protected $plot_border_type;
    /** Max X of the plot area in world coordinates */
    protected $plot_max_x;
    /** Max Y of the plot area in world coordinates */
    protected $plot_max_y;
    /** Min X of the plot area in world coordinates */
    protected $plot_min_x;
    /** Min Y of the plot area in world coordinates */
    protected $plot_min_y;
    /** X device coordinate of the plot area origin */
    protected $plot_origin_x;
    /** Y device coordinate of the plot area origin */
    protected $plot_origin_y;
    /** Selected plot type */
    protected $plot_type = 'linepoints';
    /** Plot area background image filename */
    protected $plotbgimg;
    /** Plot area background image tiling mode */
    protected $plotbgmode;
    /** Array of plot type information, indexed by plot type */
    static protected $plots = array(
        'area' => array(
            'draw_method' => 'DrawArea',
            'abs_vals' => TRUE,
        ),
        'bars' => array(
            'draw_method' => 'DrawBars',
        ),
        'boxes' => array(
            'draw_method' => 'DrawBoxes',
            'adjust_type' => 1, // See GetRangeEndAdjust()
        ),
        'bubbles' => array(
            'draw_method' => 'DrawBubbles',
            'adjust_type' => 1, // See GetRangeEndAdjust()
        ),
        'candlesticks' => array(
            'draw_method' => 'DrawOHLC',
            'draw_arg' => array(TRUE, FALSE), // Draw candlesticks, only fill if "closed down"
            'adjust_type' => 2, // See GetRangeEndAdjust()
        ),
        'candlesticks2' => array(
            'draw_method' => 'DrawOHLC',
            'draw_arg' => array(TRUE, TRUE), // Draw candlesticks, fill always
            'adjust_type' => 2, // See GetRangeEndAdjust()
        ),
        'linepoints' => array(
            'draw_method' => 'DrawLinePoints',
            'legend_alt_marker' => 'shape',
        ),
        'lines' => array(
            'draw_method' => 'DrawLines',
            'legend_alt_marker' => 'line',
        ),
        'ohlc' => array(
            'draw_method' => 'DrawOHLC',
            'draw_arg' => array(FALSE), // Don't draw candlesticks
            'adjust_type' => 2, // See GetRangeEndAdjust()
        ),
        'pie' => array(
            'draw_method' => 'DrawPieChart',
            'suppress_axes' => TRUE,
            'abs_vals' => TRUE,
        ),
        'points' => array(
            'draw_method' => 'DrawDots',
            'legend_alt_marker' => 'shape',
        ),
        'squared' => array(
            'draw_method' => 'DrawSquared',
            'legend_alt_marker' => 'line',
        ),
        'squaredarea' => array(
            'draw_method' => 'DrawSquaredArea',
            'abs_vals' => TRUE,
        ),
        'stackedarea' => array(
            'draw_method' => 'DrawArea',
            'draw_arg' => array(TRUE), // Tells DrawArea to draw stacked area plot
            'sum_vals' => TRUE,
            'abs_vals' => TRUE,
        ),
        'stackedbars' => array(
            'draw_method' => 'DrawStackedBars',
            'sum_vals' => TRUE,
        ),
        'stackedsquaredarea' => array(
            'draw_method' => 'DrawSquaredArea',
            'draw_arg' => array(TRUE), // Tells DrawSquaredArea the data is cumulative
            'sum_vals' => TRUE,
            'abs_vals' => TRUE,
        ),
        'thinbarline' => array(
            'draw_method' => 'DrawThinBarLines',
        ),
    );
    /** Size of point_shapes and point_sizes arrays  */
    protected $point_counts;
    /** Marker shapes for point plots */
    protected $point_shapes = array(
            'diamond', 'dot', 'delta', 'home', 'yield', 'box', 'circle', 'up', 'down', 'cross'
    );
    /** Marker sizes for point plots */
    protected $point_sizes = array(6);
    /** Flag: Automatic PrintImage after DrawGraph? */
    protected $print_image = TRUE;
    /** Tuning parameters for plot range calculation */
    protected $rangectl = array( 'x' => array(
                                   'adjust_mode' => 'T',      // T=adjust to next tick
                                   'adjust_amount' => NULL,   // See GetRangeEndAdjust()
                                   'zero_magnet' => 0.857142, // Value is 6/7
                                 ),
                                 'y' => array(
                                   'adjust_mode' => 'T',      // T=adjust to next tick
                                   'adjust_amount' => NULL,   // See GetRangeEndAdjust()
                                   'zero_magnet' => 0.857142, // Value is 6/7
                                ));
    /** Area for each bar in a bar chart */
    protected $record_bar_width;
    /** Maximum of num_recs[], max number of entries (including label and X if present) for all data rows */
    protected $records_per_group;
    /** Array mapping color names to array of R, G, B values */
    protected $rgb_array;
    /** Fixed extra margin used in multiple places */
    public $safe_margin = 5;
    /** Stores PHPlot version when object was serialized */
    protected $saved_version;
    /** Drop shadow size for pie and bar charts */
    protected $shading = 5;
    /** Skip bottom tick mark */
    protected $skip_bottom_tick = FALSE;
    /** Skip left tick mark */
    protected $skip_left_tick = FALSE;
    /** Skip right tick mark */
    protected $skip_right_tick = FALSE;
    /** Skip top tick mark */
    protected $skip_top_tick = FALSE;
    /** MIME boundary sequence used with streaming plots  */
    protected $stream_boundary;
    /** Boundary and MIME header, output before each frame in a plot stream  */
    protected $stream_frame_header;
    /** Name of the GD output function for this image type, used with streaming plots  */
    protected $stream_output_f;
    /** Flag: Don't produce an error image on fatal error */
    protected $suppress_error_image = FALSE;
    /** Flag: Don't draw the X axis line */
    protected $suppress_x_axis = FALSE;
    /** Flag: Don't draw the Y axis line */
    protected $suppress_y_axis = FALSE;
    /** Color (R,G,B,A) for labels and legend text */
    protected $text_color;
    /** Character to use to group 1000s in formatted numbers */
    protected $thousands_sep;
    /** Color (R,G,B,A) for tick marks */
    protected $tick_color;
    /** Tuning parameters for tick increment calculation  */
    protected $tickctl = array( 'x' => array(
                                  'tick_mode' => NULL,
                                  'min_ticks' => 8,
                                  'tick_inc_integer' => FALSE,
                                ),
                                'y' => array(
                                  'tick_mode' => NULL,
                                  'min_ticks' => 8,
                                  'tick_inc_integer' => FALSE,
                               ));
    /** Color (R,G,B,A) to use for tick labels  */
    protected $ticklabel_color;
    /** Color (R,G,B,A) for main title (and default for X and Y titles) */
    protected $title_color;
    /** Y offset of main title position  */
    protected $title_offset;
    /** Main title text */
    protected $title_txt = '';
    /** Total number of entries (rows times columns in each row) in the data array. */
    protected $total_records;
    /** Color (R,G,B,A) designated as transparent  */
    protected $transparent_color;
    /** Flag: True if serialized object had a truecolor image */
    protected $truecolor;
    /** TrueType font directory */
    protected $ttf_path = '.';
    /** Default font type, True for TrueType, False for GD */
    protected $use_ttf = FALSE;
    /** Position of X axis (in world coordinates) */
    protected $x_axis_position;
    /** Device coordinate for the X axis */
    protected $x_axis_y_pixels;
    /** Effective X data label text angle   */
    protected $x_data_label_angle;
    /** X data label text angle (see also x_data_label_angle)  */
    protected $x_data_label_angle_u = '';
    /** Position of X data labels */
    protected $x_data_label_pos;
    /** X tick label text angle (and default for x_data_label_angle) */
    protected $x_label_angle = 0;
    /** Label offset relative to plot area */
    protected $x_label_axis_offset;
    /** Label offset relative to plot area */
    protected $x_label_bot_offset;
    /** Label offset relative to plot area */
    protected $x_label_top_offset;
    /** Calculated plot area margin - left side */
    protected $x_left_margin;
    /** Calculated plot area margin - right side */
    protected $x_right_margin;
    /** X tick anchor point  */
    protected $x_tick_anchor;
    /** Length of X tick marks (inside plot area) */
    protected $x_tick_cross = 3;
    /** Effective step between X tick marks */
    protected $x_tick_inc;
    /** Step between X tick marks (see also x_tick_inc)  */
    protected $x_tick_inc_u = '';
    /** Position of X tick labels */
    protected $x_tick_label_pos;
    /** Length of X tick marks (outside plot area) */
    protected $x_tick_length = 5;
    /** Position of X tick marks */
    protected $x_tick_pos = 'plotdown';
    /** Title offset relative to plot area */
    protected $x_title_bot_offset;
    /** Color (R,G,B,A) for X title  */
    protected $x_title_color;
    /** X Axis title position */
    protected $x_title_pos = 'none';
    /** Title offset relative to plot area */
    protected $x_title_top_offset;
    /** X Axis title text */
    protected $x_title_txt = '';
    /** X scale factor for converting World to Device coordinates */
    protected $xscale;
    /** Linear or log scale on X */
    protected $xscale_type = 'linear';
    /** Position of Y axis (in world coordinates) */
    protected $y_axis_position;
    /** Device coordinate for the Y axis */
    protected $y_axis_x_pixels;
    /** Calculated plot area margin - bottom */
    protected $y_bot_margin;
    /** Y data label text angle  */
    protected $y_data_label_angle = 0;
    /** Position of Y data labels */
    protected $y_data_label_pos;
    /** Y tick label text angle */
    protected $y_label_angle = 0;
    /** Label offset relative to plot area */
    protected $y_label_axis_offset;
    /** Label offset relative to plot area */
    protected $y_label_left_offset;
    /** Label offset relative to plot area */
    protected $y_label_right_offset;
    /** Y tick anchor point  */
    protected $y_tick_anchor;
    /** Length of Y tick marks (inside plot area) */
    protected $y_tick_cross = 3;
    /** Effective step between Y tick marks */
    protected $y_tick_inc;
    /** Step between Y tick marks (see also y_tick_inc)  */
    protected $y_tick_inc_u = '';
    /** Position of Y tick labels */
    protected $y_tick_label_pos;
    /** Length of Y tick marks (outside plot area) */
    protected $y_tick_length = 5;
    /** Position of Y tick marks */
    protected $y_tick_pos = 'plotleft';
    /** Color (R,G,B,A) for Y title  */
    protected $y_title_color;
    /** Title offset relative to plot area */
    protected $y_title_left_offset;
    /** Y Axis title position */
    protected $y_title_pos = 'none';
    /** Title offset relative to plot area */
    protected $y_title_right_offset;
    /** Y Axis title text */
    protected $y_title_txt = '';
    /** Calculated plot area margin - top */
    protected $y_top_margin;
    /** Y scale factor for converting World to Device coordinates */
    protected $yscale;
    /** Linear or log scale on Y */
    protected $yscale_type = 'linear';

    /**
     * Constructor: Sets up GD palette image resource, and initializes plot style controls
     *
     * @param int $width  Image width in pixels
     * @param int $height  Image height in pixels
     * @param string $output_file  Path for output file. Omit, or NULL, or '' to mean no output file
     * @param string $input_file   Path to a file to be used as background. Omit, NULL, or '' for none
     */
    function __construct($width=600, $height=400, $output_file=NULL, $input_file=NULL)
    {
        $this->initialize('imagecreate', $width, $height, $output_file, $input_file);
    }

    /**
     * Initializes a PHPlot object (used by PHPlot and PHPlot_truecolor constructors)
     *
     * @param string $imagecreate_function  GD function to use: imagecreate or imagecreatetruecolor
     * @param int $width  Image width in pixels
     * @param int $height  Image height in pixels
     * @param string $output_file  Path for output file. Omit, or NULL, or '' to mean no output file
     * @param string $input_file   Path to a file to be used as background. Omit, NULL, or '' for none
     * @since 5.6.0
     */
    protected function initialize($imagecreate_function, $width, $height, $output_file, $input_file)
    {
        $this->SetRGBArray('small');

        if (isset($output_file) && $output_file !== '')
            $this->SetOutputFile($output_file);

        if (isset($input_file) && $input_file !== '') {
            $this->SetInputFile($input_file);
        } else {
            $this->image_width = $width;
            $this->image_height = $height;
            $this->img = call_user_func($imagecreate_function, $width, $height);
            if (!$this->img)
                return $this->PrintError(get_class($this) . '(): Could not create image resource.');
        }
        $this->SetDefaultStyles();
        $this->SetDefaultFonts();
    }

    /**
     * Prepares object for serialization
     *
     * The image resource cannot be serialized. But rather than try to filter it out from the other
     * properties, just let PHP serialize it (it will become an integer=0), and then fix it in __wakeup.
     * This way the object is still usable after serialize().
     * Note: This does not work if an input file was provided to the constructor.
     *
     * @return string[] Array of object property names, as required by PHP spec for __sleep()
     * @since 5.8.0
     */
    function __sleep()
    {
        $this->truecolor = imageistruecolor($this->img); // Remember image type
        $this->saved_version = self::version; // Remember version of PHPlot, for checking on unserialize
        return array_keys(get_object_vars($this));
    }

    /**
     * Cleans up object after unserialization
     *
     * Recreates the image resource (which is not serializable), after validating the PHPlot version.
     * @since 5.8.0
     */
    function __wakeup()
    {
        if (strcmp($this->saved_version, self::version) != 0)
            $this->PrintError(get_class($this) . '(): Unserialize version mismatch');
        $imagecreate_function = $this->truecolor ? 'imagecreatetruecolor' : 'imagecreate';
        $this->img = call_user_func($imagecreate_function, $this->image_width, $this->image_height);
        if (!$this->img)
            $this->PrintError(get_class($this) . '(): Could not create image resource.');
        unset($this->truecolor, $this->saved_version);
    }

    /**
     * Reads an image file (used by constructor via SetInput file, and by tile_img for backgrounds)
     *
     * @param string $image_filename  Filename of the image file to read
     * @param int $width  Reference variable for width of the image in pixels
     * @param int $height  Reference variable for height of the image in pixels
     * @return resource  Image resource (False on error if an error handler returns True)
     * @since 5.0.4
     */
    protected function GetImage($image_filename, &$width, &$height)
    {
        $error = '';
        $size = getimagesize($image_filename);
        if (!$size) {
            $error = "Unable to query image file $image_filename";
        } else {
            $image_type = $size[2];
            switch ($image_type) {
            case IMAGETYPE_GIF:
                $img = @ ImageCreateFromGIF ($image_filename);
                break;
            case IMAGETYPE_PNG:
                $img = @ ImageCreateFromPNG ($image_filename);
                break;
            case IMAGETYPE_JPEG:
                $img = @ ImageCreateFromJPEG ($image_filename);
                break;
            default:
                $error = "Unknown image type ($image_type) for image file $image_filename";
                break;
            }
        }
        if (empty($error) && !$img) {
            // getimagesize is OK, but GD won't read it. Maybe unsupported format.
            $error = "Failed to read image file $image_filename";
        }
        if (!empty($error)) {
            return $this->PrintError("GetImage(): $error");
        }
        $width = $size[0];
        $height = $size[1];
        return $img;
    }

    /**
     * Selects an input file to be used as background for the whole graph
     *
     * @param string $which_input_file  Pathname to the image file to use as a background
     * @deprecated  Public use discouraged; intended for use by class constructor
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetInputFile($which_input_file)
    {
        $im = $this->GetImage($which_input_file, $this->image_width, $this->image_height);
        if (!$im)
            return FALSE;  // GetImage already produced an error message.

        // Deallocate any resources previously allocated
        if (isset($this->img))
            imagedestroy($this->img);

        $this->img = $im;

        // Do not overwrite the input file with the background color.
        $this->done['background'] = TRUE;

        return TRUE;
    }

/////////////////////////////////////////////
//////////////                         COLORS
/////////////////////////////////////////////

    /**
     * Allocates a GD color index for a color specified as an array (R,G,B,A)
     *
     * At drawing time, this allocates a GD color index for the specified color, which
     * is specified as a 4 component array. Earlier, when a color is specified,
     * SetRGBColor() parsed and checked it and converted it to this component array form.
     *
     * @param int[] $color  Color specification as (R, G, B, A), or unset variable
     * @param int $default_color_index  An already-allocated GD color index to use if $color is unset
     * @return int  A GD color index that can be used when drawing
     * @since 5.2.0
     */
    protected function GetColorIndex(&$color, $default_color_index = 0)
    {
        if (empty($color)) return $default_color_index;
        list($r, $g, $b, $a) = $color;
        return imagecolorresolvealpha($this->img, $r, $g, $b, $a);
    }

    /**
     * Allocates an array of GD color indexes from an array of color specification arrays
     *
     * This is used for the data_colors array, for example.
     * Note: $color_array must use 0-based sequential integer indexes.
     *
     * @param array $color_array  Array of color specifications, each an array (R,G,B,A)
     * @param int $max_colors  Limit color allocation to no more than this number of colors
     * @return int[]  Array of GD color indexes that can be used when drawing
     * @since 5.3.1
     */
    protected function GetColorIndexArray($color_array, $max_colors)
    {
        $n = min(count($color_array), $max_colors);
        $result = array();
        for ($i = 0; $i < $n; $i++)
            $result[] = $this->GetColorIndex($color_array[$i]);
        return $result;
    }

    /**
     * Allocates an array of GD color indexes for darker shades from an array of color specifications
     *
     * This is used for shadow colors such as those in bar charts with shading.
     *
     * @param array $color_array  Array of color specifications, each an array (R,G,B,A)
     * @param int $max_colors  Limit color allocation to no more than this number of colors
     * @return int[]  Array of GD color indexes that can be used when drawing shadow colors
     * @since 5.3.1
     */
    protected function GetDarkColorIndexArray($color_array, $max_colors)
    {
        $n = min(count($color_array), $max_colors);
        $result = array();
        for ($i = 0; $i < $n; $i++)
            $result[] = $this->GetDarkColorIndex($color_array[$i]);
        return $result;
    }

    /**
     * Allocates a GD color index for a darker shade of a color specified as an array (R,G,B,A)
     *
     * See notes on GetColorIndex() above.
     *
     * @param int[] $color  Color specification as (R, G, B, A)
     * @return int  A GD color index that can be used when drawing a shadow color
     * @since 5.2.0
     */
    protected function GetDarkColorIndex($color)
    {
        list ($r, $g, $b, $a) = $color;
        $r = max(0, $r - 0x30);
        $g = max(0, $g - 0x30);
        $b = max(0, $b - 0x30);
        return imagecolorresolvealpha($this->img, $r, $g, $b, $a);
    }

    /**
     * Sets or reverts all colors and styles to their defaults
     *
     * @return bool  True always
     */
    protected function SetDefaultStyles()
    {
        $this->SetDefaultDashedStyle($this->dashed_style);
        $this->SetImageBorderColor(array(194, 194, 194));
        $this->SetPlotBgColor('white');
        $this->SetBackgroundColor('white');
        $this->SetTextColor('black');
        $this->SetGridColor('black');
        $this->SetLightGridColor('gray');
        $this->SetTickColor('black');
        $this->SetTitleColor('black');
        // These functions set up the default colors when called without parameters
        $this->SetDataColors();
        $this->SetErrorBarColors();
        $this->SetDataBorderColors();
        return TRUE;
    }

    /**
     * Sets the overall image background color
     *
     * @param string|int[] $which_color  Color name or spec (#rrggbb, (r,g,b) array, etc)
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetBackgroundColor($which_color)
    {
        return (bool)($this->bg_color = $this->SetRGBColor($which_color));
    }

    /**
     * Sets the plot area background color, which is only drawn if SetDrawPlotAreaBackground is used.
     *
     * @param string|int[] $which_color  Color name or spec (#rrggbb, (r,g,b) array, etc)
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetPlotBgColor($which_color)
    {
        return (bool)($this->plot_bg_color = $this->SetRGBColor($which_color));
    }

    /**
     * Sets the color of the plot title, and the default color of the X and Y titles.
     *
     * @param string|int[] $which_color  Color name or spec (#rrggbb, (r,g,b) array, etc)
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetTitleColor($which_color)
    {
        return (bool)($this->title_color = $this->SetRGBColor($which_color));
    }

    /**
     * Sets the color of the X title, overriding the color set with SetTitleColor()
     *
     * @param string|int[] $which_color  Color name or spec (#rrggbb, (r,g,b) array, etc)
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.2.0
     */
    function SetXTitleColor($which_color)
    {
        return (bool)($this->x_title_color = $this->SetRGBColor($which_color));
    }

    /**
     * Sets the color of the Y title, overriding the color set with SetTitleColor()
     *
     * @param string|int[] $which_color  Color name or spec (#rrggbb, (r,g,b) array, etc)
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.2.0
     */
    function SetYTitleColor($which_color)
    {
        return (bool)($this->y_title_color = $this->SetRGBColor($which_color));
    }

    /**
     * Sets the color of the axis tick marks
     *
     * @param string|int[] $which_color  Color name or spec (#rrggbb, (r,g,b) array, etc)
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetTickColor($which_color)
    {
        return (bool)($this->tick_color = $this->SetRGBColor($which_color));
    }

    /**
     * @deprecated  Use SetTitleColor() instead
     */
    function SetLabelColor($which_color)
    {
        return $this->SetTitleColor($which_color);
    }

    /**
     * Sets the general text color, which is the default color for legend text, tick and data labels
     *
     * @param string|int[] $which_color  Color name or spec (#rrggbb, (r,g,b) array, etc)
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetTextColor($which_color)
    {
        return (bool)($this->text_color = $this->SetRGBColor($which_color));
    }

    /**
     * Sets the color for data labels, overriding the default set with SetTextColor()
     *
     * @param string|int[] $which_color  Color name or spec (#rrggbb, (r,g,b) array, etc)
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.7.0
     */
    function SetDataLabelColor($which_color)
    {
        return (bool)($this->datalabel_color = $this->SetRGBColor($which_color));
    }

    /**
     * Sets the color for data value labels, overriding SetTextColor() and SetDataLabelColor()
     *
     * Note: Data Value Labels are the labels within the plot area (not the axis labels).
     *
     * @param string|int[] $which_color  Color name or spec (#rrggbb, (r,g,b) array, etc)
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.7.0
     */
    function SetDataValueLabelColor($which_color)
    {
        return (bool)($this->dvlabel_color = $this->SetRGBColor($which_color));
    }

    /**
     * Sets the color for pie chart data labels, overriding the default set with SetGridColor()
     *
     * @param string|int[] $which_color  Color name or spec (#rrggbb, (r,g,b) array, etc)
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.7.0
     */
    function SetPieLabelColor($which_color)
    {
        return (bool)($this->pielabel_color = $this->SetRGBColor($which_color));
    }

    /**
     * Sets the color for pie chart segment borders
     *
     * @param string|int[] $which_color  Color name or spec (#rrggbb, (r,g,b) array, etc)
     * @return bool  True (False on error if an error handler returns True)
     * @since 6.0.0
     */
    function SetPieBorderColor($which_color)
    {
        return (bool)($this->pieborder_color = $this->SetRGBColor($which_color));
    }

    /**
     * Sets the color for tick labels, overriding the default set with SetTextColor()
     *
     * @param string|int[] $which_color  Color name or spec (#rrggbb, (r,g,b) array, etc)
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.7.0
     */
    function SetTickLabelColor($which_color)
    {
        return (bool)($this->ticklabel_color = $this->SetRGBColor($which_color));
    }

    /**
     * Sets the X and Y grid colors, and the data label line color
     *
     * @param string|int[] $which_color  Color name or spec (#rrggbb, (r,g,b) array, etc)
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetLightGridColor($which_color)
    {
        return (bool)($this->light_grid_color = $this->SetRGBColor($which_color));
    }

    /**
     * Sets the color used for the X and Y axis lines, plot border, and legend border
     *
     * Also sets the default color for the pie chart data labels and pie chart segment borders.
     * These can be overridden by SetPieLabelColor() and SetPieBorderColor() respectively.
     * Note: This has nothing to do with the grid, and we don't know where this name came from.
     *
     * @param string|int[] $which_color  Color name or spec (#rrggbb, (r,g,b) array, etc)
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetGridColor($which_color)
    {
        return (bool)($this->grid_color = $this->SetRGBColor($which_color));
    }

    /**
     * Sets the color used for the image border, drawn if SetImageBorderType() enables it
     *
     * @param string|int[] $which_color  Color name or spec (#rrggbb, (r,g,b) array, etc)
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetImageBorderColor($which_color)
    {
        return (bool)($this->i_border = $this->SetRGBColor($which_color));
    }

    /**
     * Designates a color to be transparent, if transparency is supported by the image format
     *
     * @param string|int[]|null $which_color  Color to make transparent; empty|omit|NULL to reset to none
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetTransparentColor($which_color = NULL)
    {
        $this->transparent_color = empty($which_color) ? NULL : $this->SetRGBColor($which_color);
        return ($this->transparent_color !== FALSE); // True unless SetRGBColor() returned an error
    }

    /**
     * Sets the color used for the legend background, which defaults to the image background color
     *
     * @param string|int[] $which_color  Color name or spec (#rrggbb, (r,g,b) array, etc)
     * @return bool  True (False on error if an error handler returns True)
     * @since 6.0.0
     */
    function SetLegendBgColor($which_color)
    {
        return (bool)($this->legend_bg_color = $this->SetRGBColor($which_color));
    }

    /**
     * Sets the color used for the legend text, which defaults to the general text color
     *
     * @param string|int[] $which_color  Color name or spec (#rrggbb, (r,g,b) array, etc)
     * @return bool  True (False on error if an error handler returns True)
     * @since 6.0.0
     */
    function SetLegendTextColor($which_color)
    {
        return (bool)($this->legend_text_color = $this->SetRGBColor($which_color));
    }

    /**
     * Sets the array of colors to be used (the color map)
     *
     * The color map maps color names into arrays of R, G, B and optionally A values.
     * The selected color map can be user defined, a small predefined one,
     * or a large one included from the file 'rgb.inc.php'.
     *
     * @param array|string $which_color_array  Color map array (name=>(R,G,B[,A]), or keyword small | large
     * @return bool  True always
     */
    function SetRGBArray($which_color_array)
    {
        if (is_array($which_color_array)) {           // User defined array
            $this->rgb_array = $which_color_array;
        } elseif ($which_color_array == 'small') {      // Small predefined color array
            $this->rgb_array = array(
                'white'          => array(255, 255, 255),
                'snow'           => array(255, 250, 250),
                'PeachPuff'      => array(255, 218, 185),
                'ivory'          => array(255, 255, 240),
                'lavender'       => array(230, 230, 250),
                'black'          => array(  0,   0,   0),
                'DimGrey'        => array(105, 105, 105),
                'gray'           => array(190, 190, 190),
                'grey'           => array(190, 190, 190),
                'navy'           => array(  0,   0, 128),
                'SlateBlue'      => array(106,  90, 205),
                'blue'           => array(  0,   0, 255),
                'SkyBlue'        => array(135, 206, 235),
                'cyan'           => array(  0, 255, 255),
                'DarkGreen'      => array(  0, 100,   0),
                'green'          => array(  0, 255,   0),
                'YellowGreen'    => array(154, 205,  50),
                'yellow'         => array(255, 255,   0),
                'orange'         => array(255, 165,   0),
                'gold'           => array(255, 215,   0),
                'peru'           => array(205, 133,  63),
                'beige'          => array(245, 245, 220),
                'wheat'          => array(245, 222, 179),
                'tan'            => array(210, 180, 140),
                'brown'          => array(165,  42,  42),
                'salmon'         => array(250, 128, 114),
                'red'            => array(255,   0,   0),
                'pink'           => array(255, 192, 203),
                'maroon'         => array(176,  48,  96),
                'magenta'        => array(255,   0, 255),
                'violet'         => array(238, 130, 238),
                'plum'           => array(221, 160, 221),
                'orchid'         => array(218, 112, 214),
                'purple'         => array(160,  32, 240),
                'azure1'         => array(240, 255, 255),
                'aquamarine1'    => array(127, 255, 212)
                );
        } elseif ($which_color_array == 'large')  {    // Large color array
            if (!@include('rgb.inc.php')) {
                return $this->PrintError("SetRGBArray(): Large color map could not be loaded "
                                       . "from 'rgb.inc.php'.");
            }
            $this->rgb_array = $ColorArray;
        } else {
            return $this->PrintError("SetRGBArray(): Invalid color map selection");
        }

        return TRUE;
    }

    /**
     * Parses a color specification and returns the color component values
     *
     * Accepted color specification forms are (1) component array: array(R,G,B)
     * or array(R,G,B,A); (2) component string hexadecimal: "#RRGGBB" or
     * "#RRGGBBAA"; (3) A color name from the color map array with optional
     * alpha value suffix as ":alpha".  R, G, and B are integers 0-255, and
     * Alpha is 0 (opaque) to 127 (transparent).
     *
     * @param string|int[] $color_asked  Color spec to parse (color name, #rrggbb, (r,g,b) array, etc)
     * @param int $alpha  Optional default alpha value (0-127, default 0 for opaque)
     * @return int[]  Color component values as array (red, green, blue, alpha)
     * @deprecated  Public use discouraged; intended for class internal use
     */
    function SetRGBColor($color_asked, $alpha = 0)
    {
        if (empty($color_asked)) {
            $ret_val = array(0, 0, 0);

        } elseif (is_array($color_asked) && (($n = count($color_asked)) == 3 || $n == 4) ) {
            // Already an array of 3 or 4 elements:
            $ret_val = $color_asked;

        } elseif (preg_match('/^#([0-9a-f]{2})([0-9a-f]{2})([0-9a-f]{2})([0-9a-f]{2})?$/i',
                             $color_asked, $ss)) {
            // #RRGGBB or #RRGGBBAA notation:
            $ret_val = array(hexdec($ss[1]), hexdec($ss[2]), hexdec($ss[3]));
            if (isset($ss[4])) $ret_val[] = hexdec($ss[4]);

        } elseif (isset($this->rgb_array[$color_asked])) {
            // Color by name:
            $ret_val = $this->rgb_array[$color_asked];

        } elseif (preg_match('/(.+):([\d]+)$/', $color_asked, $ss)
                  && isset($this->rgb_array[$ss[1]])) {
            // Color by name with ":alpha" suffix, alpha is a decimal number:
            $ret_val = $this->rgb_array[$ss[1]];
            $ret_val[3] = (int)$ss[2];

        } else {
            return $this->PrintError("SetRGBColor(): Color '$color_asked' is not valid.");
        }

        // Append alpha if not already provided for:
        if (count($ret_val) == 3)
            $ret_val[] = $alpha;
        return $ret_val;
    }

    /**
     * Sets the colors used for plotting data sets, with optional default alpha value
     *
     * If passed an array, use the values as colors for sequential data sets.
     * If passed a single color specification, plot all data sets using that
     * single color.
     * Special use cases for the $which_data argument: Missing or NULL loads
     * the default data color map if no map is already set; an empty string or
     * False loads the default color map even if a color map is already set.
     * Note:  The default value for $alpha here is NULL, not 0, so we can tell
     * if it was defaulted. But the effective default value is 0 (opaque).
     *
     * @param array|string $which_data  Array of color specifications, or one color, or empty
     * @param array|string $which_border  Data border colors, deprecated - use SetDataBorderColors() instead
     * @param int $alpha  Default alpha to apply to all data colors that do not have an alpha value
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetDataColors($which_data = NULL, $which_border = NULL, $alpha = NULL)
    {
        if (is_array($which_data)) {
            $colors = $which_data;  // Use supplied array
        } elseif (!empty($which_data)) {
            $colors = array($which_data);  // Use supplied single color
        } elseif (empty($this->data_colors) || !is_null($which_data)) {
            $colors = $this->default_colors;  // Use default color array
        } else {
            // which_data is NULL or missing and a color array is already set.
            // The existing color array is left alone, except that if $alpha is
            // given this will replace the alpha value of each existing color.
            // This makes SetDataColors(NULL, NULL, $alpha) work.
            if (isset($alpha)) {
                $n_colors = count($this->data_colors);
                for ($i = 0; $i < $n_colors; $i++) {
                    $this->data_colors[$i][3] = $alpha; // Component 3 = alpha value
                }
            }
            // No need to reparse the colors or anything else.
            return TRUE;
        }

        if (!isset($alpha))
            $alpha = 0; // Actual default is opaque colors.

        // Check each color and convert to array (r,g,b,a) form.
        // Use the $alpha argument as a default for the alpha value of each color.
        $this->data_colors = array();
        foreach ($colors as $color) {
            $color_array = $this->SetRGBColor($color, $alpha);
            if (!$color_array) return FALSE; // SetRGBColor already did an error message.
            $this->data_colors[] = $color_array;
        }

        // For past compatibility:
        return $this->SetDataBorderColors($which_border);
    }

    /**
     * Sets the colors used for data borders in some plot types
     *
     * For plot types which support data borders, such as 'bars', this sets
     * the colors used for those borders. See also SetDrawDataBorders().
     * Special cases: If $which_br is missing or NULL, use the default of all
     * black if colors were not already set; if an empty string or False then
     * set the default of all black regardless.
     *
     * @param array|string $which_br  Array of color specifications, or one color, or empty
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetDataBorderColors($which_br = NULL)
    {
        if (is_array($which_br)) {
            $colors = $which_br; // Use supplied array
        } elseif (!empty($which_br)) {
            $colors = array($which_br);  // Use supplied single color
        } elseif (empty($this->data_border_colors) || !is_null($which_br)) {
            $colors = array('black'); // Use default
        } else {
            return TRUE; // Do nothing: which_br is NULL or missing and a color array is already set.
        }

        // Check each color and convert to array (r,g,b,a) form.
        $this->data_border_colors = array();
        foreach ($colors as $color) {
            $color_array = $this->SetRGBColor($color);
            if (!$color_array) return FALSE; // SetRGBColor already did an error message.
            $this->data_border_colors[] = $color_array;
        }
        return TRUE;
    }

    /**
     * Sets the colors used for data error bars
     *
     * Special cases for $which_err: Missing or NULL loads the default colors
     * (same as default data colors) if no colors are aleady set; an empty
     * string or False loads the default colors even if colors were already set.
     *
     * @param array|string $which_err  Array of color specifications, or one color, or empty
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetErrorBarColors($which_err = NULL)
    {
        if (is_array($which_err)) {
            $colors = $which_err;  // Use supplied array
        } elseif (!empty($which_err)) {
            $colors = array($which_err);  // Use supplied single color
        } elseif (empty($this->error_bar_colors) || !is_null($which_err)) {
            $colors = $this->default_colors;  // Use default color array
        } else {
            return TRUE; // Do nothing: which_err is NULL or missing and a color array is already set.
        }

        // Check each color and convert to array (r,g,b,a) form.
        $this->error_bar_colors = array();
        foreach ($colors as $color) {
            $color_array = $this->SetRGBColor($color);
            if (!$color_array) return FALSE; // SetRGBColor already did an error message.
            $this->error_bar_colors[] = $color_array;
        }
        return TRUE;
    }

    /**
     * Sets the default dashed line style (on/off pattern for dashed lines)
     *
     * For example: SetDashedStyle('2-3-1-2') means 2 dots of color, 3
     * transparent, 1 color, then 2 transparent.
     * This builds a template string $this->default_dashed_style which contains
     * a space-separated series of marker (#) for pixels on, and the value of
     * IMG_COLOR_TRANSPARENT for each pixel which is off.
     * See SetDashedStyle() for how it is used.
     *
     * @param string $which_style  Dashed line specification, in the form <pixels_on>-<pixels_off>...
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetDefaultDashedStyle($which_style)
    {
        // Validate the argument as "(number)-(number)-..." with at least 2 numbers:
        if (!preg_match('/^\d+-\d+(-\d+)*$/', $which_style)) {
            return $this->PrintError("SetDefaultDashedStyle(): Wrong parameter '$which_style'.");
        }
        $result = '';
        $use_color = TRUE;
        $transparent = ' ' . IMG_COLOR_TRANSPARENT;
        // Expand the dashed line style specifier:
        foreach (explode('-', $which_style) as $n) {
            $result .= str_repeat($use_color ? ' #' : $transparent, $n);
            $use_color = !$use_color;  // Alternate color and transparent
        }
        $this->default_dashed_style = ltrim($result);
        return TRUE;
    }

    /**
     * Returns a GD line style for drawing patterned or solid lines
     *
     * This returns a value which can be used in GD when drawing lines.
     * If styles are off, it just returns the color supplied.
     * If styles are on, it applies the given color to the pre-set dashed
     * line style (see SetDefaultDashedStyle()) and sets that as the GD
     * line style, then returns the special GD code for drawing styled lines.
     *
     * @param int $which_ndxcol  Color index to be used for drawing
     * @param bool $use_style  TRUE or omit for dashed lines, FALSE for solid lines
     * @return int  A GD color index for drawing: either $which_ndxcol or IMG_COLOR_STYLED
     */
    protected function SetDashedStyle($which_ndxcol, $use_style = TRUE)
    {
        if (!$use_style)
            return $which_ndxcol; // Styles are off; use original color for drawing
        // Set the line style, substituting the specified color for the # marker:
        imagesetstyle($this->img, explode(' ', str_replace('#', $which_ndxcol, $this->default_dashed_style)));
        return IMG_COLOR_STYLED; // Use this value as the color for drawing
    }

    /**
     * Sets line widths (thickness) for each data set
     *
     * @param int[]|int $which_lw  Array of line widths in pixels, or a single value to use for all data sets
     * @return bool  True always
     */
    function SetLineWidths($which_lw=NULL)
    {
        if (is_array($which_lw)) {
            $this->line_widths = $which_lw; // Use provided array
        } elseif (!is_null($which_lw)) {
            $this->line_widths = array($which_lw); // Convert value to array
        }
        return TRUE;
    }

    /**
     * Sets the line style (solid or dashed) for each data set
     *
     * @param string[]|string $which_ls  Array or single keyword: solid | dashed | none
     * @return bool  True always
     */
    function SetLineStyles($which_ls=NULL)
    {
        if (is_array($which_ls)) {
            $this->line_styles = $which_ls; // Use provided array
        } elseif (!is_null($which_ls)) {
            $this->line_styles = ($which_ls) ? array($which_ls) : array('solid');
        }
        return TRUE;
    }

/////////////////////////////////////////////
//////////////                 TEXT and FONTS
/////////////////////////////////////////////

    /**
     * Sets spacing between lines of multi-line labels
     *
     * @param int $which_spc Text line spacing factor (pixels for GD text, scale control for TTF text)
     * @return bool  True always
     */
    function SetLineSpacing($which_spc)
    {
        $this->line_spacing = $which_spc;
        return TRUE;
    }

    /**
     * Sets the default font type
     *
     * @param bool $which_ttf  True to default to TrueType fonts, False to default to GD (fixed) fonts
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetUseTTF($which_ttf)
    {
        $this->use_ttf = $which_ttf;
        return $this->SetDefaultFonts();
    }

    /**
     * Sets the default TrueType font directory
     *
     * @param string $which_path  Full path to a directory containing TrueType fonts
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetTTFPath($which_path)
    {
        if (!is_dir($which_path) || !is_readable($which_path)) {
            return $this->PrintError("SetTTFPath(): $which_path is not a valid path.");
        }
        $this->ttf_path = $which_path;
        return TRUE;
    }

    /**
     * Sets the default TrueType font, and resets all elements to use that TrueType font and default sizes
     *
     * @param string $which_font  Font filename or path; omit or NULL to use a default font
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetDefaultTTFont($which_font = NULL)
    {
        $this->default_ttfont = $which_font;
        return $this->SetUseTTF(TRUE);
    }

    /**
     * Returns the default TrueType font name, searching for one if necessary
     *
     * If no default has been set, this tries some likely candidates for a font which
     * can be loaded. If it finds one that works, that becomes the default TT font.
     * If there is no default and it cannot find a working font, it falls back to
     * the original PHPlot default (which will not likely work either).
     *
     * @return string  Default TrueType font filename or pathname
     * @since 5.1.3
     */
    protected function GetDefaultTTFont()
    {
        if (!isset($this->default_ttfont)) {
            // No default font yet. Try some common sans-serif fonts.
            $fonts = array('LiberationSans-Regular.ttf',  // For Linux with a correct GD font search path
                           'Verdana.ttf', 'Arial.ttf', 'Helvetica.ttf', // For Windows, maybe others
                           'liberation/LiberationSans-Regular.ttf',     // For newer Ubuntu etc
                           'ttf-liberation/LiberationSans-Regular.ttf', // For older Debian, Ubuntu, etc
                           'benjamingothic.ttf',  // Original PHPlot default
                          );
            foreach ($fonts as $font) {
                // First try the font name alone, to see if GD can find and load it.
                if (@imagettfbbox(10, 0, $font, "1") !== False)
                    break;
                // If the font wasn't found, try it with the default TTF path in front.
                $font_with_path = $this->ttf_path . DIRECTORY_SEPARATOR . $font;
                if (@imagettfbbox(10, 0, $font_with_path, "1") !== False) {
                    $font = $font_with_path;
                    break;
                }
            }
            // We either have a working font, or are using the last one regardless.
            $this->default_ttfont = $font;
        }
        return $this->default_ttfont;
    }

    /**
     * Selects all the default font values and sizes
     *
     * @return bool  True (False on error if an error handler returns True)
     */
    protected function SetDefaultFonts()
    {
        if ($this->use_ttf) {
            // Defaults for use of TrueType fonts:
            return $this->SetFontTTF('generic', '', 8)
                && $this->SetFontTTF('title', '', 14)
                && $this->SetFontTTF('legend', '', 8)
                && $this->SetFontTTF('x_label', '', 6)
                && $this->SetFontTTF('y_label', '', 6)
                && $this->SetFontTTF('x_title', '', 10)
                && $this->SetFontTTF('y_title', '', 10);
        }
        // Defaults for use of GD fonts:
        return $this->SetFontGD('generic', 2)
            && $this->SetFontGD('title', 5)
            && $this->SetFontGD('legend', 2)
            && $this->SetFontGD('x_label', 1)
            && $this->SetFontGD('y_label', 1)
            && $this->SetFontGD('x_title', 3)
            && $this->SetFontGD('y_title', 3);
    }

    /**
     * Selects a GD (fixed) font to use for a plot element
     *
     * Available element names are: title legend generic x_label y_label x_title y_title
     *
     * @param string $which_elem  Name of the element to change the font for
     * @param int|string $which_font  GD font number: 1 2 3 4 or 5
     * @param int $which_spacing  Optional spacing in pixels between text lines
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.0.6
     */
    function SetFontGD($which_elem, $which_font, $which_spacing = NULL)
    {
        if ($which_font < 1 || 5 < $which_font) {
            return $this->PrintError(__FUNCTION__ . ': Font size must be 1, 2, 3, 4 or 5');
        }
        if (!$this->CheckOption($which_elem,
                                'generic, title, legend, x_label, y_label, x_title, y_title',
                                __FUNCTION__)) {
            return FALSE;
        }

        // Store the font parameters: name/size, char cell height and width.
        $this->fonts[$which_elem] = array('ttf' => FALSE,
                                          'font' => $which_font,
                                          'height' => ImageFontHeight($which_font),
                                          'width' => ImageFontWidth($which_font),
                                          'line_spacing' => $which_spacing);
        return TRUE;
    }

    /**
     * Selects a TrueType font for to use for a plot element
     *
     * Available element names are: title legend generic x_label y_label x_title y_title
     *
     * @param string $which_elem  Name of the element to change the font for
     * @param string $which_font  TrueType font file or pathname; empty or NULL for the default font
     * @param int $which_size  Optional font size in points (default 12)
     * @param int $which_spacing  Optional line spacing adjustment factor
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.0.6
     */
    function SetFontTTF($which_elem, $which_font, $which_size = 12, $which_spacing = NULL)
    {
        if (!$this->CheckOption($which_elem,
                                'generic, title, legend, x_label, y_label, x_title, y_title',
                                __FUNCTION__)) {
            return FALSE;
        }

        // Empty font name means use the default font.
        if (empty($which_font))
            $which_font = $this->GetDefaultTTFont();
        $path = $which_font;

        // First try the font name directly, if not then try with path.
        // Use GD imagettfbbox() to determine if this is a valid font.
        // The return $bbox is used below, if valid.
        if (($bbox = @imagettfbbox($which_size, 0, $path, "E")) === False) {
            $path = $this->ttf_path . DIRECTORY_SEPARATOR . $which_font;
            if (($bbox = @imagettfbbox($which_size, 0, $path, "E")) === False) {
                return $this->PrintError(__FUNCTION__ . ": Can't find TrueType font $which_font");
            }
        }

        // Calculate the font height and inherent line spacing. TrueType fonts have this information
        // internally, but PHP/GD has no way to directly access it. So get the bounding box size of
        // an upper-case character without descenders, and the baseline-to-baseline height.
        // Note: In practice, $which_size = $height, maybe +/-1 . But which_size is in points,
        // and height is in pixels, and someday GD may be able to tell the difference.
        // The character width is saved too, but not used by the normal text drawing routines - it
        // isn't necessarily a fixed-space font. It is used in DrawLegend.
        $height = $bbox[1] - $bbox[5];
        $width = $bbox[2] - $bbox[0];
        $bbox = ImageTTFBBox($which_size, 0, $path, "E\nE");
        $spacing = $bbox[1] - $bbox[5] - 2 * $height;

        // Store the font parameters:
        $this->fonts[$which_elem] = array('ttf' => TRUE,
                                          'font' => $path,
                                          'size' => $which_size,
                                          'height' => $height,
                                          'width' => $width,
                                          'spacing' => $spacing,
                                          'line_spacing' => $which_spacing);
        return TRUE;
    }

    /**
     * Selects which font to use for a plot element
     *
     * This uses either GD (fixed) or TrueType fonts, depending on the default text
     * font type as set with SetUseTTF().
     *
     * Available element names are: title legend generic x_label y_label x_title y_title
     *
     * @param string $which_elem  Name of the element to change the font for
     * @param int|string $which_font  For GD fonts, a font number; for TrueType, a font filename or pathname
     * @param int $which_size  Optional font size in points for TrueType fonts, ignored for GD fonts
     * @param int $line_spacing  Optional line spacing adjustment factor
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetFont($which_elem, $which_font, $which_size = 12, $line_spacing = NULL)
    {
        if ($this->use_ttf)
            return $this->SetFontTTF($which_elem, $which_font, $which_size, $line_spacing);
        return $this->SetFontGD($which_elem, $which_font, $line_spacing);
    }

    /**
     * Returns the inter-line spacing for a font
     *
     * @param array $font  The font, specified as a PHPlot font array
     * @return int  Spacing between text lines in pixels for text using this font
     * @since 5.0.6
     */
    protected function GetLineSpacing($font)
    {
        // Use the per-font line spacing preference, if set, else the global value:
        if (isset($font['line_spacing']))
            $line_spacing = $font['line_spacing'];
        else
            $line_spacing = $this->line_spacing;

        // For GD fonts, that is the spacing in pixels.
        // For TTF, adjust based on the 'natural' font spacing (see SetFontTTF):
        if ($font['ttf']) {
            $line_spacing = (int)($line_spacing * $font['spacing'] / 6.0);
        }
        return $line_spacing;
    }

    /*
     * Text drawing and sizing functions:
     * ProcessText is meant for use only by DrawText and SizeText.
     *    ProcessText(True, ...)  - Draw a block of text
     *    ProcessText(False, ...) - Just return ($width, $height) of
     *       the orthogonal bounding box containing the text.
     * ProcessText is further split into separate functions for GD and TTF
     * text, due to the size of the code.
     *
     * Horizontal and vertical alignment are relative to the drawing. That is:
     * vertical text (90 deg) gets centered along Y position with
     * v_align = 'center', and adjusted to the right of X position with
     * h_align = 'right'.  Another way to look at this is to say
     * that text rotation happens first, then alignment.
     *
     * Original multiple lines code submitted by Remi Ricard.
     * Original vertical code submitted by Marlin Viss.
     *
     * Text routines rewritten by ljb to fix alignment and position problems.
     * Here is my explanation and notes.
     *
     *    + Process TTF text one line at a time, not as a block. (See below)
     *    + Flipped top vs bottom vertical alignment. The usual interpretation
     *  is: bottom align means bottom of the text is at the specified Y
     *  coordinate. For some reason, PHPlot did left/right the correct way,
     *  but had top/bottom reversed. I fixed it, and left the default valign
     *  argument as bottom, but the meaning of the default value changed.
     *
     *    For GD font text, only single-line text is handled by GD, and the
     *  basepoint is the upper left corner of each text line.
     *    For TTF text, multi-line text could be handled by GD, with the text
     *  basepoint at the lower left corner of the first line of text.
     *  (Behavior of TTF drawing routines on multi-line text is not documented.)
     *  But you cannot do left/center/right alignment on each line that way,
     *  or proper line spacing.
     *    Therefore, for either text type, we have to break up the text into
     *  lines and position each line independently.
     *
     *    There are 9 alignment modes: Horizontal = left, center, or right, and
     *  Vertical = top, center, or bottom. Alignment is interpreted relative to
     *  the image, not as the text is read. This makes sense when you consider
     *  for example X axis labels. They need to be centered below the marks
     *  (center, top alignment) regardless of the text angle.
     *  'Bottom' alignment really means baseline alignment.
     *
     *    GD font text is supported (by libgd) at 0 degrees and 90 degrees only.
     *  Multi-line or single line text works with any of the 9 alignment modes.
     *
     *    TTF text can be at any angle. The 9 alignment modes work for all angles,
     *  but the results might not be what you expect for multi-line text.  Alignment
     *  applies to the orthogonal (aligned with X and Y axes) bounding box that
     *  contains the text, and to each line in the multi-line text box. Since
     *  alignment is relative to the image, 45 degree multi-line text aligns
     *  differently from 46 degree text.
     *
     *    Note that PHPlot allows multi-line text for the 3 titles, and they
     *  are only drawn at 0 degrees (main and X titles) or 90 degrees (Y title).
     *  Data labels can also be multi-line, and they can be drawn at any angle.
     *  -ljb 2007-11-03
     *
     */

    /**
     * Draws or returns the size of a text string using GD fixed fonts
     *
     * This is intended for use only by ProcessText(). See notes there, but note that
     * the $font and alignment parameters are pre-processed there and differ here.
     * GD text only supports 0 and 90 degrees. This function treats an angle >= 45
     * as 90 degrees, and < 45 as 0 degrees.
     *
     * @param bool $draw_it  True to draw the text, False to just return the orthogonal width and height
     * @param array $font  A PHPlot font array (with 'ttf' = False)
     * @param float $angle  Text angle in degrees. GD only supports 0 and 90.
     * @param int $x  Reference point X coordinate for the text (ignored if $draw_it is False)
     * @param int $y  Reference point Y coordinate for the text (ignored if $draw_it is False)
     * @param int $color  GD color index to use for drawing the text (ignored if $draw_it is False)
     * @param string $text  The text to draw or size (can have newlines \n within)
     * @param float $h_factor  Horizontal alignment factor: 0=left|0.5=center|1=right (ignored if !$draw_it)
     * @param float $v_factor  Vertical alignment factor: 0=top|0.5=center|1=bottom (ignored if !$draw_it)
     * @return bool|int[]  True, if drawing text; an array of ($width, $height) if not.
     * @since 5.0.5
     */
    protected function ProcessTextGD($draw_it, $font, $angle, $x, $y, $color, $text, $h_factor, $v_factor)
    {
        // Extract font parameters:
        $font_number = $font['font'];
        $font_width = $font['width'];
        $font_height = $font['height'];
        $line_spacing = $this->GetLineSpacing($font);

        // Break up the text into lines, trim whitespace, find longest line.
        // Save the lines and length for drawing below.
        $longest = 0;
        foreach (explode("\n", $text) as $each_line) {
            $lines[] = $line = trim($each_line);
            $line_lens[] = $line_len = strlen($line);
            if ($line_len > $longest) $longest = $line_len;
        }
        $n_lines = count($lines);

        // Width, height are based on font size and longest line, line count respectively.
        // These are relative to the text angle.
        $total_width = $longest * $font_width;
        $total_height = $n_lines * $font_height + ($n_lines - 1) * $line_spacing;

        if (!$draw_it) {
            if ($angle < 45) return array($total_width, $total_height);
            return array($total_height, $total_width);
        }

        $interline_step = $font_height + $line_spacing; // Line-to-line step

        if ($angle >= 45) {
            // Vertical text (90 degrees):
            // (Remember the alignment convention with vertical text)
            // For 90 degree text, alignment factors change like this:
            $temp = $v_factor;
            $v_factor = $h_factor;
            $h_factor = 1 - $temp;

            $draw_func = 'ImageStringUp';

            // Rotation matrix "R" for 90 degrees (with Y pointing down):
            $r00 = 0;  $r01 = 1;
            $r10 = -1; $r11 = 0;

        } else {
            // Horizontal text (0 degrees):
            $draw_func = 'ImageString';

            // Rotation matrix "R" for 0 degrees:
            $r00 = 1; $r01 = 0;
            $r10 = 0; $r11 = 1;
        }

        // Adjust for vertical alignment (horizontal text) or horizontal alignment (vertical text):
        $factor = (int)($total_height * $v_factor);
        $xpos = $x - $r01 * $factor;
        $ypos = $y - $r11 * $factor;

        // Debug callback provides the bounding box:
        if ($this->GetCallback('debug_textbox')) {
            if ($angle >= 45) {
                $bbox_width  = $total_height;
                $bbox_height = $total_width;
                $px = $xpos;
                $py = $ypos - (1 - $h_factor) * $total_width;
            } else {
                $bbox_width  = $total_width;
                $bbox_height = $total_height;
                $px = $xpos - $h_factor * $total_width;
                $py = $ypos;
            }
            $this->DoCallback('debug_textbox', $px, $py, $bbox_width, $bbox_height);
        }

        for ($i = 0; $i < $n_lines; $i++) {

            // Adjust for alignment of this line within the text block:
            $factor = (int)($line_lens[$i] * $font_width * $h_factor);
            $x = $xpos - $r00 * $factor;
            $y = $ypos - $r10 * $factor;

            // Call ImageString or ImageStringUp:
            $draw_func($this->img, $font_number, $x, $y, $lines[$i], $color);

            // Step to the next line of text. This is a rotation of (x=0, y=interline_spacing)
            $xpos += $r01 * $interline_step;
            $ypos += $r11 * $interline_step;
        }
        return TRUE;
    }

    /**
     * Draws or returns the size of a text string using TrueType fonts (TTF)
     *
     * This is intended for use only by ProcessText(). See notes there, but note that
     * the $font and alignment parameters are pre-processed there and differ here.
     *
     * @param bool $draw_it  True to draw the text, False to just return the orthogonal width and height
     * @param array $font  A PHPlot font array (with 'ttf' = True)
     * @param float $angle  Text angle in degrees
     * @param int $x  Reference point X coordinate for the text (ignored if $draw_it is False)
     * @param int $y  Reference point Y coordinate for the text (ignored if $draw_it is False)
     * @param int $color  GD color index to use for drawing the text (ignored if $draw_it is False)
     * @param string $text  The text to draw or size (can have newlines \n within)
     * @param float $h_factor  Horizontal alignment factor: 0=left|0.5=center|1=right (ignored if !$draw_it)
     * @param float $v_factor  Vertical alignment factor: 0=top|0.5=center|1=bottom (ignored if !$draw_it)
     * @return bool|int[]  True, if drawing text; an array of ($width, $height) if not.
     * @since 5.0.5
     */
    protected function ProcessTextTTF($draw_it, $font, $angle, $x, $y, $color, $text, $h_factor, $v_factor)
    {
        // Extract font parameters (see SetFontTTF):
        $font_file = $font['font'];
        $font_size = $font['size'];
        $font_height = $font['height'];
        $line_spacing = $this->GetLineSpacing($font);

        // Break up the text into lines, trim whitespace.
        // Calculate the total width and height of the text box at 0 degrees.
        // Save the trimmed lines and their widths for later when drawing.
        // To get uniform spacing, don't use the actual line heights.
        // Total height = Font-specific line heights plus inter-line spacing.
        // Total width = width of widest line.
        // Last Line Descent is the offset from the bottom to the text baseline.
        // Note: For some reason, ImageTTFBBox uses (-1,-1) as the reference point.
        //   So 1+bbox[1] is the baseline to bottom distance.
        $total_width = 0;
        $lastline_descent = 0;
        foreach (explode("\n", $text) as $each_line) {
            $lines[] = $line = trim($each_line);
            $bbox = ImageTTFBBox($font_size, 0, $font_file, $line);
            $line_widths[] = $width = $bbox[2] - $bbox[0];
            if ($width > $total_width) $total_width = $width;
            $lastline_descent = 1 + $bbox[1];
        }
        $n_lines = count($lines);
        $total_height = $n_lines * $font_height + ($n_lines - 1) * $line_spacing;

        // Calculate the rotation matrix for the text's angle. Remember that GD points Y down,
        // so the sin() terms change sign.
        $theta = deg2rad($angle);
        $cos_t = cos($theta);
        $sin_t = sin($theta);
        $r00 = $cos_t;    $r01 = $sin_t;
        $r10 = -$sin_t;   $r11 = $cos_t;

        // Make a bounding box of the right size, with upper left corner at (0,0).
        // By convention, the point order is: LL, LR, UR, UL.
        // Note this is still working with the text at 0 degrees.
        // When sizing text (SizeText), use the overall size with descenders.
        //   This tells the caller how much room to leave for the text.
        // When drawing text (DrawText), use the size without descenders - that
        //   is, down to the baseline. This is for accurate positioning.
        $b[0] = 0;
        if ($draw_it) {
            $b[1] = $total_height;
        } else {
            $b[1] = $total_height + $lastline_descent;
        }
        $b[2] = $total_width;  $b[3] = $b[1];
        $b[4] = $total_width;  $b[5] = 0;
        $b[6] = 0;             $b[7] = 0;

        // Rotate the bounding box, then offset to the reference point:
        for ($i = 0; $i < 8; $i += 2) {
            $x_b = $b[$i];
            $y_b = $b[$i+1];
            $c[$i]   = $x + $r00 * $x_b + $r01 * $y_b;
            $c[$i+1] = $y + $r10 * $x_b + $r11 * $y_b;
        }

        // Get an orthogonal (aligned with X and Y axes) bounding box around it, by
        // finding the min and max X and Y:
        $bbox_ref_x = $bbox_max_x = $c[0];
        $bbox_ref_y = $bbox_max_y = $c[1];
        for ($i = 2; $i < 8; $i += 2) {
            $x_b = $c[$i];
            if ($x_b < $bbox_ref_x) $bbox_ref_x = $x_b;
            elseif ($bbox_max_x < $x_b) $bbox_max_x = $x_b;
            $y_b = $c[$i+1];
            if ($y_b < $bbox_ref_y) $bbox_ref_y = $y_b;
            elseif ($bbox_max_y < $y_b) $bbox_max_y = $y_b;
        }
        $bbox_width = $bbox_max_x - $bbox_ref_x;
        $bbox_height = $bbox_max_y - $bbox_ref_y;

        if (!$draw_it) {
            // Return the bounding box, rounded up (so it always contains the text):
            return array((int)ceil($bbox_width), (int)ceil($bbox_height));
        }

        $interline_step = $font_height + $line_spacing; // Line-to-line step

        // Calculate the offsets from the supplied reference point to the
        // upper-left corner of the text.
        // Start at the reference point at the upper left corner of the bounding
        // box (bbox_ref_x, bbox_ref_y) then adjust it for the 9 point alignment.
        // h,v_factor are 0,0 for top,left, .5,.5 for center,center, 1,1 for bottom,right.
        //    $off_x = $bbox_ref_x + $bbox_width * $h_factor - $x;
        //    $off_y = $bbox_ref_y + $bbox_height * $v_factor - $y;
        // Then use that offset to calculate back to the supplied reference point x, y
        // to get the text base point.
        //    $qx = $x - $off_x;
        //    $qy = $y - $off_y;
        // Reduces to:
        $qx = 2 * $x - $bbox_ref_x - $bbox_width * $h_factor;
        $qy = 2 * $y - $bbox_ref_y - $bbox_height * $v_factor;

        // Check for debug callback. Don't calculate bounding box unless it is wanted.
        if ($this->GetCallback('debug_textbox')) {
            // Calculate the orthogonal bounding box coordinates for debug testing.

            // qx, qy is upper left corner relative to the text.
            // Calculate px,py: upper left corner (absolute) of the bounding box.
            // There are 4 equation sets for this, depending on the quadrant:
            if ($sin_t > 0) {
                if ($cos_t > 0) {
                    // Quadrant: 0d - 90d:
                    $px = $qx; $py = $qy - $total_width * $sin_t;
                } else {
                    // Quadrant: 90d - 180d:
                   $px = $qx + $total_width * $cos_t; $py = $qy - $bbox_height;
                }
            } else {
                if ($cos_t < 0) {
                    // Quadrant: 180d - 270d:
                    $px = $qx - $bbox_width; $py = $qy + $total_height * $cos_t;
                } else {
                    // Quadrant: 270d - 360d:
                    $px = $qx + $total_height * $sin_t; $py = $qy;
                }
            }
            $this->DoCallback('debug_textbox', $px, $py, $bbox_width, $bbox_height);
        }

        // Since alignment is applied after rotation, which parameter is used
        // to control alignment of each line within the text box varies with
        // the angle.
        //   Angle (degrees):       Line alignment controlled by:
        //  -45 < angle <= 45          h_align
        //   45 < angle <= 135         reversed v_align
        //  135 < angle <= 225         reversed h_align
        //  225 < angle <= 315         v_align
        if ($cos_t >= $sin_t) {
            if ($cos_t >= -$sin_t) $line_align_factor = $h_factor;
            else $line_align_factor = $v_factor;
        } else {
            if ($cos_t >= -$sin_t) $line_align_factor = 1-$v_factor;
            else $line_align_factor = 1-$h_factor;
        }

        // Now we have the start point, spacing and in-line alignment factor.
        // We are finally ready to start drawing the text, line by line.
        for ($i = 0; $i < $n_lines; $i++) {

            // For drawing TTF text, the reference point is the left edge of the
            // text baseline (not the lower left corner of the bounding box).
            // The following also adjusts for horizontal (relative to
            // the text) alignment of the current line within the box.
            // What is happening is rotation of this vector by the text angle:
            //    (x = (total_width - line_width) * factor, y = font_height)

            $width_factor = ($total_width - $line_widths[$i]) * $line_align_factor;
            $rx = $qx + $r00 * $width_factor + $r01 * $font_height;
            $ry = $qy + $r10 * $width_factor + $r11 * $font_height;

            // Finally, draw the text:
            ImageTTFText($this->img, $font_size, $angle, $rx, $ry, $color, $font_file, $lines[$i]);

            // Step to position of next line.
            // This is a rotation of (x=0,y=height+line_spacing) by $angle:
            $qx += $r01 * $interline_step;
            $qy += $r11 * $interline_step;
        }
        return TRUE;
    }

    /**
     * Draws or returns the size of a text string
     *
     * This is intended for use by DrawText() and SizeText() exclusively. It hides the
     * differences between GD and TTF text from those and higher level functions. It uses
     * either ProcessTextTTF() or ProcessTextGD() to do the actual drawing or sizing.
     *
     * @param bool $draw_it  True to draw the text, False to just return the orthogonal width and height
     * @param string|array|null $font_id  Text element name, empty or NULL for 'generic', or font array
     * @param float $angle  Text angle in degrees
     * @param int $x  Reference point X coordinate for the text (ignored if $draw_it is False)
     * @param int $y  Reference point Y coordinate for the text (ignored if $draw_it is False)
     * @param int $color  GD color index to use for drawing the text (ignored if $draw_it is False)
     * @param string $text  The text to draw or size (can have newlines \n within)
     * @param string $halign  Horizontal alignment: left |  center | right (ignored if $draw_it is False)
     * @param string $valign  Vertical alignment: top | center | bottom (ignored if $draw_it is False)
     * @return bool|int[]  True, if drawing text; an array of ($width, $height) if not.
     */
    protected function ProcessText($draw_it, $font_id, $angle, $x, $y, $color, $text, $halign, $valign)
    {
        // Empty text case:
        if ($text === '') {
            if ($draw_it) return TRUE;
            return array(0, 0);
        }

        // Calculate width and height offset factors using the alignment args:
        if ($valign == 'top') $v_factor = 0;
        elseif ($valign == 'center') $v_factor = 0.5;
        else $v_factor = 1.0; // 'bottom'
        if ($halign == 'left') $h_factor = 0;
        elseif ($halign == 'center') $h_factor = 0.5;
        else $h_factor = 1.0; // 'right'

        // Preferred usage for $font_id is a text element name (see SetFont()), but for compatibility
        // accept a font array too. For external (callback) usage, support a default font.
        if (is_array($font_id)) $font = $font_id; // Use supplied array; deprecated
        elseif (!empty($font_id) && isset($this->fonts[$font_id])) $font = $this->fonts[$font_id];
        else $font = $this->fonts['generic']; // Fallback default, or font_id is empty.

        if ($font['ttf']) {
            return $this->ProcessTextTTF($draw_it, $font, $angle, $x, $y, $color, $text,
                                         $h_factor, $v_factor);
        }
        return $this->ProcessTextGD($draw_it, $font, $angle, $x, $y, $color, $text, $h_factor, $v_factor);
    }

    /**
     * Draws a string of text on the plot
     *
     * Note: This function is mostly for internal use, and is not documented
     * for public use. But it can be legitimately used from a PHPlot callback.
     *
     * @param string|array|null $which_font  Text element name, empty or NULL for 'generic', or font array
     * @param float $which_angle  Text angle in degrees
     * @param int $which_xpos  Reference point X coordinate for the text
     * @param int $which_ypos  Reference point Y coordinate for the text
     * @param int $which_color  GD color index to use for drawing the text
     * @param string $which_text  The text to draw, with newlines (\n) between lines
     * @param string $which_halign  Horizontal alignment (relative to the image): left | center | right
     * @param string $which_valign  Vertical alignment (relative to the image): top | center | bottom
     * @return bool  True always
     */
    function DrawText($which_font, $which_angle, $which_xpos, $which_ypos, $which_color, $which_text,
                      $which_halign = 'left', $which_valign = 'bottom')
    {
        return $this->ProcessText(TRUE,
                           $which_font, $which_angle, $which_xpos, $which_ypos,
                           $which_color, $which_text, $which_halign, $which_valign);
    }

    /**
     * Calculates the size of block of text
     *
     * The returned size is the orthogonal width and height of a bounding
     * box aligned with the X and Y axes of the text. Only for angle=0 is
     * this the actual width and height of the text block, but for any angle
     * it is the amount of space needed to contain the text.
     * Note: This function is mostly for internal use, and is not documented
     * for public use. But it can be legitimately used from a PHPlot callback.
     *
     * @param string|array|null $which_font  Text element name, empty or NULL for 'generic', or font array
     * @param float $which_angle  Text angle in degrees
     * @param string $which_text  The text to calculate size of
     * @return int[]  A two element array ($width, $height) of the text
     */
    function SizeText($which_font, $which_angle, $which_text)
    {
        // Color, position, and alignment are not used when calculating the size.
        return $this->ProcessText(FALSE,
                           $which_font, $which_angle, 0, 0, 1, $which_text, '', '');
    }

/////////////////////////////////////////////
///////////            INPUT / OUTPUT CONTROL
/////////////////////////////////////////////

    /**
     * Selects the graphic image format generated by DrawGraph()
     *
     * @param string $format  The format to use: jpg | png | gif | wbmp
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetFileFormat($format)
    {
        $asked = $this->CheckOption($format, 'jpg, png, gif, wbmp', __FUNCTION__);
        if (!$asked) return FALSE;
        switch ($asked) {
        case 'jpg':
            $format_test = IMG_JPG;
            break;
        case 'png':
            $format_test = IMG_PNG;
            break;
        case 'gif':
            $format_test = IMG_GIF;
            break;
        case 'wbmp':
            $format_test = IMG_WBMP;
            break;
        }
        if (!(imagetypes() & $format_test)) {
            return $this->PrintError("SetFileFormat(): File format '$format' not supported");
        }
        $this->file_format = $asked;
        return TRUE;
    }

    /**
     * Sets an image file to be used as the image background
     *
     * @param string $input_file  Path to the file to be used (jpeg, png or gif)
     * @param string $mode   Optional method for the background: centeredtile | tile | scale
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetBgImage($input_file, $mode='centeredtile')
    {
        $this->bgmode = $this->CheckOption($mode, 'tile, centeredtile, scale', __FUNCTION__);
        $this->bgimg  = $input_file;
        return (boolean)$this->bgmode;
    }

    /**
     * Sets an image file to be used as the plot area background
     *
     * @param string $input_file  Path to the file to be used (jpeg, png or gif)
     * @param string $mode   Optional method for the background: centeredtile | tile | scale
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetPlotAreaBgImage($input_file, $mode='tile')
    {
        $this->plotbgmode = $this->CheckOption($mode, 'tile, centeredtile, scale', __FUNCTION__);
        $this->plotbgimg  = $input_file;
        return (boolean)$this->plotbgmode;
    }

    /**
     * Redirects PHPlot output to a file
     *
     * Note: Output file has no effect unless SetIsInline(TRUE) is called.
     *
     * @param string $which_output_file  Pathname of the file to write the image data into
     * @return bool  True always
     */
    function SetOutputFile($which_output_file)
    {
        if (isset($which_output_file) && $which_output_file !== '')
            $this->output_file = $which_output_file;
        else
            $this->output_file = NULL;
        return TRUE;
    }

    /**
     * Sets the output image to be inline, without HTTP headers
     *
     * This will suppress the Content-Type headers that would otherwise be sent.
     *
     * @param bool $which_ii  True to suppress HTTP headers, False to include the headers
     * @return bool  True always
     */
    function SetIsInline($which_ii)
    {
        $this->is_inline = (bool)$which_ii;
        return TRUE;
    }

    /**
     * Gets the MIME type and GD output function name for the current file type
     *
     * @param string $mime_type  Reference variable where the MIME type is returned
     * @param string $output_f  Reference variable where the GD output function name is returned
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.5.0
     */
    protected function GetImageType(&$mime_type, &$output_f)
    {
        switch ($this->file_format) {
        case 'png':
            $mime_type = 'image/png';
            $output_f = 'imagepng';
            break;
        case 'jpg':
            $mime_type = 'image/jpeg';
            $output_f = 'imagejpeg';
            break;
        case 'gif':
            $mime_type = 'image/gif';
            $output_f = 'imagegif';
            break;
        case 'wbmp':
            $mime_type = 'image/wbmp';
            $output_f = 'imagewbmp';
            break;
        default:
            // Report the error on PrintImage, because that is where this code used to be.
            return $this->PrintError('PrintImage(): Please select an image type!');
        }
        return TRUE;
    }

    /**
     * Tells the browser not to cache the image
     *
     * This is used by PrintImage, depending on SetBrowserCache(). It sends
     * HTTP headers that discourage browser-side caching.
     * Originally submitted by Thiemo Nagel. Modified to add more options based on mjpg-streamer.
     *
     * @return bool  True always
     * @since 5.8.0
     */
    protected function DisableCaching()
    {
        header('Expires: Mon, 26 Jul 1997 05:00:00 GMT');
        header('Last-Modified: ' . gmdate('D, d M Y H:i:s') . 'GMT');
        header('Cache-Control: no-store, no-cache, must-revalidate, pre-check=0, post-check=0, max-age=0');
        header('Pragma: no-cache');
        return TRUE;
    }

    /**
     * Outputs the generated image to standard output or to a file
     *
     * This is automatically called by DrawGraph(), unless SetPrintImage(False) was used.
     *
     * @return bool  True always
     */
    function PrintImage()
    {
        if (!$this->browser_cache && !$this->is_inline)
            $this->DisableCaching();

        // Get MIME type and GD output function name:
        if (!$this->GetImageType($mime_type, $output_f)) return FALSE;

        if (!$this->is_inline) {
            Header("Content-type: $mime_type");
        }
        if ($this->is_inline && isset($this->output_file)) {
            $output_f($this->img, $this->output_file);
        } else {
            $output_f($this->img);
        }
        return TRUE;
    }

    /**
     * Returns the image data as raw data, base64 encoded, or data URL (see RFC2397)
     *
     * @param string $encoding  Optional encoding to use: dataurl (default) | raw | base64
     * @return string  Encoded image data (False on error if error handler returns True)
     * @since 5.5.0
     */
    function EncodeImage($encoding = 'dataurl')
    {
        $enc = $this->CheckOption($encoding, 'dataurl, raw, base64', __FUNCTION__);
        if (!$enc || !$this->GetImageType($mime_type, $output_f)) return FALSE;
        ob_start();
        $output_f($this->img);
        switch ($enc) {
        case 'raw':
            return ob_get_clean();
        case 'base64':
            return base64_encode(ob_get_clean());
        default:  // 'dataurl', checked above.
            return "data:$mime_type;base64,\n" . chunk_split(base64_encode(ob_get_clean()));
        }
    }

    /**
     * Draws a text message on the image, replacing the plot
     *
     * This is used for PHPlot error handling, and is available for
     * application-level error handling or other special purposes.
     * Options (keys in $options) are: draw_background draw_border force_print
     *   reset_font text_color text_wrap wrap_width.
     * Default option values were chosen for fail-safe error-handling.
     *
     * @param string $text  Text of the message to display in the image
     * @param string[] $options  Optional associative array of control options
     * @return bool  True always
     * @since 5.7.0
     */
    function DrawMessage($text, $options = NULL)
    {
        // Merge options with defaults, and set as local variables:
        extract( array_merge( array(
            'draw_background' => FALSE,  // Draw image background per SetBgImage(), SetBackgroundColor()
            'draw_border' => FALSE,      // Draw image border as set with SetBorder*()
            'force_print' => TRUE,       // Ignore SetPrintImage() setting and always output
            'reset_font' => TRUE,        // Reset fonts (to avoid possible TTF error)
            'text_color' => '',          // If not empty, text color specification
            'text_wrap' => TRUE,         // Wrap the message text with wordwrap()
            'wrap_width' => 75,          // Width in characters for wordwrap()
                ), (array)$options));

        // Do colors, background, and border:
        if ($draw_border && !isset($this->ndx_i_border) || $draw_background && !isset($this->ndx_bg_color))
            $this->SetBgColorIndexes();
        if ($draw_background) {  // User-specified background
            $this->DrawBackground(TRUE);  // TRUE means force overwriting of background
        } else {  // Default to plain white background
            $bgcolor = imagecolorresolve($this->img, 255, 255, 255);
            ImageFilledRectangle($this->img, 0, 0, $this->image_width, $this->image_height, $bgcolor);
        }
        if ($draw_border) $this->DrawImageBorder(TRUE);
        if (empty($text_color)) $rgb = array(0, 0, 0);
        else $rgb = $this->SetRGBColor($text_color);
        $ndx_text_color = imagecolorresolve($this->img, $rgb[0], $rgb[1], $rgb[2]);

        // Error images should reset fonts, to avoid chance of a TTF error when displaying an error.
        if ($reset_font) $this->SetUseTTF(FALSE);

        // Determine the space needed for the text, and center the text box within the image:
        if ($text_wrap) $text = wordwrap($text, $wrap_width);
        list($text_width, $text_height) = $this->SizeText('generic', 0, $text);
        $x = max($this->safe_margin, ($this->image_width - $text_width) / 2);
        $y = max($this->safe_margin, ($this->image_height - $text_height) / 2);
        $this->DrawText('generic', 0, $x, $y, $ndx_text_color, $text, 'left', 'top');
        if ($force_print || $this->print_image) $this->PrintImage();
        return TRUE;
    }

    /**
     * Handles a fatal error in PHPlot
     *
     * When a fatal error occurs (most often a parameter error in a function call),
     * PHPlot will normally produce an image containing the error message,
     * output the image, and then trigger a user-level error with the message.
     * (The error message has to be presented as an image, because the browser is
     * expecting an image.)
     * If no error handler is set up, PHP will log the message and exit.
     * If there is an error handler, and it returns TRUE, PrintError returns FALSE,
     * and this will be passed back up to the calling code as a FALSE return.
     *
     * @param string $error_message  Text of the error message
     * @return bool  False, but only if there is an error handler that returned TRUE.
     */
    protected function PrintError($error_message)
    {
        // Be sure not to loop recursively, e.g. PrintError - PrintImage - PrintError.
        if (isset($this->in_error)) return FALSE;
        $this->in_error = TRUE;

        // Output an image containing the error message:
        if (!$this->suppress_error_image) {
            // img will be empty if the error occurs very early - e.g. when allocating the image.
            if (!empty($this->img)) {
                $this->DrawMessage($error_message);
            } elseif (!$this->is_inline) {
                Header('HTTP/1.0 500 Internal Server Error');
            }
        }
        trigger_error($error_message, E_USER_ERROR);
        // This is only reached if the error handler returns TRUE
        unset($this->in_error);
        return FALSE;
    }

    /**
     * Enables or disables error image production on failure
     *
     * @param bool $error_image  True to enable the error image, False to disable it.
     * @return bool  True always
     * @since 5.5.0
     */
    function SetFailureImage($error_image)
    {
        $this->suppress_error_image = !$error_image;
        return TRUE;
    }

    /**
     * Begins a Motion-JPEG (or other type) plot stream
     *
     * @return bool  True always
     * @since 5.8.0
     */
    function StartStream()
    {
        $this->GetImageType($mime_type, $this->stream_output_f);
        $this->stream_boundary = "PHPlot-Streaming-Frame"; // Arbitrary MIME boundary
        $this->stream_frame_header = "\r\n--$this->stream_boundary\r\nContent-Type: $mime_type\r\n";
        $this->DisableCaching();  // Send headers to disable browser-side caching
        header("Content-type: multipart/x-mixed-replace; boundary=\"$this->stream_boundary\"");
        return TRUE;
    }

    /**
     * Ends a Motion-JPEG (or other type) plot stream
     *
     * @return bool  True always
     * @since 5.8.0
     */
    function EndStream()
    {
        echo "\r\n--$this->stream_boundary--\r\n";
        flush();
        return TRUE;
    }

    /**
     * Outputs the generated plot as one frame in a plot stream
     *
     * @return bool  True always
     * @since 5.8.0
     */
    function PrintImageFrame()
    {
        ob_start();
        call_user_func($this->stream_output_f, $this->img);
        $size = ob_get_length();
        $frame = ob_get_clean();
        echo $this->stream_frame_header, "Content-Length: $size\r\n\r\n", $frame, "\r\n";
        flush();
        // This gets the next DrawGraph() to do background and titles again.
        $this->done = array();
        return TRUE;
    }

/////////////////////////////////////////////
///////////                            LABELS
/////////////////////////////////////////////

    /**
     * Positions and controls X data labels
     *
     * For vertical plots, these are X axis data labels, showing label strings from the data array.
     * Accepted positions are: plotdown, plotup, both, none.
     * For horizontal plots, these are X data value labels, show the data values.
     * Accepted positions are: plotin, plotstack, none.
     *
     * @param string $which_xdlp  Desired label position: plotdown | plotup | both | none | plotin | plotstack
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetXDataLabelPos($which_xdlp)
    {
        $which_xdlp = $this->CheckOption($which_xdlp, 'plotdown, plotup, both, none, plotin, plotstack',
                                         __FUNCTION__);
        if (!$which_xdlp) return FALSE;
        $this->x_data_label_pos = $which_xdlp;

        return TRUE;
    }

    /**
     * Positions and controls Y data labels
     *
     * For vertical plots, these are Y data value labels, showing the data values.
     * Accepted positions are: plotin, plotstack, none.
     * For horizontal plots, these are Y axis data labels, showing label strings from the data array.
     * Accepted positions are: plotleft, plotright, both, none.
     *
     * @param string $which_ydlp  Desired label position: plotleft | plotright | both | none | ...
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetYDataLabelPos($which_ydlp)
    {
        $which_ydlp = $this->CheckOption($which_ydlp, 'plotleft, plotright, both, none, plotin, plotstack',
                                          __FUNCTION__);
        if (!$which_ydlp) return FALSE;
        $this->y_data_label_pos = $which_ydlp;

        return TRUE;
    }

    /**
     * Positions the X tick labels
     *
     * @param string $which_xtlp  Desired label position: plotdown | plotup | both | none | xaxis
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetXTickLabelPos($which_xtlp)
    {
        $which_xtlp = $this->CheckOption($which_xtlp, 'plotdown, plotup, both, xaxis, none',
                                         __FUNCTION__);
        if (!$which_xtlp) return FALSE;
        $this->x_tick_label_pos = $which_xtlp;

        return TRUE;
    }

    /**
     * Positions the Y tick labels
     *
     * @param string $which_ytlp  Desired label position: plotleft | plotright | both | none | yaxis
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetYTickLabelPos($which_ytlp)
    {
        $which_ytlp = $this->CheckOption($which_ytlp, 'plotleft, plotright, both, yaxis, none',
                                         __FUNCTION__);
        if (!$which_ytlp) return FALSE;
        $this->y_tick_label_pos = $which_ytlp;

        return TRUE;
    }

    /**
     * Sets the formatting type for tick, data, or pie chart labels
     *
     * This implements SetXLabelType(), SetYLabelType(), SetXYDataLabelType(), SetYDataLabelType(),
     * and part of SetPieLabelType(). Those functions combine their arguments into an array and
     * pass the array to this function as $args.
     *
     * $mode='x' or 'y' set the type for tick labels, and the default type for data labels
     * if they are not separately configured.  $mode='xd' or 'yd' set the type for data labels.
     * $mode='p' sets the type for pie chart labels.
     *
     * $args[0] sets the formatting type: 'data' | 'time' | 'printf' | 'custom' | empty.
     *     If this is missing or empty, the default formatting for $mode is restored.
     * Additional values in $args[] depend on the formatting type. All further paramters except
     * for the callback are optional.
     * For type='data': $args[1] = precision, $args[2] = prefix, $args[3] = suffix.
     * For type 'time': $args[1] = format string for strftime().
     * For type 'printf': $args[1:3] = 1, 2, or 3 format strings for sprintf().
     * For type 'custom': $args[1] = the callback (required), $args[2] = pass-through argument.
     *
     * @param string $mode  Which label type to configure: x | y | xd | yd | p
     * @param array $args  Additional arguments controlling the format type
     * @return bool  True (False on error if an error handler returns True)
     */
    protected function SetLabelType($mode, $args)
    {
        if (!$this->CheckOption($mode, 'x, y, xd, yd, p', __FUNCTION__))
            return FALSE;

        $type = isset($args[0]) ? $args[0] : '';
        $format = &$this->label_format[$mode];  // Shorthand reference to format storage variables
        switch ($type) {
        case 'data':
            if (isset($args[1]))
                $format['precision'] = $args[1];
            elseif (!isset($format['precision']))
                $format['precision'] = 1;
            $format['prefix'] = isset($args[2]) ? $args[2] : '';
            $format['suffix'] = isset($args[3]) ? $args[3] : '';
            break;

        case 'time':
            if (isset($args[1]))
                $format['time_format'] = $args[1];
            elseif (!isset($format['time_format']))
                $format['time_format'] = '%H:%M:%S';
            break;

        case 'printf':
            if (isset($args[1]))
                // Accept 1, 2, or 3 format strings (see FormatLabel)
                $format['printf_format'] = array_slice($args, 1, 3);
            elseif (!isset($format['printf_format']))
                $format['printf_format'] = '%e';
            break;

        case 'custom':
            if (isset($args[1])) {
                $format['custom_callback'] = $args[1];
                $format['custom_arg'] = isset($args[2]) ? $args[2] : NULL;
            } else {
                $type = ''; // Error, 'custom' without a function, set to no-format mode.
            }
            break;

        case '':
        case 'title':   // Retained for backwards compatibility?
            break;

        default:
            $this->CheckOption($type, 'data, time, printf, custom', __FUNCTION__);
            $type = '';
        }
        $format['type'] = $type;
        return (boolean)$type;
    }

    /**
     * Sets formatting mode for X tick labels, and default for X data labels
     *
     * @param string $type  Formatting mode: data | time | printf | custom, or '' to reset to default
     * @param mixed $varargs  One or more additional arguments that depend on $type
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetXLabelType($type=NULL, $varargs=NULL)  // Variable arguments
    {
        $args = func_get_args();
        return $this->SetLabelType('x', $args);
    }

    /**
     * Sets formatting mode for X data labels (overriding any mode set with SetXLabelType)
     *
     * @param string $type  Formatting mode: data | time | printf | custom, or '' to reset to default
     * @param mixed $varargs  One or more additional arguments that depend on $type
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.1.0
     */
    function SetXDataLabelType($type=NULL, $varargs=NULL)  // Variable arguments, named params are unused
    {
        $args = func_get_args();
        return $this->SetLabelType('xd', $args);
    }

    /**
     * Sets formatting mode for Y tick labels, and default for Y data labels
     *
     * @param string $type  Formatting mode: data | time | printf | custom, or '' to reset to default
     * @param mixed $varargs  One or more additional arguments that depend on $type
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetYLabelType($type=NULL, $varargs=NULL)  // Variable arguments, named params are unused
    {
        $args = func_get_args();
        return $this->SetLabelType('y', $args);
    }

    /**
     * Sets formatting mode for Y data labels (overriding any mode set with SetYLabelType)
     *
     * @param string $type  Formatting mode: data | time | printf | custom, or '' to reset to default
     * @param mixed $varargs  One or more additional arguments that depend on $type
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.1.0
     */
    function SetYDataLabelType($type=NULL, $varargs=NULL)  // Variable arguments, named params are unused
    {
        $args = func_get_args();
        return $this->SetLabelType('yd', $args);
    }

    /**
     * Sets type and formatting mode for pie chart labels.
     *
     * @param string|string[] $source_  Label source keyword or array: percent | value | label | index | ''
     * @param string $type  Optional formatting mode: data | printf | custom
     * @param mixed $varargs  Zero or more additional arguments telling how to format the label
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.6.0
     */
    function SetPieLabelType($source_, $type=NULL, $varargs=NULL)  // Variable arguments, named params unused
    {
        $args = func_get_args();
        $source = array_shift($args);
        if (empty($source)) {
            $this->pie_label_source = NULL; // Restore default
            $args = array(''); // See below - tells SetLabelType to do no formatting or default.
        } else {
            $this->pie_label_source = $this->CheckOptionArray($source, 'percent, value, label, index',
                                                              __FUNCTION__);
            if (empty($this->pie_label_source)) return FALSE;
        }
        return $this->SetLabelType('p', $args);
    }

    /**
     * Sets the date/time formatting string for X labels
     *
     * This does not enable date/time formatting. For that you need to use
     * SetXLabelType('time'). But since you can pass the formatting string
     * to SetXLabelType() also, there is no need to use SetXTimeFormat().
     *
     * @param string $which_xtf  Formatting string to use (see PHP function strftime())
     * @return bool  True always
     */
    function SetXTimeFormat($which_xtf)
    {
        $this->label_format['x']['time_format'] = $which_xtf;
        return TRUE;
    }

    /**
     * Sets the date/time formatting string for Y labels
     *
     * This does not enable date/time formatting. For that you need to use
     * SetYLabelType('time'). But since you can pass the formatting string
     * to SetYLabelType() also, there is no need to use SetYTimeFormat().
     *
     * @param string $which_ytf  Formatting string (see PHP function strftime())
     * @return bool  True always
     */
    function SetYTimeFormat($which_ytf)
    {
        $this->label_format['y']['time_format'] = $which_ytf;
        return TRUE;
    }

    /**
     * Sets the separators used when formatting number labels
     *
     * Separators are used with 'data' label formatting. The defaults
     * are set from the system locale (if available).
     *
     * @param string $decimal_point  The character to use as a decimal point
     * @param string $thousands_sep  The character to use as a thousands grouping separator
     * @return bool  True always
     * @since 5.0.4
     */
    function SetNumberFormat($decimal_point, $thousands_sep)
    {
        $this->decimal_point = $decimal_point;
        $this->thousands_sep = $thousands_sep;
        return TRUE;
    }

    /**
     * Sets the text angle for X tick labels, and the default angle for X data labels
     *
     * @param float $which_xla  Desired angle for label text, in degrees
     * @return bool  True always
     */
    function SetXLabelAngle($which_xla)
    {
        $this->x_label_angle = $which_xla;
        return TRUE;
    }

    /**
     * Sets the text angle for Y tick labels
     *
     * Note: Unlike SetXLabelAngle(), this does not also apply to data labels.
     *
     * @param float $which_yla  Desired angle for label text, in degrees
     * @return bool  True always
     */
    function SetYLabelAngle($which_yla)
    {
        $this->y_label_angle = $which_yla;
        return TRUE;
    }

    /**
     * Sets the text angle for X data labels (overriding an angle set with SetXLabelAngle)
     *
     * @param float $which_xdla  Desired angle for label text, in degrees
     * @return bool  True always
     * @since 5.1.0
     */
    function SetXDataLabelAngle($which_xdla)
    {
        $this->x_data_label_angle_u = $which_xdla;
        return TRUE;
    }

    /**
     * Sets the angle for Y data labels
     *
     * @param float $which_ydla  Desired angle for label text, in degrees
     * @return bool  True always
     * @since 5.1.0
     */
    function SetYDataLabelAngle($which_ydla)
    {
        $this->y_data_label_angle = $which_ydla;
        return TRUE;
    }

/////////////////////////////////////////////
///////////                              MISC
/////////////////////////////////////////////

    /**
     * Checks the validity of an option (a multiple-choice function parameter)
     *
     * @param string $which_opt  String to check, usually the provided value of a function argument
     * @param string $which_acc  String of accepted choices, lower-case, choices separated by comma space
     * @param string $which_func  Name of the calling function, for error messages, usually __FUNCTION__
     * @return string|null  Downcased/trimmed option value if valid; NULL on error if error handler returns
     */
    protected function CheckOption($which_opt, $which_acc, $which_func)
    {
        $asked = strtolower(trim($which_opt));

        // Look for the supplied value in a comma/space separated list.
        if (strpos(", $which_acc,", ", $asked,") !== FALSE)
            return $asked;

        $this->PrintError("$which_func(): '$which_opt' not in available choices: '$which_acc'.");
        return NULL;
    }

    /**
     * Checks the validity of an array of options (multiple-choice function parameters)
     *
     * This is used to validate arguments to functions that accept either a single value
     * or an array of values (example: SetPlotBorderType).
     *
     * @param string|string[] $opt  String or array of strings to check
     * @param string $acc  String of accepted choices, lower-case, choices separated by comma space
     * @param string $func  Name of the calling function, for error messages, usually __FUNCTION__
     * @return string[]|null  Downcased/trimmed option values if valid; NULL on error if error handler returns
     * @since 5.1.2
     */
    protected function CheckOptionArray($opt, $acc, $func)
    {
        $opt_array = (array)$opt;
        $result = array();
        foreach ($opt_array as $option) {
            $choice = $this->CheckOption($option, $acc, $func);
            if (is_null($choice)) return NULL; // In case CheckOption error handler returns
            $result[] = $choice;
        }
        return $result;
    }

    /**
     * Checks for compatibility of the plot type and data type
     *
     * This is called by the plot-type-specific drawing functions, such as DrawBars().
     * It checks to make sure that the current data type is supported by the
     * drawing function.
     *
     * @param string $valid_types  Valid data types, separated by comma space
     * @return bool  True if data type is valid; False on error if an error handler returns True
     * @since 5.1.2
     */
    protected function CheckDataType($valid_types)
    {
        if (strpos(", $valid_types,", ", $this->data_type,") !== FALSE)
            return TRUE;

        $this->PrintError("Data type '$this->data_type' is not valid for '$this->plot_type' plots."
               . " Supported data type(s): '$valid_types'");
        return FALSE;
    }

    /**
     * Decodes the data type into variables used to determine how to process a data array
     *
     * This sets the 'datetype_*' class variables, which are used by other functions
     * that need to access the data array. This keeps the information about the meaning
     * of each data type in a single place (the datatypes static array).
     * @since 5.1.2
     */
    protected function DecodeDataType()
    {
        $v = &self::$datatypes[$this->data_type]; // Shortcut reference, already validated in SetDataType()
        $this->datatype_implied =    !empty($v['implied']);     // X (Y for horizontal plots) is implied
        $this->datatype_error_bars = !empty($v['error_bars']);  // Has +error, -error values
        $this->datatype_pie_single = !empty($v['pie_single']);  // Single-row pie chart
        $this->datatype_swapped_xy = !empty($v['swapped_xy']);  // Horizontal plot with swapped X:Y
        $this->datatype_yz =         !empty($v['yz']);          // Has a Z value for each Y
    }

    /**
     * Validates the data array, making sure it is properly structured
     *
     * This function is used by DrawGraph() to make sure the data array is populated
     * and each row is structured correctly, according to the data type.
     *
     * It also calculates data_columns, which is the maximum number of dependent
     * variable values (usually Y) in the data array rows.  (For pie charts, this is
     * the number of slices.) It depends on the data_type, unlike records_per_group
     * (which was previously used to pad style arrays, but is not accurate).
     *
     * Note error messages refer to the caller, the public DrawGraph().
     *
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.1.3
     */
    protected function CheckDataArray()
    {
        // Test for missing image, which really should never happen.
        if (!$this->img) {
            return $this->PrintError('DrawGraph(): No image resource allocated');
        }

        // Test for missing or empty data array:
        if (empty($this->data) || !is_array($this->data)) {
            return $this->PrintError("DrawGraph(): No data array");
        }
        if ($this->total_records == 0) {
            return $this->PrintError('DrawGraph(): Empty data set');
        }

        // Decode the data type into functional flags.
        $this->DecodeDataType();

        // Calculate the maximum number of dependent values per independent value
        // (e.g. Y for each X), or the number of pie slices. Also validate the rows.
        $skip = $this->datatype_implied ? 1 : 2; // Skip factor for data label and independent variable
        if ($this->datatype_error_bars) {
            $this->data_columns = (int)(($this->records_per_group - $skip) / 3);
            // Validate the data array for error plots: (label, X, then groups of Y, +err, -err):
            for ($i = 0; $i < $this->num_data_rows; $i++) {
                if ($this->num_recs[$i] < $skip || ($this->num_recs[$i] - $skip) % 3 != 0)
                    return $this->PrintError("DrawGraph(): Invalid $this->data_type data array (row $i)");
            }
        } elseif ($this->datatype_pie_single) {
            $this->data_columns = $this->num_data_rows; // Special case for this type of pie chart.
            // Validate the data array for text-data-single pie charts. Requires 1 value per row.
            for ($i = 0; $i < $this->num_data_rows; $i++) {
                if ($this->num_recs[$i] != 2)
                    return $this->PrintError("DrawGraph(): Invalid $this->data_type data array (row $i)");
            }
        } elseif ($this->datatype_yz) {
            $this->data_columns = (int)(($this->records_per_group - $skip) / 2); //  (y, z) pairs
            // Validate the data array for plots using X, Y, Z: (label, X, then pairs of Y, Z)
            for ($i = 0; $i < $this->num_data_rows; $i++) {
                if ($this->num_recs[$i] < $skip || ($this->num_recs[$i] - $skip) % 2 != 0)
                    return $this->PrintError("DrawGraph(): Invalid $this->data_type data array (row $i)");
            }
        } else {
            $this->data_columns = $this->records_per_group - $skip;
            // Validate the data array for non-error plots:
            for ($i = 0; $i < $this->num_data_rows; $i++) {
                if ($this->num_recs[$i] < $skip)
                    return $this->PrintError("DrawGraph(): Invalid $this->data_type data array (row $i)");
            }
        }
        return TRUE;
    }

    /**
     * Controls browser-side image caching
     *
     * @param bool $which_browser_cache  True to allow the browser to cache the image, false to not allow
     * @return bool  True always
     */
    function SetBrowserCache($which_browser_cache)
    {
        $this->browser_cache = $which_browser_cache;
        return TRUE;
    }

    /**
     * Determines whether or not DrawGraph() automatically outputs the image when the plot is drawn
     *
     * @param bool $which_pi  True to have DrawGraph() call PrintImage() when done, false to not output
     * @return bool  True always
     */
    function SetPrintImage($which_pi)
    {
        $this->print_image = $which_pi;
        return TRUE;
    }

    /**
     * Sets how much of a border is drawn around the plot area
     *
     * The argument can be a single value, or any array of values, indicating
     * which sides should get a border. 'full' means all 4 sides.
     *
     * @param string|string[] $pdt  Border control keyword(s):  left|right|top|bottom|sides|none|full
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetPlotBorderType($pbt)
    {
        $this->plot_border_type = $this->CheckOptionArray($pbt, 'left, right, top, bottom, sides, none, full',
                                                          __FUNCTION__);
        return !empty($this->plot_border_type);
    }

    /**
     * Sets the type of border drawn around the image
     *
     * @param string $sibt  Border type: raised | solid | plain | none
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetImageBorderType($sibt)
    {
        $this->image_border_type = $this->CheckOption($sibt, 'raised, plain, solid, none', __FUNCTION__);
        return (boolean)$this->image_border_type;
    }

    /**
     * Sets the width of the image border, if enabled
     *
     * @param int $width  Image border width in pixels
     * @return bool  True always
     * @since 5.1.2
     */
    function SetImageBorderWidth($width)
    {
        $this->image_border_width = $width;
        return TRUE;
    }

    /**
     * Enables or disables drawing of the plot area background color
     *
     * @param bool $dpab  True to draw the plot area background color, false to not draw it
     * @return bool  True always
     */
    function SetDrawPlotAreaBackground($dpab)
    {
        $this->draw_plot_area_background = (bool)$dpab;
        return TRUE;
    }

    /**
     * Enables or disables drawing of the X (vertical) grid lines
     *
     * @param bool $dxg  True to draw the X grid lines, false to not draw them; or NULL to restore default
     * @return bool  True always
     */
    function SetDrawXGrid($dxg = NULL)
    {
        $this->draw_x_grid = $dxg;
        return TRUE;
    }

    /**
     * Enables or disables drawing of the Y grid lines
     *
     * @param bool $dyg  True to draw the Y grid lines, false to not draw them; or NULL to restore default
     * @return bool  True always
     */
    function SetDrawYGrid($dyg = NULL)
    {
        $this->draw_y_grid = $dyg;
        return TRUE;
    }

    /**
     * Selects dashed or solid grid lines
     *
     * @param bool $ddg  True to draw the grid with dashed lines, false to use solid lines
     * @return bool  True always
     */
    function SetDrawDashedGrid($ddg)
    {
        $this->dashed_grid = (bool)$ddg;
        return TRUE;
    }

    /**
     * Enables or disables drawing of X data label lines
     *
     * @param bool $dxdl  True to draw the X data label lines, false to not draw them
     * @return bool  True always
     */
    function SetDrawXDataLabelLines($dxdl)
    {
        $this->draw_x_data_label_lines = (bool)$dxdl;
        return TRUE;
    }

    /**
     * Enables or disables drawing of Y data label Lines (horizontal plots only)
     *
     * @param bool $dydl  True to draw the Y data label lines, false to not draw them
     * @return bool  True always
     * @since 6.0.0
     */
    function SetDrawYDataLabelLines($dydl)
    {
        $this->draw_y_data_label_lines = (bool)$dydl;
        return TRUE;
    }

    /**
     * Enables or disables drawing of borders around pie chart segments
     *
     * @param bool $dpb  True to draw the pie chart segment borders, false to not draw them
     * @return bool  True always
     * @since 6.0.0
     */
    function SetDrawPieBorders($dpb)
    {
        $this->draw_pie_borders = (bool)$dpb;
        return TRUE;
    }

    /**
     * Enables or disables drawing of data borders for plot types that support them
     *
     * For plot types which support data borders, such as 'bars', this enables
     * or disables them. The default depends on the plot type.
     *
     * @param bool $ddb  True to draw the data borders, false to not draw them
     * @return bool  True always
     * @since 6.0.0
     */
    function SetDrawDataBorders($ddb)
    {
        $this->draw_data_borders = (bool)$ddb;
        return TRUE;
    }

    /**
     * Sets the main title text for the plot
     *
     * @param string $which_title  The text to use for the main plot title. Can contain multiple lines
     * @return bool  True always
     */
    function SetTitle($which_title)
    {
        $this->title_txt = $which_title;
        return TRUE;
    }

    /**
     * Sets the X axis title, and optionally its position
     *
     * Sets the text to be displayed as the X axis title. Optionally, it
     * also sets the position of the title and the axis itself: below the
     * graph (the usual place), above the graph, both, or neither.
     *
     * @param string $which_xtitle The text string to use for the X axis title. Can contain multiple lines
     * @param string $which_xpos   Optional position for the X axis and title: plotdown plotup both none
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetXTitle($which_xtitle, $which_xpos = 'plotdown')
    {
        if (!($which_xpos = $this->CheckOption($which_xpos, 'plotdown, plotup, both, none', __FUNCTION__)))
            return FALSE;
        if (($this->x_title_txt = $which_xtitle) === '')
            $this->x_title_pos = 'none';
        else
            $this->x_title_pos = $which_xpos;
        return TRUE;
    }

    /**
     * Sets the Y axis title, and optionally its position
     *
     * Sets the text to be displayed as the Y axis title. Optionally, it
     * also sets the position of the title and the axis itself: on the left
     * side of the graph (the usual place), on the right side, both, or neither.
     *
     * @param string $which_ytitle The text string to use for the Y axis title. Can contain multiple lines
     * @param string $which_ypos   Optional position for the X axis and title: plotleft plotright both none
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetYTitle($which_ytitle, $which_ypos = 'plotleft')
    {
        if (!($which_ypos = $this->CheckOption($which_ypos, 'plotleft, plotright, both, none', __FUNCTION__)))
            return FALSE;
        if (($this->y_title_txt = $which_ytitle) === '')
            $this->y_title_pos = 'none';
        else
            $this->y_title_pos = $which_ypos;
        return TRUE;
    }

    /**
     * Sets the size of the drop shadow for bar and pie charts
     *
     * Sets the size in pixels of the drop shadow used to give bar and pie
     * charts a 3-D look. The 3-D look can be disabled by setting the shading
     * to zero.
     *
     * @param int $which_s Size of the drop shadow in pixels
     * @return bool  True always
     */
    function SetShading($which_s)
    {
        $this->shading = (int)$which_s;
        return TRUE;
    }

    /**
     * Selects the type of plot - how the data will be graphed
     *
     * @param string $which_pt  The plot type, such as bars, lines, pie, ...
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetPlotType($which_pt)
    {
        $avail_plot_types = implode(', ', array_keys(self::$plots)); // List of known plot types
        $this->plot_type = $this->CheckOption($which_pt, $avail_plot_types, __FUNCTION__);
        return (boolean)$this->plot_type;
    }

    /**
     * Sets the position of the X axis
     *
     * @param float $pos  Axis position as an integer Y world coordinate; '' or omit for default
     * @return bool  True always
     */
    function SetXAxisPosition($pos='')
    {
        $this->x_axis_position = ($pos === '') ? NULL : (int)$pos;
        return TRUE;
    }

    /**
     * Sets the position of the Y axis
     *
     * @param float $pos  Axis position as an integer X world coordinate; '' or omit for default
     * @return bool  True always
     */
    function SetYAxisPosition($pos='')
    {
        $this->y_axis_position = ($pos === '') ? NULL : (int)$pos;
        return TRUE;
    }

    /**
     * Enables or disables drawing of the X axis line
     *
     * Note: This controls drawing of the axis line only, and not the ticks, labels, or grid.
     *
     * @param bool $draw  True to draw the axis line, False to not draw it
     * @return bool  True always
     * @since 5.3.0
     */
    function SetDrawXAxis($draw)
    {
        $this->suppress_x_axis = !$draw; // See DrawXAxis()
        return TRUE;
    }

    /**
     * Enables or disables drawing of the Y axis line
     *
     * Note: This controls drawing of the axis line only, and not the ticks, labels, or grid.
     *
     * @param bool $draw  True to draw the axis line, False to not draw it
     * @return bool  True always
     * @since 5.3.0
     */
    function SetDrawYAxis($draw)
    {
        $this->suppress_y_axis = !$draw; // See DrawYAxis()
        return TRUE;
    }

    /**
     * Selects linear or logarithmic scale for the X axis
     *
     * @param string $which_xst  The scale type: linear | log
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetXScaleType($which_xst)
    {
        $this->xscale_type = $this->CheckOption($which_xst, 'linear, log', __FUNCTION__);
        return (boolean)$this->xscale_type;
    }

    /**
     * Selects linear or logarithmic scale for the Y axis
     *
     * @param string $which_yst  The scale type: linear | log
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetYScaleType($which_yst)
    {
        $this->yscale_type = $this->CheckOption($which_yst, 'linear, log',  __FUNCTION__);
        return (boolean)$this->yscale_type;
    }

    /**
     * Sets the precision for numerically formatted X labels
     *
     * Note: Use of the equivalent SetXLabelType('data', $which_prec) is preferred.
     *
     * @param int $which_prec  Number of digits to display
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetPrecisionX($which_prec)
    {
        return $this->SetXLabelType('data', $which_prec);
    }

    /**
     * Sets the precision for numerically formatted Y labels
     *
     * Note: Use of the equivalent SetYLabelType('data', $which_prec) is preferred.
     *
     * @param int $which_prec  Number of digits to display
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetPrecisionY($which_prec)
    {
        return $this->SetYLabelType('data', $which_prec);
    }

    /**
     * Sets the line width used for error bars
     *
     * @param int $which_seblw  Desired width in pixels of the lines used to draw error bars
     * @return bool  True always
     */
    function SetErrorBarLineWidth($which_seblw)
    {
        $this->error_bar_line_width = $which_seblw;
        return TRUE;
    }

    /**
     * Sets the position for pie chart labels
     *
     * @param float $which_blp  Label position factor (0 <= blp <= 1); 0 or False for no labels
     * @return bool  True always
     */
    function SetLabelScalePosition($which_blp)
    {
        $this->label_scale_position = $which_blp;
        return TRUE;
    }

    /**
     * Sets the size of the error bar tee
     *
     * @param int $which_ebs  Length in pixels of the error bar "T"
     * @return bool  True always
     */
    function SetErrorBarSize($which_ebs)
    {
        $this->error_bar_size = $which_ebs;
        return TRUE;
    }

    /**
     * Selects the shape of the error bars
     *
     * @param string $which_ebs  Error bar shape: tee | line
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetErrorBarShape($which_ebs)
    {
        $this->error_bar_shape = $this->CheckOption($which_ebs, 'tee, line', __FUNCTION__);
        return (boolean)$this->error_bar_shape;
    }

    /**
     * Synchronizes the lengths of the point shapes and point sizes arrays
     *
     * This pads the smaller of $point_shapes[] and $point_sizes[], making them the same size.
     * It is called just before drawing any plot that needs 'points'.
     * @since 5.1.0
     */
    protected function CheckPointParams()
    {
        $ps = count($this->point_sizes);
        $pt = count($this->point_shapes);

        if ($ps < $pt) {
            $this->pad_array($this->point_sizes, $pt);
            $this->point_counts = $pt;
        } elseif ($ps > $pt) {
            $this->pad_array($this->point_shapes, $ps);
            $this->point_counts = $ps;
        } else {
            $this->point_counts = $ps;
        }
    }

    /**
     * Selects the point shape for each data set
     *
     * Valid point shapes are known here and in DrawShape(). Includes: circle | dot | diamond | ...
     * The point shape and point sizes arrays are synchronized before drawing a graph
     * that uses points. See CheckPointParams()
     *
     * @param string|string[] $which_pt  Array (or single value) of valid point shapes
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetPointShapes($which_pt)
    {
        $this->point_shapes = $this->CheckOptionArray($which_pt, 'halfline, line, plus, cross, rect,'
                       . ' circle, dot, diamond, triangle, trianglemid, delta, yield, star, hourglass,'
                       . ' bowtie, target, box, home, up, down, none', __FUNCTION__);
        return !empty($this->point_shapes);
    }

    /**
     * Sets the point size for each data set
     *
     * The point shape and point sizes arrays are synchronized before drawing a graph
     * that uses points. See CheckPointParams()
     *
     * @param string[]|string $which_ps  Array (or single value) of point sizes in pixels
     * @return bool  True always
     */
    function SetPointSizes($which_ps)
    {
        if (is_array($which_ps)) {
            // Use provided array:
            $this->point_sizes = $which_ps;
        } elseif (!is_null($which_ps)) {
            // Make the single value into an array:
            $this->point_sizes = array($which_ps);
        }
        return TRUE;
    }

    /**
     * Sets whether lines should be broken at missing data, for 'lines' and 'squared' plots.
     *
     * @param bool $bl  True to break the lines, false to connect around missing data
     * @return bool  True always
     */
    function SetDrawBrokenLines($bl)
    {
        $this->draw_broken_lines = (bool)$bl;
        return TRUE;
    }

    /**
     * Sets the data type, which defines the structure of the data array
     *
     * For a list of available data types, see the static arrays $datatypes and $datatypes_map.
     *
     * @param string $which_dt  The data array format type: text-data | data-data | ...
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetDataType($which_dt)
    {
        // Handle data type aliases - mostly for backward compatibility:
        if (isset(self::$datatypes_map[$which_dt]))
            $which_dt = self::$datatypes_map[$which_dt];
        // Validate the datatype argument against the available data types:
        $valid_data_types = implode(', ', array_keys(self::$datatypes));
        $this->data_type = $this->CheckOption($which_dt, $valid_data_types, __FUNCTION__);
        return (boolean)$this->data_type;
    }

    /**
     * Sets the data array for plotting
     *
     * This copy the array of data values, converting rows to numerical indexes.
     * It also validates that the array uses 0-based sequential integer indexes,
     * and that each array value (row) is another array. Other validation is
     * deferred to CheckDataArray().
     *
     * @param array $which_dv  The data array, an array of row arrays, interpreted per SetDataType()
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetDataValues($which_dv)
    {
        $this->num_data_rows = count($which_dv);
        $this->total_records = 0;
        $this->data = array();
        $this->num_recs = array();
        for ($i = 0; $i < $this->num_data_rows; $i++) {
            if (!isset($which_dv[$i]) || !is_array($which_dv[$i])) {
                return $this->PrintError("SetDataValues(): Invalid data array (row $i)");
            }
            $this->data[$i] = array_values($which_dv[$i]);   // convert to numerical indices.

            // Count size of each row, and total for the array.
            $this->total_records += $this->num_recs[$i] = count($this->data[$i]);
        }
        // This is the size of the widest row in the data array
        // Note records_per_group isn't used much anymore. See data_columns in CheckDataArray()
        $this->records_per_group = empty($this->num_recs) ? 0 : max($this->num_recs);
        return TRUE;
    }

    /**
     * Pads the style arrays so they are large enough for the number of data sets
     *
     * The style arrays to be padded are line_widths, line_styles, data_colors, data_border_colors.
     * This ensures they have at least $data_columns entries (maximum number of data sets), which
     * simplifies the plot drawing functions.
     * Other data color arrays are handled in the Need*Colors() functions instead (if needed).
     *
     * @return bool  True always
     */
    protected function PadArrays()
    {
        $this->pad_array($this->line_widths, $this->data_columns);
        $this->pad_array($this->line_styles, $this->data_columns);
        $this->pad_array($this->ndx_data_colors, $this->data_columns);
        $this->pad_array($this->ndx_data_border_colors, $this->data_columns);
        return TRUE;
    }

    /**
     * Pads an array with copies of itself until it reaches the given size
     *
     * pad_array only works on 0-based sequential integer indexed arrays. It also
     * accepts a scalar, which is first converted to a single element array.
     * Elements of the array are appended until it reaches the given size.
     *
     * @param array|mixed $arr  Reference variable for the array (or scalar) to pad
     * @param int $size  Minimum size of the resulting array
     */
    protected function pad_array(&$arr, $size)
    {
        if (! is_array($arr)) {
            $arr = array($arr);
        }
        $n = count($arr);
        $base = 0;
        while ($n < $size) $arr[$n++] = $arr[$base++];
    }

    /**
     * Formats a floating point number, with decimal separator and thousands groups separator
     *
     * This is like PHP's number_format, but uses class variables for separators, and tries to
     * get the separators from the current locale.
     * Note: The locale is saved and reset after getting the values. This is needed due to an issue with
     * PHP (see PHP bug 45365 and others): It uses a locale-specific decimal separator when converting
     * numbers to strings, but fails to convert back if the separator is other than dot. This would cause
     * pie chart labels to fail with "A non well formed numeric value encountered".
     *
     * @param float $number  A floating point number to format
     * @param int $decimals  Number of decimal places in the result
     * @return string  The formatted result
     */
    protected function number_format($number, $decimals=0)
    {
        // Try to get the proper decimal and thousands separators if they are not already set.
        if (!isset($this->decimal_point, $this->thousands_sep)) {
            // Load locale-specific values from environment, unless disabled (for testing):
            if (!$this->locale_override) {
                $save_locale = @setlocale(LC_NUMERIC, '0');
                @setlocale(LC_NUMERIC, '');
            }
            // Fetch locale settings:
            $locale = @localeconv();
            // Restore locale. (See note above.)
            if (!empty($save_locale)) @setlocale(LC_NUMERIC, $save_locale);
            if (isset($locale['decimal_point'], $locale['thousands_sep'])) {
                $this->decimal_point = $locale['decimal_point'];
                $this->thousands_sep = $locale['thousands_sep'];
            } else {
                // Locale information not available.
                $this->decimal_point = '.';
                $this->thousands_sep = ',';
            }
        }
        return number_format($number, $decimals, $this->decimal_point, $this->thousands_sep);
    }

    /**
     * Registers a callback (hook) function
     *
     * See the $callbacks array (class property) for the available callback names
     *
     * @param string $reason  A pre-defined name where a callback can be defined
     * @param callback $function  Function or method to register for callback
     * @param mixed $arg  Optional opaque argument to supply to the callback function when called
     * @return bool  True if the callback reason is valid, else False
     * @since 5.0.4
     */
    function SetCallback($reason, $function, $arg = NULL)
    {
        // Use array_key_exists because valid reason keys have NULL as value.
        if (!array_key_exists($reason, $this->callbacks))
            return FALSE;
        $this->callbacks[$reason] = array($function, $arg);
        return TRUE;
    }

    /**
     * Returns the current callback function registered for the given reason
     *
     * Note you can safely test the return value with a simple 'if', as no valid
     * function name evaluates to false. PHPlot uses if (GetCallback(...)) to
     * to avoid preparing arguments to an unused callback.
     *
     * @param string $reason  A pre-defined name where a callback can be defined
     * @return callback|false  The current callback for the reason; False if none or invalid
     * @since 5.0.4
     */
    function GetCallback($reason)
    {
        if (isset($this->callbacks[$reason]))
            return $this->callbacks[$reason][0];
        return FALSE;
    }

    /**
     * Un-registers any callback registered for the given reason
     *
     * Note: A True return means $reason is valid; it does not mean a callback
     * was actually registered for that reason.
     *
     * @param string $reason  A pre-defined name where a callback can be defined
     * @return bool  True if it was a valid callback reason, else False
     * @since 5.0.4
     */
    function RemoveCallback($reason)
    {
        if (!array_key_exists($reason, $this->callbacks))
            return FALSE;
        $this->callbacks[$reason] = NULL;
        return TRUE;
    }

    /**
     * Invokes a callback function, if one is registered
     *
     * Callbacks are called like this: callback_function($image, $passthru, [$arg,...])
     * Here $passthru is the argument specified when the callback was defined by SetCallback()
     * and is under control of the application. $arg... is zero or more additional arguments
     * specified when then callback is called. These are under control of PHPlot itself.
     *
     * @param string $reason  A string naming one of the pre-defined callback reasons
     * @param mixed $varargs  Zero or more additional arguments to be passed to the callback
     * @return mixed  Whatever value is returned by the callback function (if any)
     */
    protected function DoCallback($reason, $varargs = NULL)
    {
        if (!isset($this->callbacks[$reason]))
            return;
        $args = func_get_args();
        // Make the argument vector $args[] look like:  $image, $passthru, [$arg...]
        list($function, $args[0]) = $this->callbacks[$reason];
        array_unshift($args, $this->img);
        return call_user_func_array($function, $args);
    }

    /**
     * Allocates colors for the image background and image border
     *
     * This is separate from SetColorIndexes() below so that DrawMessage can use it.
     *
     * @since 5.7.0
     */
    protected function SetBgColorIndexes()
    {
        $this->ndx_bg_color = $this->GetColorIndex($this->bg_color); // Background first
        $this->ndx_plot_bg_color = $this->GetColorIndex($this->plot_bg_color);
        if ($this->image_border_type != 'none') {
            $this->ndx_i_border = $this->GetColorIndex($this->i_border);
            $this->ndx_i_border_dark = $this->GetDarkColorIndex($this->i_border);
        }
    }

    /**
     * Allocates all the colors needed for the plot
     *
     * This is called by DrawGraph to allocate the colors needed for the plot.  Each selectable
     * color has already been validated, parsed into an array (r,g,b,a), and stored into a member
     * variable. Now the GD color indexes are assigned and stored into the ndx_*_color variables.
     * This is deferred here to avoid allocating unneeded colors and to avoid order dependencies,
     * especially with the transparent color.
     *
     * For drawing data elements, only the main data colors and border colors are allocated here.
     * Dark colors and error bar colors are allocated by Need*Color() functions.
     * (Data border colors default to just black, so there is no cost to always allocating.)
     *
     * Data color allocation works as follows. If there is a data_color callback, then allocate all
     * defined data colors (because the callback can use them however it wants). Otherwise, only allocate
     * the number of colors that will be used. This is the larger of the number of data sets and the
     * number of legend lines.
     *
     * @since 5.2.0
     */
    protected function SetColorIndexes()
    {
        $this->SetBgColorIndexes(); // Background and border colors

        // Handle defaults for X and Y title colors.
        $this->ndx_title_color   = $this->GetColorIndex($this->title_color);
        $this->ndx_x_title_color = $this->GetColorIndex($this->x_title_color, $this->ndx_title_color);
        $this->ndx_y_title_color = $this->GetColorIndex($this->y_title_color, $this->ndx_title_color);

        // General text color, which is the default color for tick and data labels unless overridden.
        $this->ndx_text_color      = $this->GetColorIndex($this->text_color);
        $this->ndx_ticklabel_color = $this->GetColorIndex($this->ticklabel_color, $this->ndx_text_color);
        $this->ndx_datalabel_color = $this->GetColorIndex($this->datalabel_color, $this->ndx_text_color);
        $this->ndx_dvlabel_color   = $this->GetColorIndex($this->dvlabel_color, $this->ndx_datalabel_color);

        $this->ndx_grid_color       = $this->GetColorIndex($this->grid_color);
        $this->ndx_light_grid_color = $this->GetColorIndex($this->light_grid_color);
        $this->ndx_tick_color       = $this->GetColorIndex($this->tick_color);
        // Pie label and border colors default to grid color, for historical reasons (PHPlot <= 5.6.1)
        $this->ndx_pielabel_color   = $this->GetColorIndex($this->pielabel_color, $this->ndx_grid_color);
        $this->ndx_pieborder_color  = $this->GetColorIndex($this->pieborder_color, $this->ndx_grid_color);

        // Maximum number of data & border colors to allocate:
        if ($this->GetCallback('data_color')) {
            $n_data = count($this->data_colors); // Need all of them
            $n_border = count($this->data_border_colors);
        } else {
            $n_data = max($this->data_columns, empty($this->legend) ? 0 : count($this->legend));
            $n_border = $n_data; // One border color per data color
        }

        // Allocate main data colors. For other colors used for data, see the functions which follow.
        $this->ndx_data_colors = $this->GetColorIndexArray($this->data_colors, $n_data);
        $this->ndx_data_border_colors = $this->GetColorIndexArray($this->data_border_colors, $n_border);

        // Legend colors: background defaults to image background, text defaults to general text color.
        $this->ndx_legend_bg_color = $this->GetColorIndex($this->legend_bg_color, $this->ndx_bg_color);
        $this->ndx_legend_text_color = $this->GetColorIndex($this->legend_text_color, $this->ndx_text_color);

        // Set up a color as transparent, if SetTransparentColor was used.
        if (!empty($this->transparent_color)) {
            imagecolortransparent($this->img, $this->GetColorIndex($this->transparent_color));
        }
    }

    /**
     * Allocates dark-shade data colors used for shading
     *
     * This is called if needed by graph drawing functions that need shading.
     *
     * @since 5.2.0
     */
    protected function NeedDataDarkColors()
    {
        // This duplicates the calculation in SetColorIndexes() for number of data colors to allocate.
        if ($this->GetCallback('data_color')) {
            $n_data = count($this->data_colors);
        } else {
            $n_data = max($this->data_columns, empty($this->legend) ? 0 : count($this->legend));
        }
        $this->ndx_data_dark_colors = $this->GetDarkColorIndexArray($this->data_colors, $n_data);
        $this->pad_array($this->ndx_data_dark_colors, $this->data_columns);
    }

    /**
     * Allocates error bar colors
     *
     * This is called if needed by graph drawing functions that draw error bars.
     *
     * @since 5.2.0
     */
    protected function NeedErrorBarColors()
    {
        // This is similar to the calculation in SetColorIndexes() for number of data colors to allocate.
        if ($this->GetCallback('data_color')) {
            $n_err = count($this->error_bar_colors);
        } else {
            $n_err = max($this->data_columns, empty($this->legend) ? 0 : count($this->legend));
        }
        $this->ndx_error_bar_colors = $this->GetColorIndexArray($this->error_bar_colors, $n_err);
        $this->pad_array($this->ndx_error_bar_colors, $this->data_columns);
    }

    /**
     * Selects the best alignment for text, based on its vector angle from a point
     *
     * This picks one of 8 alignments (horizontal = left, center, or right; vertical = top, center
     * or bottom; but never center/center) for text that needs to be close to a point but directed
     * away from the point. The angle of the vector from the reference point determines the alignment.
     *
     * How it works: Picture a unit circle with 16 slices of 22.5 degrees each.
     * Draw horizontal lines at the 22.5 degree and -22.5 degree positions on the circle.
     * Text above the upper line will have 'bottom' vertical alignment; below the lower line will
     * have 'top' vertical alignment, and between the lines will have 'center' vertical alignment.
     * Horizontal alignment is similar, using +/- 22.5 degrees from vertical.
     *
     * @param float $sin_t  sin() of the angle of the text offset from a reference point
     * @param float $cos_t  cos() of the angle of the text offset from a reference point
     * @param string $h_align  Reference variable to get the horizontal alignment, for DrawText()
     * @param string $v_align  Reference variable to get the vertical alignment, for DrawText()
     * @param bool $reverse  True to reverse the alignment, e.g. for text inside an ellipse
     * @since 5.6.0
     */
    protected function GetTextAlignment($sin_t, $cos_t, &$h_align, &$v_align, $reverse = FALSE)
    {
        if ($reverse) {   // Return the opposite alignment, align(T-180) vs align(T)
            $sin_t = -$sin_t;   // sin(T-180) = -sin(T)
            $cos_t = -$cos_t;   // cos(T-180) = -cos(T)
        }
        if ($sin_t >= 0.383) $v_align = 'bottom';       // 0.383 = sin(22.5 degrees)
        elseif ($sin_t >= -0.383) $v_align = 'center';
        else $v_align = 'top';
        if ($cos_t >= 0.383) $h_align = 'left';         // 0.383 = cos(90 - 22.5 degrees)
        elseif ($cos_t >= -0.383) $h_align = 'center';
        else $h_align = 'right';
    }

    /**
     * Determines if and where to draw Data Value Labels
     *
     * This is called by plot drawing functions that support Data Value Labels (other
     * than bars and stackedbars, which have their own way of doing it). If those
     * labels are on, it returns True and sets 4 keys in $dvl[] which are used by
     * DrawDataValueLabel to position the label: x_offset, y_offset = pixel offsets
     * for the label; h_align, v_align = text alignment choices.
     * It uses two member variables: data_value_label_angle and data_value_label_distance
     * to define the vector to the label.
     *
     * @param string $label_control  Label position control; either $x_data_label_pos or $y_data_label_pos
     * @param array $dvl  Reference argument for result parameters for DrawDataValueLabel()
     * @return bool  False if data value labels are off; True if on and $dvl is set
     * @since 5.3.0
     */
    protected function CheckDataValueLabels($label_control, &$dvl)
    {
        if ($label_control != 'plotin')
            return FALSE; // No data value labels
        $angle = deg2rad($this->data_value_label_angle);
        $cos = cos($angle);
        $sin = sin($angle);
        $dvl['x_offset'] = (int)($this->data_value_label_distance * $cos);
        $dvl['y_offset'] = -(int)($this->data_value_label_distance * $sin); // Y is reversed (device coords)

        // Choose text alignment based on angle:
        $this->GetTextAlignment($sin, $cos, $dvl['h_align'], $dvl['v_align']);
        return TRUE;
    }

    /**
     * Enables or disables automatic pie chart size calculation
     *
     * If autosize is disabled, PHPlot uses the full plot area (as PHPlot-5.5.0
     * and earlier always did). Note the flag pie_full_size is unset by default,
     * and stores the complement of $enable.
     *
     * @param bool $enable  True to enable automatic size calculation, False to use the maximum area
     * @return bool  True always
     * @since 5.6.0
     */
    function SetPieAutoSize($enable)
    {
        $this->pie_full_size = !$enable;
        return TRUE;
    }

    /**
     * Sets the starting angle for pie chart segments
     *
     * @param float $angle  Starting angle in degrees
     * @return bool  True always
     * @since 6.0.0
     */
    function SetPieStartAngle($angle)
    {
        $this->pie_start_angle = $angle;
        return TRUE;
    }

    /**
     * Sets the direction for pie chart segments
     *
     * @param string $which  Direction for pie segments: clockwise | cw | counterclockwise | ccw
     * @return bool  True (False on error if an error handler returns True)
     * @since 6.0.0
     */
    function SetPieDirection($which)
    {
        $control = $this->CheckOption($which, 'clockwise, cw, counterclockwise, ccw', __FUNCTION__);
        if (empty($control)) return FALSE;
        $this->pie_direction_cw = ($control == 'clockwise' || $control == 'cw');
        return TRUE;
    }

//////////////////////////////////////////////////////////
///////////         DATA ANALYSIS, SCALING AND TRANSLATION
//////////////////////////////////////////////////////////

    /**
     * Analyzes the data array and calculates the minimum and maximum values
     *
     * In this function, IV refers to the independent variable, and DV the dependent
     * variable.  For vertical plots (most common), IV is X and DV is Y. For
     * horizontal plots (swapped X/Y), IV is Y and DV is X.  At the end of the
     * function, IV and DV ranges get assigned into X or Y variables.
     *
     * The data type mostly determines the data array structure, but some plot types
     * do special things such as sum the values in a row. This information is in the
     * plots[] array.
     *
     * This calculates min_x, max_x, min_y, and max_y. It also calculates two arrays
     * data_min[] and data_max[] with per-row min and max values. These are used for
     * data label lines. For vertical plots, these are the Y range for each X. For
     * vertical (swapped X/Y) plots, they are the X range for each Y.  For X/Y/Z
     * plots, it also calculates min_z and max_z.
     *
     * @return bool  True always
     */
    protected function FindDataLimits()
    {
        // Does this plot type need special processing of the data values?
        $sum_vals = !empty(self::$plots[$this->plot_type]['sum_vals']); // Add up values in each row
        $abs_vals = !empty(self::$plots[$this->plot_type]['abs_vals']); // Take absolute values

        // Initialize arrays which track the min/max per-row dependent values:
        $this->data_min = array();
        $this->data_max = array();

        // Independent values are in the data array or assumed?
        if ($this->datatype_implied) {
            // Range for text-data is 0.5 to num_data_rows-0.5. Add 0.5 fixed margins on each side.
            $all_iv = array(0, $this->num_data_rows);
        } else {
            $all_iv = array(); // Calculated below
        }
        // For X/Y/Z plots, make sure these are not left over from a previous plot.
        if ($this->datatype_yz)
            $this->min_z = $this->max_z = NULL;

        // Process all rows of data:
        for ($i = 0; $i < $this->num_data_rows; $i++) {
            $n_vals = $this->num_recs[$i];
            $j = 1; // Skips label at [0]

            if (!$this->datatype_implied) {
                $all_iv[] = (double)$this->data[$i][$j++];
            }

            if ($sum_vals) {
                $all_dv = array(0, 0); // One limit is 0, other calculated below
            } else {
                $all_dv = array();
            }
            while ($j < $n_vals) {
                if (is_numeric($val = $this->data[$i][$j++])) {

                    if ($this->datatype_error_bars) {
                        $all_dv[] = $val + (double)$this->data[$i][$j++];
                        $all_dv[] = $val - (double)$this->data[$i][$j++];
                    } else {
                        if ($abs_vals) {
                            $val = abs($val); // Use absolute values
                        }
                        if ($sum_vals) {
                            $all_dv[1] += $val;  // Sum of values
                        } else {
                            $all_dv[] = $val; // List of all values
                        }
                        if ($this->datatype_yz) {
                            $z = $this->data[$i][$j++]; // Note Z is required if Y is present.
                            if (!isset($this->min_z) || $z < $this->min_z) $this->min_z = $z;
                            if (!isset($this->max_z) || $z > $this->max_z) $this->max_z = $z;
                        }
                    }
                } else {    // Missing DV value
                  if ($this->datatype_error_bars) $j += 2;
                  elseif ($this->datatype_yz) $j++;
                }
            }
            if (!empty($all_dv)) {
                $this->data_min[$i] = min($all_dv);  // Store per-row DV range
                $this->data_max[$i] = max($all_dv);
            }
        }

        if ($this->datatype_swapped_xy) {
            // Assign min and max for swapped X/Y plots: IV=Y and DV=X
            $this->min_y = min($all_iv);
            $this->max_y = max($all_iv);
            if (empty($this->data_min)) { // Guard against regressive case: No X at all
                $this->min_x = 0;
                $this->max_x = 0;
            } else {
                $this->min_x = min($this->data_min);  // Store global X range
                $this->max_x = max($this->data_max);
            }
        } else {
            // Assign min and max for normal plots: IV=X and DV=Y
            $this->min_x = min($all_iv);
            $this->max_x = max($all_iv);
            if (empty($this->data_min)) { // Guard against regressive case: No Y at all
                $this->min_y = 0;
                $this->max_y = 0;
            } else {
                $this->min_y = min($this->data_min);  // Store global Y range
                $this->max_y = max($this->data_max);
            }
        }
        // For X/Y/Z plots, make sure these are set. If there are no valid data values,
        // they will be unset, so set them here to prevent undefined property warnings.
        if ($this->datatype_yz && !isset($this->min_z)) {   // Means max_z is also unset
            $this->max_z = $this->min_z = 0; // Actual values do not matter.
        }

        if ($this->GetCallback('debug_scale')) {
            $this->DoCallback('debug_scale', __FUNCTION__, array(
                'min_x' => $this->min_x, 'min_y' => $this->min_y,
                'max_x' => $this->max_x, 'max_y' => $this->max_y,
                'min_z' => isset($this->min_z) ? $this->min_z : '',
                'max_z' => isset($this->max_z) ? $this->max_z : ''));
        }
        return TRUE;
    }

    /**
     * Calculates the plot area margin size and related positions and offsets
     *
     * Calculates the title sizes: title_height, x_title_height, and y_title_width.
     * These are local, not class variables, since they are only used here.
     * The X and Y title size variables are 0 if there is no corresponding title.
     *
     * Calculates the tick label and axis data label offsets, relative to the plot
     * area: x_label_top_offset, x_label_bot_offset, x_label_axis_offset,
     * y_label_left_offset, y_label_right_offset, and y_label_axis_offset.
     *
     * Calculates the title position offsets, relative to the plot area:
     * x_title_top_offset, x_title_bot_offset, y_title_left_offset, and
     * y_title_left_offset. Also calculates the main title offset, which is relative
     * to the top of the image.
     *
     * Finally, calculates the plot area margins using the above to figure out how
     * much space outside the plot area is needed. The class variables are:
     * y_top_margin, y_bot_margin, x_left_margin, and x_right_margin.  All 4 margins
     * are calculated, but only those not set with SetPlotAreaPixels() or
     * SetMarginsPixels() are stored into the class variables.
     *
     * A plot with $minimize True, such as a pie chart, does not have an X or Y axis
     * or X/Y titles, and so can use more of the image space.
     *
     * A picture of the locations of elements and spacing can be found in the
     * PHPlot Reference Manual.
     *
     * @param bool $maximize  If True, use full image area (less margins and title space)
     * @return bool  True always
     */
    protected function CalcMargins($maximize)
    {
        // This is the line-to-line or line-to-text spacing:
        $gap = $this->safe_margin;
        // Initial margin on each side takes into account a possible image border.
        // For compatibility, if border is 1 or 2, don't increase the margins.
        $base_margin = max($gap, $this->GetImageBorderWidth() + 3);
        $this->title_offset = $base_margin;  // For use in DrawTitle

        // Minimum margin on each side. This reduces the chance that the
        // right-most tick label (for example) will run off the image edge
        // if there are no titles on that side.
        $min_margin = 2 * $gap + $base_margin;

        // Calculate the title sizes (main here, axis titles below):
        list($unused, $title_height) = $this->SizeText('title', 0, $this->title_txt);

        // Special case for maximum area usage with no X/Y titles or labels, only main title:
        if ($maximize) {
            if (!isset($this->x_left_margin))
                $this->x_left_margin = $base_margin;
            if (!isset($this->x_right_margin))
                $this->x_right_margin = $base_margin;
            if (!isset($this->y_top_margin)) {
                $this->y_top_margin = $base_margin;
                if ($title_height > 0)
                    $this->y_top_margin += $title_height + $gap;
            }
            if (!isset($this->y_bot_margin))
                $this->y_bot_margin = $base_margin;

            return TRUE;
        }

        list($unused, $x_title_height) = $this->SizeText('x_title', 0, $this->x_title_txt);
        list($y_title_width, $unused) = $this->SizeText('y_title', 90, $this->y_title_txt);

        // For X/Y tick and label position of 'xaxis' or 'yaxis', determine if the axis happens to be
        // on an edge of a plot. If it is, we need to account for the margins there.
        if ($this->x_axis_position <= $this->plot_min_y)
            $x_axis_pos = 'bottom';
        elseif ($this->x_axis_position >= $this->plot_max_y)
            $x_axis_pos = 'top';
        else
            $x_axis_pos = 'none';
        if ($this->y_axis_position <= $this->plot_min_x)
            $y_axis_pos = 'left';
        elseif ($this->y_axis_position >= $this->plot_max_x)
            $y_axis_pos = 'right';
        else
            $y_axis_pos = 'none';

        // Calculate the heights for X tick and data labels, and the max (used if they are overlaid):
        $x_data_label_height = ($this->x_data_label_pos == 'none') ? 0 : $this->CalcMaxDataLabelSize('x');
        $x_tick_label_height = ($this->x_tick_label_pos == 'none') ? 0 : $this->CalcMaxTickLabelSize('x');
        $x_max_label_height = max($x_data_label_height, $x_tick_label_height);

        // Calculate the space needed above and below the plot for X tick and X data labels:

        // Above the plot:
        $tick_labels_above = ($this->x_tick_label_pos == 'plotup' || $this->x_tick_label_pos == 'both'
                          || ($this->x_tick_label_pos == 'xaxis' && $x_axis_pos == 'top'));
        $data_labels_above = ($this->x_data_label_pos == 'plotup' || $this->x_data_label_pos == 'both');
        if ($tick_labels_above) {
            if ($data_labels_above) {
                $label_height_above = $x_max_label_height;
            } else {
                $label_height_above = $x_tick_label_height;
            }
        } elseif ($data_labels_above) {
            $label_height_above = $x_data_label_height;
        } else {
            $label_height_above = 0;
        }

        // Below the plot:
        $tick_labels_below = ($this->x_tick_label_pos == 'plotdown' || $this->x_tick_label_pos == 'both'
                          || ($this->x_tick_label_pos == 'xaxis' && $x_axis_pos == 'bottom'));
        $data_labels_below = ($this->x_data_label_pos == 'plotdown' || $this->x_data_label_pos == 'both');
        if ($tick_labels_below) {
            if ($data_labels_below) {
                $label_height_below = $x_max_label_height;
            } else {
                $label_height_below = $x_tick_label_height;
            }
        } elseif ($data_labels_below) {
            $label_height_below = $x_data_label_height;
        } else {
            $label_height_below = 0;
        }

        // Calculate the width for Y tick and data labels, if on, and the max:
        // Note CalcMaxDataLabelSize('y') returns 0 except for swapped X/Y plots.
        $y_data_label_width = ($this->y_data_label_pos == 'none') ? 0 : $this->CalcMaxDataLabelSize('y');
        $y_tick_label_width = ($this->y_tick_label_pos == 'none') ? 0 : $this->CalcMaxTickLabelSize('y');
        $y_max_label_width = max($y_data_label_width, $y_tick_label_width);

        // Calculate the space needed left and right of the plot for Y tick and Y data labels:
        // (Y data labels here are for swapped X/Y plots such has horizontal bars)

        // Left of the plot:
        $tick_labels_left = ($this->y_tick_label_pos == 'plotleft' || $this->y_tick_label_pos == 'both'
                         || ($this->y_tick_label_pos == 'yaxis' && $y_axis_pos == 'left'));
        $data_labels_left = ($this->y_data_label_pos == 'plotleft' || $this->y_data_label_pos == 'both');
        if ($tick_labels_left) {
            if ($data_labels_left) {
                $label_width_left = $y_max_label_width;
            } else {
                $label_width_left = $y_tick_label_width;
            }
        } elseif ($data_labels_left) {
            $label_width_left = $y_data_label_width;
        } else {
            $label_width_left = 0;
        }

        // Right of the plot:
        $tick_labels_right = ($this->y_tick_label_pos == 'plotright' || $this->y_tick_label_pos == 'both'
                          || ($this->y_tick_label_pos == 'yaxis' && $y_axis_pos == 'right'));
        $data_labels_right = ($this->y_data_label_pos == 'plotright' || $this->y_data_label_pos == 'both');
        if ($tick_labels_right) {
            if ($data_labels_right) {
                $label_width_right = $y_max_label_width;
            } else {
                $label_width_right = $y_tick_label_width;
            }
        } elseif ($data_labels_right) {
            $label_width_right = $y_data_label_width;
        } else {
            $label_width_right = 0;
        }

        ///////// Calculate margins:

        // Calculating Top and Bottom margins:
        // y_top_margin: Main title, Upper X title, X ticks and tick labels, and X data labels:
        // y_bot_margin: Lower title, ticks and tick labels, and data labels:
        $top_margin = $base_margin;
        $bot_margin = $base_margin;
        $this->x_title_top_offset = $gap;
        $this->x_title_bot_offset = $gap;

        // Space for main title?
        if ($title_height > 0)
            $top_margin += $title_height + $gap;

        // Reserve space for X title, above and/or below as needed:
        if ($x_title_height > 0 && ($pos = $this->x_title_pos) != 'none') {
            if ($pos == 'plotup' || $pos == 'both')
                $top_margin += $x_title_height + $gap;
            if ($pos == 'plotdown' || $pos == 'both')
                $bot_margin += $x_title_height + $gap;
        }

        // Space for X Labels above the plot?
        if ($label_height_above > 0) {
            $top_margin += $label_height_above + $gap;
            $this->x_title_top_offset += $label_height_above + $gap;
        }

        // Space for X Labels below the plot?
        if ($label_height_below > 0) {
            $bot_margin += $label_height_below + $gap;
            $this->x_title_bot_offset += $label_height_below + $gap;
        }

        // Space for X Ticks above the plot?
        if ($this->x_tick_pos == 'plotup' || $this->x_tick_pos == 'both'
           || ($this->x_tick_pos == 'xaxis' && $x_axis_pos == 'top')) {
            $top_margin += $this->x_tick_length;
            $this->x_label_top_offset = $this->x_tick_length + $gap;
            $this->x_title_top_offset += $this->x_tick_length;
        } else {
            // No X Ticks above the plot:
            $this->x_label_top_offset = $gap;
        }

        // Space for X Ticks below the plot?
        if ($this->x_tick_pos == 'plotdown' || $this->x_tick_pos == 'both'
           || ($this->x_tick_pos == 'xaxis' && $x_axis_pos == 'bottom')) {
            $bot_margin += $this->x_tick_length;
            $this->x_label_bot_offset = $this->x_tick_length + $gap;
            $this->x_title_bot_offset += $this->x_tick_length;
        } else {
            // No X Ticks below the plot:
            $this->x_label_bot_offset = $gap;
        }
        // Label offsets for on-axis ticks:
        if ($this->x_tick_pos == 'xaxis') {
            $this->x_label_axis_offset = $this->x_tick_length + $gap;
        } else {
            $this->x_label_axis_offset = $gap;
        }

        // Calculating Left and Right margins:
        // x_left_margin: Left Y title, Y ticks and tick labels:
        // x_right_margin: Right Y title, Y ticks and tick labels:
        $left_margin = $base_margin;
        $right_margin = $base_margin;
        $this->y_title_left_offset = $gap;
        $this->y_title_right_offset = $gap;

        // Reserve space for Y title, on left and/or right as needed:
        if ($y_title_width > 0 && ($pos = $this->y_title_pos) != 'none') {
            if ($pos == 'plotleft' || $pos == 'both')
                $left_margin += $y_title_width + $gap;
            if ($pos == 'plotright' || $pos == 'both')
                $right_margin += $y_title_width + $gap;
        }

        // Space for Y Labels left of the plot?
        if ($label_width_left > 0) {
            $left_margin += $label_width_left + $gap;
            $this->y_title_left_offset += $label_width_left + $gap;
        }

        // Space for Y Labels right of the plot?
        if ($label_width_right > 0) {
            $right_margin += $label_width_right + $gap;
            $this->y_title_right_offset += $label_width_right + $gap;
        }

        // Space for Y Ticks left of plot?
        if ($this->y_tick_pos == 'plotleft' || $this->y_tick_pos == 'both'
           || ($this->y_tick_pos == 'yaxis' && $y_axis_pos == 'left')) {
            $left_margin += $this->y_tick_length;
            $this->y_label_left_offset = $this->y_tick_length + $gap;
            $this->y_title_left_offset += $this->y_tick_length;
        } else {
            // No Y Ticks left of plot:
            $this->y_label_left_offset = $gap;
        }

        // Space for Y Ticks right of plot?
        if ($this->y_tick_pos == 'plotright' || $this->y_tick_pos == 'both'
           || ($this->y_tick_pos == 'yaxis' && $y_axis_pos == 'right')) {
            $right_margin += $this->y_tick_length;
            $this->y_label_right_offset = $this->y_tick_length + $gap;
            $this->y_title_right_offset += $this->y_tick_length;
        } else {
            // No Y Ticks right of plot:
            $this->y_label_right_offset = $gap;
        }

        // Label offsets for on-axis ticks:
        if ($this->x_tick_pos == 'yaxis') {
            $this->y_label_axis_offset = $this->y_tick_length + $gap;
        } else {
            $this->y_label_axis_offset = $gap;
        }

        // Apply the minimum margins and store in the object.
        // Do not set margins which were user-defined (see note at top of function).
        if (!isset($this->y_top_margin))
            $this->y_top_margin = max($min_margin, $top_margin);
        if (!isset($this->y_bot_margin))
            $this->y_bot_margin = max($min_margin, $bot_margin);
        if (!isset($this->x_left_margin))
            $this->x_left_margin = max($min_margin, $left_margin);
        if (!isset($this->x_right_margin))
            $this->x_right_margin = max($min_margin, $right_margin);

        if ($this->GetCallback('debug_scale')) {
            // (Too bad compact() doesn't work on class member variables...)
            $this->DoCallback('debug_scale', __FUNCTION__, array(
                'label_height_above' => $label_height_above,
                'label_height_below' => $label_height_below,
                'label_width_left' => $label_width_left,
                'label_width_right' => $label_width_right,
                'x_tick_length' => $this->x_tick_length,
                'y_tick_length' => $this->y_tick_length,
                'x_left_margin' => $this->x_left_margin,
                'x_right_margin' => $this->x_right_margin,
                'y_top_margin' => $this->y_top_margin,
                'y_bot_margin' => $this->y_bot_margin,
                'x_label_top_offset' => $this->x_label_top_offset,
                'x_label_bot_offset' => $this->x_label_bot_offset,
                'y_label_left_offset' => $this->y_label_left_offset,
                'y_label_right_offset' => $this->y_label_right_offset,
                'x_title_top_offset' => $this->x_title_top_offset,
                'x_title_bot_offset' => $this->x_title_bot_offset,
                'y_title_left_offset' => $this->y_title_left_offset,
                'y_title_right_offset' => $this->y_title_right_offset));
        }

        return TRUE;
    }

    /**
     * Calculates the plot area (in pixels) from the margins
     *
     * This does the deferred calculation of class variables plot_area,
     * plot_area_width, and plot_area_height. The margins might come
     * from SetMarginsPixels(), SetPlotAreaPixels(), or CalcMargins().
     *
     * @return bool  True always
     * @since 5.0.5
     */
    protected function CalcPlotAreaPixels()
    {
        $this->plot_area = array($this->x_left_margin, $this->y_top_margin,
                                 $this->image_width - $this->x_right_margin,
                                 $this->image_height - $this->y_bot_margin);
        $this->plot_area_width = $this->plot_area[2] - $this->plot_area[0];
        $this->plot_area_height = $this->plot_area[3] - $this->plot_area[1];

        $this->DoCallback('debug_scale', __FUNCTION__, $this->plot_area);
        return TRUE;
    }

    /**
     * Sets the margins around the plot area
     *
     * This determines the plot area, equivalent to SetPlotAreaPixels()
     * but instead of giving the plot area size, you give the margin sizes.
     *
     * @param int $which_lm  Left margin in pixels; omit or NULL to auto-calculate
     * @param int $which_rm  Right margin in pixels; omit or NULL to auto-calculate
     * @param int $which_tm  Top margin in pixels; omit or NULL to auto-calculate
     * @param int $which_bm  Bottom margin in pixels; omit or NULL to auto-calculate
     * @return bool  True always
     */
    function SetMarginsPixels($which_lm = NULL, $which_rm = NULL, $which_tm = NULL, $which_bm = NULL)
    {
        $this->x_left_margin = $which_lm;
        $this->x_right_margin = $which_rm;
        $this->y_top_margin = $which_tm;
        $this->y_bot_margin = $which_bm;
        return TRUE;
    }

    /**
     * Sets the limits for the plot area, in device coordinates
     *
     * This determines the plot area, equivalent to SetMarginsPixels()
     * but instead of giving the margin sizes, you give the plot area size,
     *
     * This stores the margins, not the area. That may seem odd, but the idea is
     * to make SetPlotAreaPixels and SetMarginsPixels two ways to accomplish the
     * same thing, and the deferred calculations in CalcMargins and
     * CalcPlotAreaPixels don't need to know which was used.
     *
     * @param int $x1  Top left corner X coordinate in pixels; omit or NULL to auto-calculate
     * @param int $y1  Top left corner Y coordinate in pixels; omit or NULL to auto-calculate
     * @param int $x2  Bottom right corner X coordinate in pixels; omit or NULL to auto-calculate
     * @param int $y2  Bottom right corner Y coordinate in pixels; omit or NULL to auto-calculate
     * @return bool  True always
     */
    function SetPlotAreaPixels($x1 = NULL, $y1 = NULL, $x2 = NULL, $y2 = NULL)
    {
        $this->x_left_margin = $x1;
        $this->x_right_margin = isset($x2) ? $this->image_width - $x2 : NULL;
        $this->y_top_margin = $y1;
        $this->y_bot_margin = isset($y2) ? $this->image_height - $y2 : NULL;
        return TRUE;
    }

    /**
     * Calculates an appropriate tick increment in 'decimal' mode
     *
     * This is used by CalcStep().  It returns the largest value that is 1, 2, or 5
     * times an integer power of 10, and which divides the data range into no fewer
     * than min_ticks tick intervals.
     *
     * @param float $range  The data range (max - min), already checked as > 0
     * @param int $min_ticks  Smallest number of intervals allowed, already checked > 0
     * @return float  The calculated tick increment
     * @since 6.0.0
     */
    protected function CalcStep125($range, $min_ticks)
    {
        $v = log10($range / $min_ticks);
        $vi = (int)floor($v);
        $tick_step = pow(10, $vi);
        $f = $v - $vi;
        if ($f > 0.69897) $tick_step *= 5;   // Note 0.69897 = log10(5)
        elseif ($f > 0.301) $tick_step *= 2;  // Note 0.30103 = log10(2), truncated to fix edge cases
        return $tick_step;
    }

    /**
     * Calculates an appropriate tick increment in 'date/time' mode
     *
     * This is used by CalcStep() when the axis values use date/time units.
     * Unlike in CalcStep125(), there is no equation to compute this, so an array
     * $datetime_steps is used.  The values are "natural" time intervals, keeping
     * the ratio between adjacent entries <= 2.5 (so that max_ticks <= 2.5*min_ticks).
     * For seconds or minutes, it uses: 1 2 5 10 15 30. For hours, it uses 1 2 4 8 12
     * 24 48 96 and 168 (=7 days). Above that, it falls back to CalcStep125 using days.
     *
     * @param float $range  The data range (max - min), already checked as > 0
     * @param int $min_ticks  Smallest number of intervals allowed, already checked > 0
     * @return int  The calculated tick increment. This will always be >= 1 second
     * @since 6.0.0
     */
    protected function CalcStepDatetime($range, $min_ticks)
    {
        static $datetime_steps = array(1, 2, 5, 10, 15, 30, 60, 120, 300, 600, 900, 1800, 3600,
                                    7200, 14400, 28800, 43200, 86400, 172800, 345600, 604800);
        static $datetime_limit = 1512000;  // 1 week times 2.5, in seconds.

        if ($range < $min_ticks) {
            $tick_step = 1;    // Range is too small; minimum interval is 1 second.
        } elseif (($tick_limit = $range / $min_ticks) <= $datetime_limit) {
            // Find the biggest value in the table <= tick_limit (which is the
            // exact interval which would give min_ticks steps):
            foreach ($datetime_steps as $v) {
                if ($v <= $tick_limit) $tick_step = $v;
                else break;
            }
        } else {
            // Use the numeric-mode algorithm to find a 1,2,5*10**n solution, in units of days.
            $tick_step = $this->CalcStep125($range / 86400, $min_ticks) * 86400;
        }
        return $tick_step;
    }

    /**
     * Calculates an appropriate tick increment in 'binary' mode
     *
     * This is used by CalcStep(). It returns the largest power of 2 that divides
     * the range into at least min_ticks intervals.
     * Note: This contains an ugly work-around to a round-off problem. Using
     * floor(log2(2^N)) should produce N for all integer N, but with glibc, it turns
     * out that log2(8) is slightly < 3, and similar for a few other values (64, 4096,
     * 8192). So they truncate to N-1. Other tested values, and all negative values,
     * and all values on Windows, were found to truncate with floor() in the right
     * direction. The adjustment below makes all values N=-50 to 50 truncate correctly.
     *
     * @param float $range  The data range (max - min), already checked as > 0
     * @param int $min_ticks  Smallest number of intervals allowed, already checked > 0
     * @return float  The calculated tick increment
     * @since 6.0.0
     */
    protected function CalcStepBinary($range, $min_ticks)
    {
        $log2 = log($range / $min_ticks, 2);
        if ($log2 > 0) $log2 *= 1.000001; // See note above
        return pow(2, (int)floor($log2));
    }

    /**
     * Calculates an ideal tick increment for a given range
     *
     * This is only used when neither Set[XY]TickIncrement nor SetNum[XY]Ticks was used.
     *
     * @param string $which  Which axis to calculate for. Must be 'x' or 'y'
     * @param float $range  The data range (max - min), already checked as > 0
     * @return float  The tick increment, using one of 3 methods depending on the 'tick_mode'
     * @since 6.0.0
     */
    protected function CalcStep($which, $range)
    {
        // Get tick control variables: min_ticks, tick_mode, tick_inc_integer.
        extract($this->tickctl[$which]);

        // If tick_mode is null, default to decimal mode unless the axis uses date/time formatting:
        if (!isset($tick_mode)) {
            if (isset($this->label_format[$which]['type']) && $this->label_format[$which]['type'] == 'time')
                $tick_mode = 'date';
            else
                $tick_mode = 'decimal';
        }

        // Use proper mode to calculate the tick increment, with integer override option.
        if ($tick_mode == 'date') {
            $tick_step = $this->CalcStepDatetime($range, $min_ticks);
        } elseif ($tick_inc_integer && $range <= $min_ticks) {
            $tick_step = 1;  // Whole integer ticks selected but range is too small.
        } elseif ($tick_mode == 'binary') {
            $tick_step = $this->CalcStepBinary($range, $min_ticks);
        } else {
            $tick_step = $this->CalcStep125($range, $min_ticks);
        }
        return $tick_step;
    }

    /**
     * Initializes range variables for CalcPlotRange()
     *
     * This is a helper for CalcPlotRange(), which calls it 4 times, to initialize
     * each end of the range for each axis. It also sets flags to indicate
     * whether automatic adjustment of the range end is needed.
     *
     * @param float $plot_limit  Reference to (possibly unset) plot_min_[xy] or plot_max_[xy]
     * @param bool $implied  True if this is the implied variable (X for vertical plots)
     * @param float $data_limit  Actual data limit at this end: one of min_x, max_x,  etc.
     * @return array  Array with (initial value of the range limit, adjustment flag)
     * @since 6.0.0
     */
    protected function CalcRangeInit(&$plot_limit, $implied, $data_limit)
    {
        if (isset($plot_limit) && $plot_limit !== '') {
            // Use the user-supplied value, and do no further adjustments.
            return array($plot_limit, FALSE);
        }
        // Start with the actual data range. Set adjustment flag TRUE unless the range was implied.
        return array($data_limit, !$implied);
    }

    /**
     * Checks for a positive plot area range, and adjust if necessary
     *
     * This makes sure that the X or Y plot range is positive. The tick increment and
     * other calculations cannot handle negative or zero range, so we need to do
     * something to prevent it. There are 2 general cases: 1) automatic range, and
     * data is 'flat' (all same value). 2) One side of range given in
     * SetPlotAreaWorld(), and all the data is on the wrong side of that.
     *
     * Note that values specified in SetPlotAreaWorld() are never adjusted, even if it
     * means an empty plot (because all the data is outside the range).
     *
     * Called by CalcPlotRange() after CalcRangeInit() applies the defaults.
     *
     * @param string $which  Which axis: 'x' or 'y', used only for reporting
     * @param float $plot_min  Reference variable for the low end limit, changed if necessary
     * @param float $plot_max  Reference variable for the high end limit, changed if necessary
     * @param bool $adjust_min  True means $plot_min was auto-calculated, and may be adjusted
     * @param bool $adjust_max  True means $plot_max was auto-calculated, and may be adjusted
     * @return bool  True (False on error if an error handler returns True)
     * @since 6.0.0
     */
    protected function CheckPlotRange($which, &$plot_min, &$plot_max, $adjust_min, $adjust_max)
    {
        if ($plot_min < $plot_max)
            return TRUE; // No adjustment needed.

        // Bad range, plot_min >= plot_max, needs fixing.
        if ($adjust_max && $adjust_min) {
            // Both min and max are calculated, so either or both can be adjusted.
            // It should not be possible that plot_min > plot_max here, but check it to be safe:
            if ($plot_max != $plot_min)
                return $this->PrintError("SetPlotAreaWorld(): Inverse auto $which range error");

            if ($plot_max == 0.0) {
                // All 0. Use the arbitrary range 0:10
                $plot_max = 10;
            } elseif ($plot_min > 0) {
                // All same positive value. Use the range 0:10 (or larger).
                $plot_min = 0;
                $plot_max = max($plot_max, 10);
            } else {
                // All same negative value. Use the range -10:0 (or larger).
                $plot_min = min($plot_min, -10);
                $plot_max = 0;
            }
        } elseif ($adjust_max) {  // Equivalent to: ($adjust_max && !$adjust_min)
            // Max is calculated, min was set, so adjust max
            if ($plot_min < 0) $plot_max = 0;
            else $plot_max = $plot_min + 10;

        } elseif ($adjust_min) {  // Equivalent to: (!$adjust_max && $adjust_min)
            // Min is calculated, max was set, so adjust min
            if ($plot_max > 0) $plot_min = 0;
            else $plot_min = $plot_max - 10;

        } else {  // Equivalent to: (!$adjust_max && !$adjust_min)
            // Both limits are set. This should never happen, since SetPlotAreaWorld stops it.
            return $this->PrintError("SetPlotAreaWorld(): Inverse $which range error");
        }
        return TRUE;
    }

    /**
     * Gets the plot range end adjustment factor
     *
     * This is a helper for CalcPlotRange().  If $adjust is already set, it is left
     * alone, otherwise it uses the current plot type to apply a default setting.
     *
     * @param string $which  Which axis to calculate for. Must be 'x' or 'y'
     * @param float $adjust  Reference variable for the range end adjustment factor, NULL or already set
     * @since 6.0.0
     */
    protected function GetRangeEndAdjust($which, &$adjust)
    {
        if (isset($adjust)) return;  // Already set, nothing to do

        // The plot type can customize how an end adjustment is applied:
        if (empty(self::$plots[$this->plot_type]['adjust_type'])) {
            // Default (adjust_type missing or 0) means pad the dependent variable axis only.
            $adjust = ($which == 'x' XOR $this->datatype_swapped_xy) ? 0 : 0.03;
        } else {
            switch (self::$plots[$this->plot_type]['adjust_type']) {
            case 1:
                // Adjust type = 1 means add extra padding to both X and Y axis ends
                $adjust = 0.03;
                break;
            case 2:
                // Adjust type = 2 means do not add extra padding to either axis.
                $adjust = 0;
                break;
            }
        }
    }

    /**
     * Calculates the plot range and tick increment for X or Y
     *
     * This is a helper for CalcPlotAreaWorld(). It returns the plot range (plot_min
     * and plot_max), and the tick increment, for the X or Y axis. Priority is given
     * to user-set values with SetPlotAreaWorld() and Set[XY]TickIncrement(), but if
     * these were defaulted then values are automatically calculated.
     *
     * @param string $which  Which axis to calculate for. Must be 'x' or 'y'
     * @return float[]  Array of (tick_increment, plot_min, plot_max) or FALSE on handled error
     * @since 6.0.0
     */
    protected function CalcPlotRange($which)
    {
        // Independent variable is X in the usual vertical plots; Y in horizontal plots:
        $independent_variable = ($this->datatype_swapped_xy XOR $which == 'x');
        // 'implied' means this is a non-explicitly given independent variable, e.g. X in 'text-data'.
        $implied = $this->datatype_implied && $independent_variable;

        // Initialize the range (plot_min : plot_max) and get the adjustment flags:
        list($plot_min, $adjust_min) =
            $this->CalcRangeInit($this->{"plot_min_$which"}, $implied, $this->{"min_$which"});
        list($plot_max, $adjust_max) =
            $this->CalcRangeInit($this->{"plot_max_$which"}, $implied, $this->{"max_$which"});

        // Get local copies of variables used for range adjustment: adjust_{mode,amount} zero_magnet
        extract($this->rangectl[$which]);
        $this->GetRangeEndAdjust($which, $adjust_amount);  // Apply default to $adjust_amount if needed

        // Get local copies of other variables for X or Y:
        if ($which == 'x') {
            $num_ticks = $this->num_x_ticks;
            $tick_inc = $this->x_tick_inc_u;
            // Tick anchor is only used in 'T' adjust mode, where no tick anchor means anchor at 0.
            $tick_anchor = isset($this->x_tick_anchor) ? $this->x_tick_anchor : 0;
        } else {
            $num_ticks = $this->num_y_ticks;
            $tick_inc = $this->y_tick_inc_u;
            $tick_anchor = isset($this->y_tick_anchor) ? $this->y_tick_anchor : 0;
        }

        // Validate the range, which must be positive. Adjusts plot_min and plot_max if necessary.
        if (!$this->CheckPlotRange($which, $plot_min, $plot_max, $adjust_min, $adjust_max))
            return FALSE;

        // Adjust the min and max values, if flagged above for adjustment.

        // Notes: (zero_magnet / (1 - zero_magnet)) is just a way to map a control with range 0:1
        // into the range 0:infinity (with zero_magnet==1 handled as a special case).
        //    (plot_max / (plot_max - plot_min)) compares the range after plot_min would be set
        // to zero with the original range. Similar for negative data: (plot_min / (plot_min - plot_max))
        // compares the range with plot_max=0 to the original range.

        $range = $plot_max - $plot_min;

        // When all data > 0, test to see if the zero magnet is strong enough to pull the min down to zero:
        if ($adjust_min && $plot_min > 0 && $zero_magnet > 0 && ($zero_magnet == 1.0 ||
                 $plot_max / $range < $zero_magnet / (1 - $zero_magnet))) {
            $plot_min = 0;
            $range = $plot_max;
        }

        // Similar to above, but for negative data: zero magnet pulls max up to zero:
        if ($adjust_max && $plot_max < 0 && $zero_magnet > 0 && ($zero_magnet == 1.0 ||
                 -$plot_min / $range < $zero_magnet / (1 - $zero_magnet))) {
            $plot_max = 0;
            $range = 0 - $plot_min;
        }

        // Calculate the tick increment, if it wasn't set using Set[XY]TickIncrement().
        $num_ticks_override = FALSE;
        if (empty($tick_inc)) {
            if (empty($num_ticks)) {
                // Calculate a reasonable tick increment, based on the current plot area limits
                $tick_inc = $this->CalcStep($which, $range);
            } else {
                // Number of ticks was provided: use exactly that.
                // Adjustment is below, after range is calculated using mode 'R':
                $adjust_mode = 'R';
                $num_ticks_override = TRUE;
            }
        }

        // Adjust the lower bound, if necessary, using one of 3 modes:
        if ($adjust_min && $plot_min != 0) {
            // Mode 'R' and basis for other modes: Extend the limit by a percentage of the
            // plot range, but only when the data is negative (to leave room below for labels).
            if ($plot_min < 0)
                $plot_min -= $adjust_amount * $range;

            if ($adjust_mode == 'T') {
                // Mode 'T': Adjust to previous tick mark, taking tick anchor into account.
                $pm = $tick_anchor + $tick_inc * floor(($plot_min - $tick_anchor) / $tick_inc);
                // Don't allow the tick anchor adjustment to result in the range end moving across 0:
                $plot_min = (($plot_min >= 0) === ($pm >= 0)) ? $pm : 0;
            } elseif ($adjust_mode == 'I') {
                // Mode 'I': Adjust to previous integer:
                $plot_min = floor($plot_min);
            }
        }

        // Adjust the upper bound, if necessary, using one of 3 modes:
        if ($adjust_max && $plot_max != 0) {
            // Mode 'R' and basis for other modes: Extend the limit by a percentage of the
            // plot range, but only when the max is positive (leaves room above for labels).
            if ($plot_max > 0)
                $plot_max += $adjust_amount * $range;

            if ($adjust_mode == 'T') {
                // Mode 'T': Adjust to next tick mark, taking tick anchor into account:
                $pm = $tick_anchor + $tick_inc * ceil(($plot_max - $tick_anchor) / $tick_inc);
                // Don't allow the tick anchor adjustment to result in the range end moving across 0:
                $plot_max = (($plot_max >= 0) === ($pm >= 0)) ? $pm : 0;
            } elseif ($adjust_mode == 'I') {
                // Mode 'I': Adjustment to next higher integer.
                $plot_max = ceil($plot_max);
            }
        }

        // Calculate the tick increment for the case where number of ticks was given:
        if ($num_ticks_override) {
            $tick_inc = ($plot_max - $plot_min) / $num_ticks;
        }

        // Check log scale range - plot_min and plot_max must be > 0.
        if ($which == 'y' && $this->yscale_type == 'log' || $which == 'x' && $this->xscale_type == 'log') {
            if ($plot_min <= 0) $plot_min = 1;
            if ($plot_max <= 0) {
                // Note: Error message names the public function, not this function.
                return $this->PrintError("SetPlotAreaWorld(): Invalid $which range for log scale");
            }
        }
        // Final error check to ensure the range is positive.
        if ($plot_min >= $plot_max) $plot_max = $plot_min + 1;

        // Return the calculated values. (Note these get stored back into class variables.)
        return array($tick_inc, $plot_min, $plot_max);
    }

    /**
     * Calculates the World Coordinate limits of the plot area, and the tick increments
     *
     * This is called by DrawGraph(), after FindDataLimits() determines the data
     * limits, to calculate the plot area scale and tick increments.  The plot range
     * and increment are related, which is why they are calculated together.
     *
     * The plot range variables (plot_min_x, plot_max_x, plot_min_y, plot_max_y) are
     * calculated if necessary, then stored back into the object ('sticky' for
     * multiple plots on an image).
     *
     * The tick increments (x_tick_inc, y_tick_inc) are calculated. These default to
     * the user-set values (x_tick_inc_u, y_tick_inc_u) but we keep the effective
     * values separate so that they can be recalculated for a second plot (which may
     * have a different data range).
     *
     * @return bool  True, unless an handled error occurred in a called function
     * @since 5.0.5
     */
    protected function CalcPlotAreaWorld()
    {
        list($this->x_tick_inc, $this->plot_min_x, $this->plot_max_x) = $this->CalcPlotRange('x');
        list($this->y_tick_inc, $this->plot_min_y, $this->plot_max_y) = $this->CalcPlotRange('y');
        if ($this->GetCallback('debug_scale')) {
            $this->DoCallback('debug_scale', __FUNCTION__, array(
                'plot_min_x' => $this->plot_min_x, 'plot_min_y' => $this->plot_min_y,
                'plot_max_x' => $this->plot_max_x, 'plot_max_y' => $this->plot_max_y,
                'x_tick_inc' => $this->x_tick_inc, 'y_tick_inc' => $this->y_tick_inc));
        }
        return isset($this->x_tick_inc, $this->y_tick_inc); // Pass thru FALSE return from CalcPlotRange()
    }

    /**
     * Overrides automatic data scaling to device coordinates
     *
     * This fixes one or more ends of the range of the plot to specific
     * value(s), given in World Coordinates.
     * Any limit not set or set to NULL will be calculated in
     * CalcPlotAreaWorld().  If both ends of either X or Y range are
     * supplied, the range is validated to ensure min < max.
     *
     * @param float $xmin  X data range minimum; omit or NULL to auto-calculate
     * @param float $ymin  Y data range minimum; omit or NULL to auto-calculate
     * @param float $xmax  X data range maximum; omit or NULL to auto-calculate
     * @param float $ymax  Y data range maximum; omit or NULL to auto-calculate
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetPlotAreaWorld($xmin=NULL, $ymin=NULL, $xmax=NULL, $ymax=NULL)
    {
        $this->plot_min_x = $xmin;
        $this->plot_max_x = $xmax;
        $this->plot_min_y = $ymin;
        $this->plot_max_y = $ymax;
        if (isset($xmin) && isset($xmax) && $xmin >= $xmax) $bad = 'X';
        elseif (isset($ymin) && isset($ymax) && $ymin >= $ymax) $bad = 'Y';
        else return TRUE;
        return $this->PrintError("SetPlotAreaWorld(): $bad range error - min >= max");
    }

    /**
     * Calculates sizes of bars for bars and stackedbars plots
     *
     * This calculates the following class variables, which control the size and
     * spacing of bars in vertical and horizontal 'bars' and 'stackedbars' plots:
     * record_bar_width (allocated width for each bar, including gaps),
     * actual_bar_width (actual drawn width of each bar), and
     * bar_adjust_gap (gap on each side of each bar, 0 if they touch).
     *
     * Note that when $verticals is False, the bars are horizontal, but the same
     * variable names are used.  Think of "bar_width" as being the width if you
     * are standing on the Y axis looking towards positive X.
     *
     * @param bool $stacked  If true, this is a stacked bar plot (1 bar per group)
     * @param bool $verticals  If false, this is a horizontal bar plot
     * @return bool  True always
     */
    protected function CalcBarWidths($stacked, $verticals)
    {
        // group_width is the width of a group, including padding
        if ($verticals) {
            $group_width = $this->plot_area_width / $this->num_data_rows;
        } else {
            $group_width = $this->plot_area_height / $this->num_data_rows;
        }

        // Number of bar spaces in the group, including actual bars and bar_extra_space extra:
        if ($stacked) {
            $num_spots = 1 + $this->bar_extra_space;
        } else {
            $num_spots = $this->data_columns + $this->bar_extra_space;
        }

        // record_bar_width is the width of each bar's allocated area.
        // If bar_width_adjust=1 this is the width of the bar, otherwise
        // the bar is centered inside record_bar_width.
        // The equation is:
        //   group_frac_width * group_width = record_bar_width * num_spots
        $this->record_bar_width = $this->group_frac_width * $group_width / $num_spots;

        // Note that the extra space due to group_frac_width and bar_extra_space will be
        // evenly divided on each side of the group: the drawn bars are centered in the group.

        // Within each bar's allocated space, if bar_width_adjust=1 the bar fills the
        // space, otherwise it is centered.
        // This is the actual drawn bar width:
        $this->actual_bar_width = $this->record_bar_width * $this->bar_width_adjust;
        // This is the gap on each side of the bar (0 if bar_width_adjust=1):
        $this->bar_adjust_gap = ($this->record_bar_width - $this->actual_bar_width) / 2;

        if ($this->GetCallback('debug_scale')) {
            $this->DoCallback('debug_scale', __FUNCTION__, array(
                'record_bar_width' => $this->record_bar_width,
                'actual_bar_width' => $this->actual_bar_width,
                'bar_adjust_gap' => $this->bar_adjust_gap));
        }
        return TRUE;
    }

    /**
     * Calculates the X and Y axis positions in world coordinates
     *
     * This validates or calculates the class variables x_axis_position and
     * y_axis_position. Note x_axis_position is the Y value where the X axis
     * goes; y_axis_position is the X value where the Y axis goes.
     * If they were set by the user, they are used as-is, unless they are
     * outside the data range. If they are not set, they are calculated here.
     *
     * For vertical plots, the X axis defaults to Y=0 if that is inside the plot
     * range, else whichever of the top or bottom that has the smallest absolute
     * value (that is, the value closest to 0).  The Y axis defaults to the left
     * edge. For horizontal plots, the axis roles and defaults are switched.
     *
     * @return bool  True always
     * @since 5.0.5
     */
    protected function CalcAxisPositions()
    {
        // Validate user-provided X axis position, or calculate a default if not provided:
        if (isset($this->x_axis_position)) {
            // Force user-provided X axis position to be within the plot range:
            $this->x_axis_position = min(max($this->plot_min_y, $this->x_axis_position), $this->plot_max_y);
        } elseif ($this->yscale_type == 'log') {
            // Always use 1 for X axis position on log scale plots.
            $this->x_axis_position = 1;
        } elseif ($this->datatype_swapped_xy || $this->plot_min_y > 0) {
            // Horizontal plot, or Vertical Plot with all Y > 0: Place X axis on the bottom.
            $this->x_axis_position = $this->plot_min_y;
        } elseif ($this->plot_max_y < 0) {
            // Vertical plot with all Y < 0, so place the X axis at the top.
            $this->x_axis_position = $this->plot_max_y;
        } else {
            // Vertical plot range includes Y=0, so place X axis at 0.
            $this->x_axis_position = 0;
        }

        // Validate user-provided Y axis position, or calculate a default if not provided:
        if (isset($this->y_axis_position)) {
            // Force user-provided Y axis position to be within the plot range:
            $this->y_axis_position = min(max($this->plot_min_x, $this->y_axis_position), $this->plot_max_x);
        } elseif ($this->xscale_type == 'log') {
            // Always use 1 for Y axis position on log scale plots.
            $this->y_axis_position = 1;
        } elseif (!$this->datatype_swapped_xy || $this->plot_min_x > 0) {
            // Vertical plot, or Horizontal Plot with all X > 0: Place Y axis on left side.
            $this->y_axis_position = $this->plot_min_x;
        } elseif ($this->plot_max_x < 0) {
            // Horizontal plot with all X < 0, so place the Y axis on the right side.
            $this->y_axis_position = $this->plot_max_x;
        } else {
            // Horizontal plot range includes X=0: place Y axis at 0.
            $this->y_axis_position = 0;
        }

        if ($this->GetCallback('debug_scale')) {
            $this->DoCallback('debug_scale', __FUNCTION__, array(
                'x_axis_position' => $this->x_axis_position,
                'y_axis_position' => $this->y_axis_position));
        }

        return TRUE;
    }

    /**
     * Calculates parameters for transforming world coordinates to pixel coordinates
     *
     * This calculates xscale, yscale, plot_origin_x, and plot_origin_y, which map
     * world coordinate space into the plot area. These are used by xtr() and ytr()
     *
     * @return bool  True always
     */
    protected function CalcTranslation()
    {
        if ($this->plot_max_x - $this->plot_min_x == 0) { // Check for div by 0
            $this->xscale = 0;
        } else {
            if ($this->xscale_type == 'log') {
                $this->xscale = $this->plot_area_width /
                                (log10($this->plot_max_x) - log10($this->plot_min_x));
            } else {
                $this->xscale = $this->plot_area_width / ($this->plot_max_x - $this->plot_min_x);
            }
        }

        if ($this->plot_max_y - $this->plot_min_y == 0) { // Check for div by 0
            $this->yscale = 0;
        } else {
            if ($this->yscale_type == 'log') {
                $this->yscale = $this->plot_area_height /
                                (log10($this->plot_max_y) - log10($this->plot_min_y));
            } else {
                $this->yscale = $this->plot_area_height / ($this->plot_max_y - $this->plot_min_y);
            }
        }
        // GD defines x = 0 at left and y = 0 at TOP so -/+ respectively
        if ($this->xscale_type == 'log') {
            $this->plot_origin_x = $this->plot_area[0] - ($this->xscale * log10($this->plot_min_x) );
        } else {
            $this->plot_origin_x = $this->plot_area[0] - ($this->xscale * $this->plot_min_x);
        }
        if ($this->yscale_type == 'log') {
            $this->plot_origin_y = $this->plot_area[3] + ($this->yscale * log10($this->plot_min_y));
        } else {
            $this->plot_origin_y = $this->plot_area[3] + ($this->yscale * $this->plot_min_y);
        }

        // Convert axis positions to device coordinates:
        $this->y_axis_x_pixels = $this->xtr($this->y_axis_position);
        $this->x_axis_y_pixels = $this->ytr($this->x_axis_position);

        if ($this->GetCallback('debug_scale')) {
            $this->DoCallback('debug_scale', __FUNCTION__, array(
                'xscale' => $this->xscale, 'yscale' => $this->yscale,
                'plot_origin_x' => $this->plot_origin_x, 'plot_origin_y' => $this->plot_origin_y,
                'y_axis_x_pixels' => $this->y_axis_x_pixels,
                'x_axis_y_pixels' => $this->x_axis_y_pixels));
        }

        return TRUE;
    }

    /**
     * Translates an X world coordinate value into a pixel coordinate value
     *
     * @param float $x_world  X world coordinate value to translate
     * @return int  Translated X device (pixel) coordinate
     * @deprecated  Public use discouraged; use GetDeviceXY() instead
     */
    function xtr($x_world)
    {
        if ($this->xscale_type == 'log') {
            $x_pixels = $this->plot_origin_x + log10($x_world) * $this->xscale ;
        } else {
            $x_pixels = $this->plot_origin_x + $x_world * $this->xscale ;
        }
        return round($x_pixels);
    }

    /**
     * Translates a Y world coordinate value into a pixel coordinate value
     *
     * @param float $y_world  Y world coordinate value to translate
     * @return int  Translated Y device (pixel) coordinate
     * @deprecated  Public use discouraged; use GetDeviceXY() instead
     */
    function ytr($y_world)
    {
        if ($this->yscale_type == 'log') {
            //minus because GD defines y = 0 at top. doh!
            $y_pixels =  $this->plot_origin_y - log10($y_world) * $this->yscale ;
        } else {
            $y_pixels =  $this->plot_origin_y - $y_world * $this->yscale ;
        }
        return round($y_pixels);
    }

    /**
     * Translates world coordinates into device coordinates
     *
     * This is a public interface to xtr() and ytr(), which are left as public
     * for historical reasons but deprecated for public use. It maps (x,y) in
     * world coordinates to (x,y) into device (pixel) coordinates. Typical usage
     * is: list($x_pixel, $y_pixel) = $plot->GetDeviceXY($x_world, $y_world)
     *
     * Note: This only works after scaling has been set up, which happens in
     * DrawGraph(). So it is only useful from a drawing callback, or if
     * SetPrintImage(False) was used and after DrawGraph().
     *
     * @param float $x_world  X world coordinate value to translate
     * @param float $y_world  Y world coordinate value to translate
     * @return int[]  Array of ($x, $y) device coordinates; False on error if error handler returns True
     * @since 5.1.0
     */
    function GetDeviceXY($x_world, $y_world)
    {
        if (!isset($this->xscale)) {
            return $this->PrintError("GetDeviceXY() was called before translation factors were calculated");
        }
        return array($this->xtr($x_world), $this->ytr($y_world));
    }

    /**
     * Gets the tick mark parameters
     *
     * This is used by DrawXTicks(), DrawYTicks(), and CalcMaxTickLabelSize().
     * It returns the parameters needed to draw tick marks: start value, end value,
     * and step.  Note CalcTicks() used to but no longer actually does the
     * calculations.  That is done in CalcPlotAreaWorld().
     *
     * @param string $which  Which axis to calculate tick parameters for. Must be 'x' or 'y'
     * @return float[]  Array of (tick_start, tick_end, tick_step)
     * @since 5.0.5
     */
    protected function CalcTicks($which)
    {
        if ($which == 'x') {
            $tick_step = $this->x_tick_inc;
            $anchor = &$this->x_tick_anchor;  // Reference used because it might not be set.
            $plot_max = $this->plot_max_x;
            $plot_min = $this->plot_min_x;
            $skip_lo = $this->skip_left_tick;
            $skip_hi = $this->skip_right_tick;
        } else { // Assumed 'y'
            $tick_step = $this->y_tick_inc;
            $anchor = &$this->y_tick_anchor;
            $plot_max = $this->plot_max_y;
            $plot_min = $this->plot_min_y;
            $skip_lo = $this->skip_bottom_tick;
            $skip_hi = $this->skip_top_tick;
        }

        // To avoid losing a final tick mark due to round-off errors, push tick_end out slightly.
        $tick_start = (double)$plot_min;
        $tick_end = (double)$plot_max + ($plot_max - $plot_min) / 10000.0;

        // If a tick anchor was given, adjust the start of the range so the anchor falls
        // at an exact tick mark (or would, if it was within range).
        if (isset($anchor))
            $tick_start = $anchor - $tick_step * floor(($anchor - $tick_start) / $tick_step);

        // Lastly, adjust for option to skip left/bottom or right/top tick marks:
        if ($skip_lo)
            $tick_start += $tick_step;
        if ($skip_hi)
            $tick_end -= $tick_step;

        if ($this->GetCallback('debug_scale'))
            $this->DoCallback('debug_scale', __FUNCTION__,
                              compact('which', 'tick_start', 'tick_end', 'tick_step'));
        return array($tick_start, $tick_end, $tick_step);
    }

    /**
     * Calculates the size of the biggest tick label
     *
     * This is used by CalcMargins() to figure out how much margin space is needed
     * for the tick labels.
     * For 'x' ticks, it returns the height (delta Y) of the tallest label.
     * For 'y' ticks, it returns the width (delta X) of the widest label.
     *
     * @param string $which  Which axis to calculate for. Must be 'x' or 'y'
     * @return float  The needed tick label width (for Y) or height (for X)
     * @since 5.0.5
     */
    protected function CalcMaxTickLabelSize($which)
    {
        list($tick_start, $tick_end, $tick_step) = $this->CalcTicks($which);

        $angle = ($which == 'x') ? $this->x_label_angle : $this->y_label_angle;
        $font_id = $which . '_label';  // Use x_label or y_label font.
        $max_width = 0;
        $max_height = 0;

        // Loop over ticks, same as DrawXTicks and DrawYTicks:
        // Avoid cumulative round-off errors from $val += $delta
        $n = 0;
        $tick_val = $tick_start;
        while ($tick_val <= $tick_end) {
            $tick_label = $this->FormatLabel($which, $tick_val);
            list($width, $height) = $this->SizeText($font_id, $angle, $tick_label);
            if ($width > $max_width) $max_width = $width;
            if ($height > $max_height) $max_height = $height;
            $tick_val = $tick_start + ++$n * $tick_step;
        }
        if ($this->GetCallback('debug_scale')) {
            $this->DoCallback('debug_scale', __FUNCTION__, array(
                'which' => $which, 'height' => $max_height, 'width' => $max_width));
        }

        if ($which == 'x')
            return $max_height;
        return $max_width;
    }

    /**
     * Calculates the size of the biggest axis data label
     *
     * This is used by CalcMargins() to figure out how much margin space is needed
     * for the axis data labels.
     * For X axis labels, it returns the height (delta Y) of the tallest label.
     * For Y axis labels, it returns the width (delta X) of the widest label.
     *
     * There can be at most one set of axis data labels. For vertical plots, these
     * are X axis data labels, and go along the top or bottom or both. For horizontal
     * plots, these are Y axis data labels, and go along the left or right or both.
     * CalcMaxDataLabelSize(axis) returns 0 if data labels do not apply to that axis.
     * To do this, it needs to check the plottype flag indicating swapped X/Y.
     *
     * @param string $which  Which axis to calculate for. Must be 'x' or 'y'
     * @return float  The needed axis data label width (for Y) or height (for X)
     * @since 5.0.5
     */
    protected function CalcMaxDataLabelSize($which = 'x')
    {
        // Shortcut: Y data labels for vertical plots, and X data labels for horizontal plots,
        // are inside the plot, rather than along the axis lines, and so take up no margin space.
        if ($which == 'y' XOR $this->datatype_swapped_xy)
            return 0;

        $angle = ($which == 'x') ? $this->x_data_label_angle : $this->y_data_label_angle;
        $font_id = $which . '_label';  // Use x_label or y_label font.
        $format_code = $which . 'd';   // Use format code 'xd' or 'yd'
        $max_width = 0;
        $max_height = 0;

        // Loop over all data labels and find the biggest:
        for ($i = 0; $i < $this->num_data_rows; $i++) {
            $label = $this->FormatLabel($format_code, $this->data[$i][0], $i);
            list($width, $height) = $this->SizeText($font_id, $angle, $label);
            if ($width > $max_width) $max_width = $width;
            if ($height > $max_height) $max_height = $height;
        }
        if ($this->GetCallback('debug_scale')) {
            $this->DoCallback('debug_scale', __FUNCTION__, array(
                'height' => $max_height, 'width' => $max_width));
        }

        if ($this->datatype_swapped_xy)
            return $max_width;
        return $max_height;
    }

    /**
     * Determines if there are any non-empty data labels in the data array
     *
     * This is used by CheckLabels() to determine if data labels are available.
     *
     * @return bool  True if all data labels are empty, else False.
     * @since 5.1.2
     */
    protected function CheckLabelsAllEmpty()
    {
        for ($i = 0; $i < $this->num_data_rows; $i++)
            if ($this->data[$i][0] !== '') return FALSE;
        return TRUE;
    }

    /**
     * Checks and sets label parameters
     *
     * This handles deferred processing for label positioning and other label-related
     * parameters. It sets defaults for label angles, and applies defaults to X and Y
     * tick and data label positions.
     *
     * @return bool  True always
     * @since 5.1.0
     */
    protected function CheckLabels()
    {
        // Default for X data label angle is a special case (different from Y).
        if ($this->x_data_label_angle_u === '')
            $this->x_data_label_angle = $this->x_label_angle; // Not set with SetXDataLabelAngle()
        else
            $this->x_data_label_angle = $this->x_data_label_angle_u; // Set with SetXDataLabelAngle()

        // X Label position fixups, for x_data_label_pos and x_tick_label_pos:
        if ($this->datatype_swapped_xy) {
            // Just apply defaults - there is no position conflict for X labels.
            if (!isset($this->x_tick_label_pos))
                $this->x_tick_label_pos = 'plotdown';
            if (!isset($this->x_data_label_pos))
                $this->x_data_label_pos = 'none';
        } else {
            // Apply defaults but do not allow conflict between tick and data labels.
            if (isset($this->x_data_label_pos)) {
                if (!isset($this->x_tick_label_pos)) {
                    // Case: data_label_pos is set, tick_label_pos needs a default:
                    if ($this->x_data_label_pos == 'none')
                        $this->x_tick_label_pos = 'plotdown';
                    else
                        $this->x_tick_label_pos = 'none';
                }
            } elseif (isset($this->x_tick_label_pos)) {
                // Case: tick_label_pos is set, data_label_pos needs a default:
                if ($this->x_tick_label_pos == 'none')
                    $this->x_data_label_pos = 'plotdown';
                else
                    $this->x_data_label_pos = 'none';
            } else {
                // Case: Neither tick_label_pos nor data_label_pos is set.
                // We do not want them to be both on (as PHPlot used to do in this case).
                // Turn on data labels if any were supplied, else tick labels.
                if ($this->CheckLabelsAllEmpty()) {
                    $this->x_data_label_pos = 'none';
                    $this->x_tick_label_pos = 'plotdown';
                } else {
                    $this->x_data_label_pos = 'plotdown';
                    $this->x_tick_label_pos = 'none';
                }
            }
        }

        // Y Label position fixups, for y_data_label_pos and y_tick_label_pos:
        if (!$this->datatype_swapped_xy) {
            // Just apply defaults - there is no position conflict.
            if (!isset($this->y_tick_label_pos))
                $this->y_tick_label_pos = 'plotleft';
            if (!isset($this->y_data_label_pos))
                $this->y_data_label_pos = 'none';
        } else {
            // Apply defaults but do not allow conflict between tick and data labels.
            if (isset($this->y_data_label_pos)) {
                if (!isset($this->y_tick_label_pos)) {
                    // Case: data_label_pos is set, tick_label_pos needs a default:
                    if ($this->y_data_label_pos == 'none')
                        $this->y_tick_label_pos = 'plotleft';
                    else
                        $this->y_tick_label_pos = 'none';
                }
            } elseif (isset($this->y_tick_label_pos)) {
                // Case: tick_label_pos is set, data_label_pos needs a default:
                if ($this->y_tick_label_pos == 'none')
                    $this->y_data_label_pos = 'plotleft';
                else
                    $this->y_data_label_pos = 'none';
            } else {
                // Case: Neither tick_label_pos nor data_label_pos is set.
                // Turn on data labels if any were supplied, else tick labels.
                if ($this->CheckLabelsAllEmpty()) {
                    $this->y_data_label_pos = 'none';
                    $this->y_tick_label_pos = 'plotleft';
                } else {
                    $this->y_data_label_pos = 'plotleft';
                    $this->y_tick_label_pos = 'none';
                }
            }
        }
        return TRUE;
    }

    /**
     * Formats a value for use as a tick, data, or pie chart label
     *
     * @param string $which_pos  Which format controls to use: x | y | xd | yd | p  (tick, data, pie)
     * @param mixed $which_lab  The value of the label to be formatted (usually a float)
     * @param mixed $varargs  Zero or more additional arguments to pass to a custom format function
     * @return string  The formatted label value (original value if no formatting is enabled)
     */
    protected function FormatLabel($which_pos, $which_lab, $varargs=NULL) // Variable additional arguments
    {
        // Assign a reference shortcut to the label format controls, default xd,yd to x,y.
        if ($which_pos == 'xd' && empty($this->label_format['xd']))
            $which_pos = 'x';
        elseif ($which_pos == 'yd' && empty($this->label_format['yd']))
            $which_pos = 'y';
        $format = &$this->label_format[$which_pos];

        // Don't format empty strings (especially as time or numbers), or if no type was set.
        if ($which_lab !== '' && !empty($format['type'])) {
            switch ($format['type']) {
            case 'title':  // Note: This is obsolete
                $which_lab = @ $this->data[$which_lab][0];
                break;
            case 'data':
                $which_lab = $format['prefix']
                           . $this->number_format($which_lab, $format['precision'])
                           . $this->data_units_text  // Obsolete
                           . $format['suffix'];
                break;
            case 'time':
                $which_lab = strftime($format['time_format'], $which_lab);
                break;
            case 'printf':
                if (!is_array($format['printf_format'])) {
                    $use_format = $format['printf_format'];
                } else {
                    // Select from 1, 2, or 3 formats based on the sign of the value (like spreadsheets).
                    // With 2 formats, use [0] for >= 0, [1] for < 0.
                    // With 3 formats, use [0] for > 0, [1] for < 0, [2] for = 0.
                    $n_formats = count($format['printf_format']);
                    if ($n_formats == 3 && $which_lab == 0) {
                        $use_format = $format['printf_format'][2];
                    } elseif ($n_formats > 1 && $which_lab < 0) {
                        $use_format = $format['printf_format'][1];
                        $which_lab = -$which_lab; // Format the absolute value
                    } else $use_format = $format['printf_format'][0];
                }
                $which_lab = sprintf($use_format, $which_lab);
                break;
            case 'custom':
                // Build argument vector: (text, custom_callback_arg, other_args...)
                $argv = func_get_args();
                $argv[0] = $which_lab;
                $argv[1] = $format['custom_arg'];
                $which_lab = call_user_func_array($format['custom_callback'], $argv);
                break;
            }
        }
        return $which_lab;
    }

    /**
     * Sets range tuning parameters for X or Y
     *
     * This implements TuneXAutoRange() and TuneYAutoRange(). Note that
     * parameter values are checked, but invalid values are silently ignored.
     *
     * @param string $which  Which axis to adjust parameters for: 'x' or 'y'
     * @param float $zero_magnet  Zero magnet value, NULL to ignore
     * @param string $adjust_mode  Range extension mode, NULL to ignore
     * @param float $adjust_amount  Range extension amount, NULL to ignore
     * @return bool  True always
     * @since 6.0.0
     */
    protected function TuneAutoRange($which, $zero_magnet, $adjust_mode, $adjust_amount)
    {
        if (isset($zero_magnet) && $zero_magnet >= 0 && $zero_magnet <= 1.0)
            $this->rangectl[$which]['zero_magnet'] = $zero_magnet;
        if (isset($adjust_mode) && strpos('TRI', $adjust_mode[0]) !== FALSE)
            $this->rangectl[$which]['adjust_mode'] = $adjust_mode;
        if (isset($adjust_amount) && $adjust_amount >= 0)
            $this->rangectl[$which]['adjust_amount'] = $adjust_amount;
        return TRUE;
    }

    /**
     * Adjusts tuning parameters for X axis range calculation
     *
     * See TuneAutoRange() above, which implements this function.
     *
     * @param float $zero_magnet  Optional X axis zero magnet value, controlling range extension to include 0
     * @param string $adjust_mode  Optional X axis range extension mode: T | R | I (Tick, Range, Integer)
     * @param float $adjust_amount  Optional X axis range extension amount
     * @return bool  True always
     * @since 6.0.0
     */
    function TuneXAutoRange($zero_magnet = NULL, $adjust_mode = NULL, $adjust_amount = NULL)
    {
        return $this->TuneAutoRange('x', $zero_magnet, $adjust_mode, $adjust_amount);
    }

    /**
     * Adjusts tuning parameters for Y axis range calculation
     *
     * See TuneAutoRange() above, which implements this function.
     *
     * @param float $zero_magnet  Optional Y axis zero magnet value, controlling range extension to include 0
     * @param string $adjust_mode  Optional Y axis range extension mode: T | R | I (Tick, Range, Integer)
     * @param float $adjust_amount  Optional Y axis range extension amount
     * @return bool  True always
     * @since 6.0.0
     */
    function TuneYAutoRange($zero_magnet = NULL, $adjust_mode = NULL, $adjust_amount = NULL)
    {
        return $this->TuneAutoRange('y', $zero_magnet, $adjust_mode, $adjust_amount);
    }

    /**
     * Sets tick tuning parameters for X or Y
     *
     * This implements TuneXAutoTicks() and TuneYAutoTicks().
     *
     * @param string $which  Which axis to adjust parameters for: 'x' or 'y'
     * @param int $min_ticks  Minimum number of tick intervals
     * @param string $tick_mode  Tick increment calculation mode
     * @param bool $tick_inc_integer  True to always use integer tick increments
     * @return bool  True (False on error if an error handler returns True)
     * @since 6.0.0
     */
    protected function TuneAutoTicks($which, $min_ticks, $tick_mode, $tick_inc_integer)
    {
        if (isset($min_ticks) && $min_ticks > 0)
            $this->tickctl[$which]['min_ticks'] = (integer)$min_ticks;
        if (isset($tick_mode)) {
            $tick_mode = $this->CheckOption($tick_mode, 'decimal, binary, date',
                                            'Tune' . strtoupper($which) . 'AutoTicks');
            if (!$tick_mode)
                return FALSE;
            $this->tickctl[$which]['tick_mode'] = $tick_mode;
        }
        if (isset($tick_inc_integer))
            $this->tickctl[$which]['tick_inc_integer'] = (bool)$tick_inc_integer;
        return TRUE;
    }

    /**
     * Adjusts tuning parameters for X axis tick increment calculation
     *
     * See TuneAutoTicks() above, which implements this function.
     *
     * @param int $min_ticks  Minimum number of tick intervals along the axis
     * @param string $tick_mode  Tick increment calculation mode: decimal | binary | date
     * @param bool $tick_inc_integer  True to always use integer tick increments, false to allow fractions
     * @return bool  True (False on error if an error handler returns True)
     * @since 6.0.0
     */
    function TuneXAutoTicks($min_ticks = NULL, $tick_mode = NULL, $tick_inc_integer = NULL)
    {
        return $this->TuneAutoTicks('x', $min_ticks, $tick_mode, $tick_inc_integer);
    }

    /**
     * Adjusts tuning parameters for Y axis tick increment calculation
     *
     * See TuneAutoTicks() above, which implements this function.
     *
     * @param int $min_ticks  Minimum number of tick intervals along the axis
     * @param string $tick_mode  Tick increment calculation mode: decimal | binary | date
     * @param bool $tick_inc_integer  True to always use integer tick increments, false to allow fractions
     * @return bool  True (False on error if an error handler returns True)
     * @since 6.0.0
     */
    function TuneYAutoTicks($min_ticks = NULL, $tick_mode = NULL, $tick_inc_integer = NULL)
    {
        return $this->TuneAutoTicks('y', $min_ticks, $tick_mode, $tick_inc_integer);
    }


/////////////////////////////////////////////
///////////////                         TICKS
/////////////////////////////////////////////

    /**
     * Sets the length of the interval between X ticks
     *
     * @param float $which_ti  X tick increment in world coordinates; omit or '' for default auto-calculate
     * @return bool  True always
     */
    function SetXTickIncrement($which_ti='')
    {
        $this->x_tick_inc_u = $which_ti;
        return TRUE;
    }

    /**
     * Sets the length of the interval between Y ticks
     *
     * @param float $which_ti  Y tick increment in world coordinates; omit or '' for default auto-calculate
     * @return bool  True always
     */
    function SetYTickIncrement($which_ti='')
    {
        $this->y_tick_inc_u = $which_ti;
        return TRUE;
    }

    /**
     * Sets the number of X tick intervals
     *
     * @param int $which_nt  Number of X tick intervals; omit or '' for default auto-calculate
     * @return bool  True always
     */
    function SetNumXTicks($which_nt='')
    {
        $this->num_x_ticks = $which_nt;
        return TRUE;
    }

    /**
     * Sets the number of Y tick intervals
     *
     * @param int $which_nt  Number of Y tick intervals; omit or '' for default auto-calculate
     * @return bool  True always
     */
    function SetNumYTicks($which_nt='')
    {
        $this->num_y_ticks = $which_nt;
        return TRUE;
    }

    /**
     * Positions the X tick marks (above the plot, below, both above and below; at the X axis, or suppressed)
     *
     * @param string $which_tp  Tick mark position: plotdown | plotup | both | xaxis | none
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetXTickPos($which_tp)
    {
        $this->x_tick_pos = $this->CheckOption($which_tp, 'plotdown, plotup, both, xaxis, none',
                                               __FUNCTION__);
        return (boolean)$this->x_tick_pos;
    }

    /**
     * Positions the Y tick marks (left, right, or both sides; at the Y axis, or suppressed)
     *
     * @param string $which_tp  Tick mark position: plotleft | plotright | both | yaxis | none
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetYTickPos($which_tp)
    {
        $this->y_tick_pos = $this->CheckOption($which_tp, 'plotleft, plotright, both, yaxis, none',
                                              __FUNCTION__);
        return (boolean)$this->y_tick_pos;
    }

    /**
     * Suppress the top Y axis tick mark and label
     *
     * @param bool $skip  True to skip the tick mark and label; false to draw them
     * @return bool  True always
     */
    function SetSkipTopTick($skip)
    {
        $this->skip_top_tick = (bool)$skip;
        return TRUE;
    }

    /**
     * Suppress the bottom Y axis tick mark and label
     *
     * @param bool $skip  True to skip the tick mark and label; false to draw them
     * @return bool  True always
     */
    function SetSkipBottomTick($skip)
    {
        $this->skip_bottom_tick = (bool)$skip;
        return TRUE;
    }

    /**
     * Suppress the left-most (first) X axis tick mark and label
     *
     * @param bool $skip  True to skip the tick mark and label; false to draw them
     * @return bool  True always
     */
    function SetSkipLeftTick($skip)
    {
        $this->skip_left_tick = (bool)$skip;
        return TRUE;
    }

    /**
     * Suppress the right-most (last) X axis tick mark and label
     *
     * @param bool $skip  True to skip the tick mark and label; false to draw them
     * @return bool  True always
     */
    function SetSkipRightTick($skip)
    {
        $this->skip_right_tick = (bool)$skip;
        return TRUE;
    }

    /**
     * Sets the outer length of X tick marks (the part that sticks out from the plot area)
     *
     * @param int $which_xln  Outer length of the tick marks, in pixels
     * @return bool  True always
     */
    function SetXTickLength($which_xln)
    {
        $this->x_tick_length = $which_xln;
        return TRUE;
    }

    /**
     * Sets the outer length of Y tick marks (the part that sticks out from the plot area)
     *
     * @param int $which_yln  Outer length of the tick marks, in pixels
     * @return bool  True always
     */
    function SetYTickLength($which_yln)
    {
        $this->y_tick_length = $which_yln;
        return TRUE;
    }

    /**
     * Sets the crossing length of X tick marks (the part that sticks into the plot area)
     *
     * @param int $which_xc  Crossing length of the tick marks, in pixels
     * @return bool  True always
     */
    function SetXTickCrossing($which_xc)
    {
        $this->x_tick_cross = $which_xc;
        return TRUE;
    }

    /**
     * Sets the crossing length of Y tick marks (the part that sticks into the plot area)
     *
     * @param int $which_yc  Crossing length of the tick marks, in pixels
     * @return bool  True always
     */
    function SetYTickCrossing($which_yc)
    {
        $this->y_tick_cross = $which_yc;
        return TRUE;
    }

    /**
     * Sets an anchor point for X tick marks
     *
     * A tick anchor forces a tick mark at that exact value (if the data range were extended to include it).
     *
     * @param float $xta  Tick anchor position in World Coordinates; omit or NULL for no anchor
     * @return bool  True always
     * @since 5.4.0
     */
    function SetXTickAnchor($xta = NULL)
    {
        $this->x_tick_anchor = $xta;
        return TRUE;
    }

    /**
     * Sets an anchor point for Y tick marks
     *
     * A tick anchor forces a tick mark at that exact value (if the data range were extended to include it).
     *
     * @param float $yta  Tick anchor position in World Coordinates; omit or NULL for no anchor
     * @return bool  True always
     * @since 5.4.0
     */
    function SetYTickAnchor($yta = NULL)
    {
        $this->y_tick_anchor = $yta;
        return TRUE;
    }

/////////////////////////////////////////////
////////////////////          GENERIC DRAWING
/////////////////////////////////////////////

    /**
     * Fills the image background, with a tiled image file or solid color
     *
     * @param bool $overwrite  True to do it even if already done, False or omit to do once only
     * @return bool  True always
     */
    protected function DrawBackground($overwrite=FALSE)
    {
        // Check if background should be drawn:
        if (empty($this->done['background']) || $overwrite) {
            if (isset($this->bgimg)) {    // If bgimg is defined, use it
                $this->tile_img($this->bgimg, 0, 0, $this->image_width, $this->image_height, $this->bgmode);
            } else {                        // Else use solid color
                ImageFilledRectangle($this->img, 0, 0, $this->image_width, $this->image_height,
                                     $this->ndx_bg_color);
            }
            $this->done['background'] = TRUE;
        }
        return TRUE;
    }

    /**
     * Fills the plot area background, with a tiled image file or solid color
     *
     * @return bool  True always
     */
    protected function DrawPlotAreaBackground()
    {
        if (isset($this->plotbgimg)) {
            $this->tile_img($this->plotbgimg, $this->plot_area[0], $this->plot_area[1],
                            $this->plot_area_width, $this->plot_area_height, $this->plotbgmode);
        } elseif ($this->draw_plot_area_background) {
            ImageFilledRectangle($this->img, $this->plot_area[0], $this->plot_area[1],
                                 $this->plot_area[2], $this->plot_area[3], $this->ndx_plot_bg_color);
        }
        return TRUE;
    }

    /**
     * Tiles an image from a file onto the plot image (for backgrounds)
     *
     * @param string $file Filename of the picture to be used as tile
     * @param int $xorig  X device coordinate of where the tile is to begin
     * @param int $yorig  Y device coordinate of where the tile is to begin
     * @param int $width  Width of the area to be tiled
     * @param int $height  Height of the area to be tiled
     * @param string $mode  Tiling mode: centeredtile | tile | scale
     * @return bool  True (False on error if an error handler returns True)
     *
     */
    protected function tile_img($file, $xorig, $yorig, $width, $height, $mode)
    {
        $im = $this->GetImage($file, $tile_width, $tile_height);
        if (!$im)
            return FALSE;  // GetImage already produced an error message.

        if ($mode == 'scale') {
            imagecopyresampled($this->img, $im, $xorig, $yorig, 0, 0, $width, $height,
                               $tile_width, $tile_height);
            return TRUE;
        }

        if ($mode == 'centeredtile') {
            $x0 = - floor($tile_width/2);   // Make the tile look better
            $y0 = - floor($tile_height/2);
        } else {      // Accept anything else as $mode == 'tile'
            $x0 = 0;
            $y0 = 0;
        }

        // Draw the tile onto a temporary image first.
        $tmp = imagecreate($width, $height);
        if (! $tmp)
            return $this->PrintError('tile_img(): Could not create image resource.');

        for ($x = $x0; $x < $width; $x += $tile_width)
            for ($y = $y0; $y < $height; $y += $tile_height)
                imagecopy($tmp, $im, $x, $y, 0, 0, $tile_width, $tile_height);

        // Copy the temporary image onto the final one.
        imagecopy($this->img, $tmp, $xorig, $yorig, 0,0, $width, $height);

        // Free resources
        imagedestroy($tmp);
        imagedestroy($im);

        return TRUE;
    }

    /**
     * Returns the width of the image border, for CalcMargins() and DrawImageBorder().
     *
     * @return int  Border width in pixels, 0 for no borders
     * @since 5.1.2
     */
    protected function GetImageBorderWidth()
    {
        if ($this->image_border_type == 'none')
            return 0; // No border
        if (!empty($this->image_border_width))
            return $this->image_border_width; // Specified border width
        if ($this->image_border_type == 'raised')
            return 2; // Default for raised border is 2 pixels.
        return 1; // Default for other border types is 1 pixel.
    }

    /**
     * Draws a border around the final image
     *
     * This draws a border around the image, if enabled by SetImageBorderType().
     * Note: type 'plain' draws a flat border using the dark shade of the border color.
     * This probably should have been written to use the actual border color, but
     * it is too late to fix it without changing plot appearances. Therefore a
     * new type 'solid' was added to use the SetImageBorderColor color.
     *
     * @param bool $overwrite  True to do it even if already done, False or omit to do once only
     * @return bool  True (False on error if an error handler returns True)
     *
     */
    protected function DrawImageBorder($overwrite=FALSE)
    {
        // Check if border should be drawn:
        if ($this->image_border_type == 'none' || !(empty($this->done['border']) || $overwrite))
            return TRUE;
        $width = $this->GetImageBorderWidth();
        $color1 = $this->ndx_i_border;
        $color2 = $this->ndx_i_border_dark;
        $ex = $this->image_width - 1;
        $ey = $this->image_height - 1;
        switch ($this->image_border_type) {
        case 'raised':
            // Top and left lines use border color, right and bottom use the darker shade.
            // Drawing order matters in the upper right and lower left corners.
            for ($i = 0; $i < $width; $i++, $ex--, $ey--) {
                imageline($this->img, $i,  $i,  $ex, $i,  $color1); // Top
                imageline($this->img, $ex, $i,  $ex, $ey, $color2); // Right
                imageline($this->img, $i,  $i,  $i,  $ey, $color1); // Left
                imageline($this->img, $i,  $ey, $ex, $ey, $color2); // Bottom
            }
            break;
        case 'plain': // See note above re colors
            $color1 = $color2;
            // Fall through
        case 'solid':
            for ($i = 0; $i < $width; $i++, $ex--, $ey--) {
                imagerectangle($this->img, $i, $i, $ex, $ey, $color1);
            }
            break;
        default:
            return $this->PrintError(
                          "DrawImageBorder(): unknown image_border_type: '$this->image_border_type'");
        }
        $this->done['border'] = TRUE; // Border should only be drawn once per image.
        return TRUE;
    }

    /**
     * Draws the main plot title
     *
     * @return bool  True always
     */
    protected function DrawTitle()
    {
        if (!empty($this->done['title']) || $this->title_txt === '')
            return TRUE;

        // Center of the image:
        $xpos = $this->image_width / 2;

        // Place it at almost at the top
        $ypos = $this->title_offset;

        $this->DrawText('title', 0, $xpos, $ypos, $this->ndx_title_color, $this->title_txt, 'center', 'top');

        $this->done['title'] = TRUE;
        return TRUE;
    }

    /**
     * Draws the X axis title, on the top or bottom (or both) of the plot area
     *
     * @return bool  True always
     */
    protected function DrawXTitle()
    {
        if ($this->x_title_pos == 'none')
            return TRUE;

        // Center of the plot
        $xpos = ($this->plot_area[2] + $this->plot_area[0]) / 2;

        // Upper title
        if ($this->x_title_pos == 'plotup' || $this->x_title_pos == 'both') {
            $ypos = $this->plot_area[1] - $this->x_title_top_offset;
            $this->DrawText('x_title', 0, $xpos, $ypos, $this->ndx_x_title_color,
                            $this->x_title_txt, 'center', 'bottom');
        }
        // Lower title
        if ($this->x_title_pos == 'plotdown' || $this->x_title_pos == 'both') {
            $ypos = $this->plot_area[3] + $this->x_title_bot_offset;
            $this->DrawText('x_title', 0, $xpos, $ypos, $this->ndx_x_title_color,
                            $this->x_title_txt, 'center', 'top');
        }
        return TRUE;
    }

    /**
     * Draws the Y axis title, on the left or right side (or both) of the plot area
     *
     * @return bool  True always
     */
    protected function DrawYTitle()
    {
        if ($this->y_title_pos == 'none')
            return TRUE;

        // Center the title vertically to the plot area
        $ypos = ($this->plot_area[3] + $this->plot_area[1]) / 2;

        if ($this->y_title_pos == 'plotleft' || $this->y_title_pos == 'both') {
            $xpos = $this->plot_area[0] - $this->y_title_left_offset;
            $this->DrawText('y_title', 90, $xpos, $ypos, $this->ndx_y_title_color,
                            $this->y_title_txt, 'right', 'center');
        }
        if ($this->y_title_pos == 'plotright' || $this->y_title_pos == 'both') {
            $xpos = $this->plot_area[2] + $this->y_title_right_offset;
            $this->DrawText('y_title', 90, $xpos, $ypos, $this->ndx_y_title_color,
                            $this->y_title_txt, 'left', 'center');
        }

        return TRUE;
    }

    /**
     * Draws the X axis, including ticks and labels, and vertical grid lines
     *
     * @return bool  True always
     */
    protected function DrawXAxis()
    {
        // Draw ticks, labels and grid
        $this->DrawXTicks();

        //Draw X Axis at Y = x_axis_y_pixels, unless suppressed (See SetXAxisPosition)
        if (!$this->suppress_x_axis) {
            ImageLine($this->img, $this->plot_area[0]+1, $this->x_axis_y_pixels,
                      $this->plot_area[2]-1, $this->x_axis_y_pixels, $this->ndx_grid_color);
        }
        return TRUE;
    }

    /**
     * Draws the Y axis, including ticks and labels, and horizontal grid lines
     *
     * This draws the Y axis and grid lines. It must be called before DrawXAxis() to avoid
     * having a horizontal grid line overwrite the X axis.
     *
     * @return bool  True always
     */
    protected function DrawYAxis()
    {
        // Draw ticks, labels and grid
        $this->DrawYTicks();

        // Draw Y axis at X = y_axis_x_pixels, unless suppressed (See SetYAxisPosition)
        if (!$this->suppress_y_axis) {
            ImageLine($this->img, $this->y_axis_x_pixels, $this->plot_area[1],
                      $this->y_axis_x_pixels, $this->plot_area[3], $this->ndx_grid_color);
        }
        return TRUE;
    }

    /**
     * Draws one X tick mark and its tick label
     *
     * @param float $x  X value for the label
     * @param int $x_pixels  X device coordinate for this tick mark
     * @return bool  True always
     * @since 5.0.5
     */
    protected function DrawXTick($x, $x_pixels)
    {
        // Ticks on X axis
        if ($this->x_tick_pos == 'xaxis') {
            ImageLine($this->img, $x_pixels, $this->x_axis_y_pixels - $this->x_tick_cross,
                      $x_pixels, $this->x_axis_y_pixels + $this->x_tick_length, $this->ndx_tick_color);
        }

        // Ticks on top of the Plot Area
        if ($this->x_tick_pos == 'plotup' || $this->x_tick_pos == 'both') {
            ImageLine($this->img, $x_pixels, $this->plot_area[1] - $this->x_tick_length,
                      $x_pixels, $this->plot_area[1] + $this->x_tick_cross, $this->ndx_tick_color);
        }

        // Ticks on bottom of Plot Area
        if ($this->x_tick_pos == 'plotdown' || $this->x_tick_pos == 'both') {
            ImageLine($this->img, $x_pixels, $this->plot_area[3] + $this->x_tick_length,
                      $x_pixels, $this->plot_area[3] - $this->x_tick_cross, $this->ndx_tick_color);
        }

        if ($this->x_tick_label_pos != 'none') {
            $x_label = $this->FormatLabel('x', $x);

            // Label on X axis
            if ($this->x_tick_label_pos == 'xaxis') {
                $this->DrawText('x_label', $this->x_label_angle,
                                $x_pixels, $this->x_axis_y_pixels + $this->x_label_axis_offset,
                                $this->ndx_ticklabel_color, $x_label, 'center', 'top');
            }

            // Label on top of the plot area
            if ($this->x_tick_label_pos == 'plotup' || $this->x_tick_label_pos == 'both') {
                $this->DrawText('x_label', $this->x_label_angle,
                                $x_pixels, $this->plot_area[1] - $this->x_label_top_offset,
                                $this->ndx_ticklabel_color, $x_label, 'center', 'bottom');
            }

            // Label on bottom of the plot area
            if ($this->x_tick_label_pos == 'plotdown' || $this->x_tick_label_pos == 'both') {
                $this->DrawText('x_label', $this->x_label_angle,
                                $x_pixels, $this->plot_area[3] + $this->x_label_bot_offset,
                                $this->ndx_ticklabel_color, $x_label, 'center', 'top');
            }
        }
        return TRUE;
    }

    /**
     * Draws one Y tick mark and its tick label
     *
     * @param float $y  Y value for the label
     * @param int $y_pixels  Y device coordinate for this tick mark
     * @return bool  True always
     * @since 5.8.0
     */
    protected function DrawYTick($y, $y_pixels)
    {
        // Ticks on Y axis
        if ($this->y_tick_pos == 'yaxis') {
            ImageLine($this->img, $this->y_axis_x_pixels - $this->y_tick_length, $y_pixels,
                      $this->y_axis_x_pixels + $this->y_tick_cross, $y_pixels, $this->ndx_tick_color);
        }

        // Ticks to the left of the Plot Area
        if (($this->y_tick_pos == 'plotleft') || ($this->y_tick_pos == 'both') ) {
            ImageLine($this->img, $this->plot_area[0] - $this->y_tick_length, $y_pixels,
                      $this->plot_area[0] + $this->y_tick_cross, $y_pixels, $this->ndx_tick_color);
        }

        // Ticks to the right of the Plot Area
        if (($this->y_tick_pos == 'plotright') || ($this->y_tick_pos == 'both') ) {
            ImageLine($this->img, $this->plot_area[2] + $this->y_tick_length, $y_pixels,
                      $this->plot_area[2] - $this->y_tick_cross, $y_pixels, $this->ndx_tick_color);
        }

        if ($this->y_tick_label_pos != 'none') {
            $y_label = $this->FormatLabel('y', $y);

            // Labels on Y axis
            if ($this->y_tick_label_pos == 'yaxis') {
                $this->DrawText('y_label', $this->y_label_angle,
                                $this->y_axis_x_pixels - $this->y_label_axis_offset, $y_pixels,
                                $this->ndx_ticklabel_color, $y_label, 'right', 'center');
            }

            // Labels to the left of the plot area
            if ($this->y_tick_label_pos == 'plotleft' || $this->y_tick_label_pos == 'both') {
                $this->DrawText('y_label', $this->y_label_angle,
                                $this->plot_area[0] - $this->y_label_left_offset, $y_pixels,
                                $this->ndx_ticklabel_color, $y_label, 'right', 'center');
            }

            // Labels to the right of the plot area
            if ($this->y_tick_label_pos == 'plotright' || $this->y_tick_label_pos == 'both') {
                $this->DrawText('y_label', $this->y_label_angle,
                                $this->plot_area[2] + $this->y_label_right_offset, $y_pixels,
                                $this->ndx_ticklabel_color, $y_label, 'left', 'center');
            }
        }
        return TRUE;
    }

    /**
     * Draws the vertical grid lines, the X axis tick marks, and X axis tick labels
     *
     * @return bool  True always
     */
    protected function DrawXTicks()
    {
        // Set color for solid, or flag for dashed line:
        $style = $this->SetDashedStyle($this->ndx_light_grid_color, $this->dashed_grid);

        // Draw grids lines?
        $draw_grid = $this->GetGridSetting('x');

        // Calculate the tick start, end, and step:
        list($x_start, $x_end, $delta_x) = $this->CalcTicks('x');

        // Loop, avoiding cumulative round-off errors from $x += $delta_x
        for ($n = 0; ($x = $x_start + $n * $delta_x) <= $x_end; $n++) {
            $x_pixels = $this->xtr($x);

            // Draw vertical grid line:
            if ($draw_grid) {
                ImageLine($this->img, $x_pixels, $this->plot_area[1], $x_pixels, $this->plot_area[3], $style);
            }

            // Draw tick mark and tick label:
            $this->DrawXTick($x, $x_pixels);
        }
        return TRUE;
    }

    /**
     * Draws the horizontal grid lines, the Y axis tick marks, and Y axis tick labels
     *
     * @return bool  True always
     */
    protected function DrawYTicks()
    {
        // Set color for solid, or flag for dashed line:
        $style = $this->SetDashedStyle($this->ndx_light_grid_color, $this->dashed_grid);

        // Draw grids lines?
        $draw_grid = $this->GetGridSetting('y');

        // Calculate the tick start, end, and step:
        list($y_start, $y_end, $delta_y) = $this->CalcTicks('y');

        // Loop, avoiding cumulative round-off errors from $y += $delta_y
        for ($n = 0; ($y = $y_start + $n * $delta_y) <= $y_end; $n++) {
            $y_pixels = $this->ytr($y);

            // Draw horizontal grid line:
            if ($draw_grid) {
                ImageLine($this->img, $this->plot_area[0]+1, $y_pixels, $this->plot_area[2]-1,
                          $y_pixels, $style);
            }

            // Draw tick mark and tick label:
            $this->DrawYTick($y, $y_pixels);
        }
        return TRUE;
    }

    /**
     * Draws the border around the plot area
     *
     * This draws the plot border, as set by SetPlotBorderType(). The
     * plot_border_type can be unset/NULL, a scaler, or an array. If unset or null,
     * the default is used ('sides' if the plot includes axes, 'none' if not).
     *
     * @param bool $draw_axes  True or omit to draw the X axis and Y axis, false to not (for pie charts)
     * @return bool  True always
     */
    protected function DrawPlotBorder($draw_axes = TRUE)
    {
        // Force plot_border_type to array and apply defaults.
        if (isset($this->plot_border_type)) {
            $pbt = (array)$this->plot_border_type;
        } elseif ($draw_axes) $pbt = array('sides');
        else return TRUE; // Default to no border for plots without axes (e.g. pie charts)

        $sides = 0;  // Bitmap: 1=left 2=top 4=right 8=bottom
        $map = array('left' => 1, 'plotleft' => 1, 'right' => 4, 'plotright' => 4, 'top' => 2,
                      'bottom' => 8, 'both' => 5, 'sides' => 5, 'full' => 15, 'none' => 0);
        foreach ($pbt as $option) $sides |= $map[$option];
        if ($sides == 15) { // Border on all 4 sides
            imagerectangle($this->img, $this->plot_area[0], $this->plot_area[1],
                           $this->plot_area[2], $this->plot_area[3], $this->ndx_grid_color);
        } else {
            if ($sides & 1) // Left
                imageline($this->img, $this->plot_area[0], $this->plot_area[1],
                                      $this->plot_area[0], $this->plot_area[3], $this->ndx_grid_color);
            if ($sides & 2) // Top
                imageline($this->img, $this->plot_area[0], $this->plot_area[1],
                                      $this->plot_area[2], $this->plot_area[1], $this->ndx_grid_color);
            if ($sides & 4) // Right
                imageline($this->img, $this->plot_area[2], $this->plot_area[1],
                                      $this->plot_area[2], $this->plot_area[3], $this->ndx_grid_color);
            if ($sides & 8) // Bottom
                imageline($this->img, $this->plot_area[0], $this->plot_area[3],
                                      $this->plot_area[2], $this->plot_area[3], $this->ndx_grid_color);
        }
        return TRUE;
    }

    /**
     * Draws the data value label associated with a point in the plot
     *
     * The labels drawn by this function are those that show the value (usually
     * the Y value) of the data point. They are drawn within the plot area,
     * not to be confused with axis data labels.
     *
     * The $dvl parameter array can contain these keys:
     *    h_align v_align : Selects from 9-point text alignment (default center, center);
     *    x_offset y_offset : Text position offsets, in device coordinates (default 0,0);
     *    min_width min_height : Suppress the text if it will not fit (default null,null = no check).
     * See also CheckDataValueLabels() which sets some of these.
     *
     * @param string $x_or_y  Which labels: x | y, used to select font, angle, formatting
     * @param int $row  Identifies the row of the data point (for custom label formatting)
     * @param int $column  Identifies the column of the data point (for custom label formatting)
     * @param float $x_world  X world coordinate of the base point
     * @param float $y_world  Y world coordinate of the base point
     * @param mixed $text The text to draw after formatting with FormatLabel()
     * @param mixed[] $dvl  Associative array with additional label position controls (see above)
     * @return bool  True, if the text was drawn, or False, if it will not fit
     * @since 5.1.3
     */
    protected function DrawDataValueLabel($x_or_y, $row, $column, $x_world, $y_world, $text, $dvl)
    {
        if ($x_or_y == 'x') {
            $angle = $this->x_data_label_angle;
            $font_id = 'x_label';
            $formatted_text = $this->FormatLabel('xd', $text, $row, $column);
        } else { // Assumed 'y'
            $angle = $this->y_data_label_angle;
            $font_id = 'y_label';
            $formatted_text = $this->FormatLabel('yd', $text, $row, $column);
        }
        // Assign defaults and then extract control variables from $dvl:
        $x_offset = $y_offset = 0;
        $h_align = $v_align = 'center';
        extract($dvl);

        // Check to see if the text fits in the available space, if requested.
        if (isset($min_width) || isset($min_height)) {
            list($width, $height) = $this->SizeText($font_id, $angle, $formatted_text);
            if ((isset($min_width) && ($min_width - $width)  < 2)
                || (isset($min_height) && ($min_height - $height) < 2))
                return FALSE;
        }

        $this->DrawText($font_id, $angle, $this->xtr($x_world) + $x_offset, $this->ytr($y_world) + $y_offset,
                        $this->ndx_dvlabel_color, $formatted_text, $h_align, $v_align);
        return TRUE;
    }

    /**
     * Draws an X axis data label, and optional data label line (used in vertical plots)
     *
     * @param string $xlab  Text of the label to draw
     * @param int $xpos  X position for the label, in device coordinates
     * @param int $row  Row index, 0 for the first X, 1 for the second, etc.
     * @param bool $do_lines  True for plot types that support data label lines, False or omit if not
     * @return bool  True always
     */
    protected function DrawXDataLabel($xlab, $xpos, $row, $do_lines=FALSE)
    {
        $xlab = $this->FormatLabel('xd', $xlab, $row);

        // Labels below the plot area
        if ($this->x_data_label_pos == 'plotdown' || $this->x_data_label_pos == 'both')
            $this->DrawText('x_label', $this->x_data_label_angle,
                            $xpos, $this->plot_area[3] + $this->x_label_bot_offset,
                            $this->ndx_datalabel_color, $xlab, 'center', 'top');

        // Labels above the plot area
        if ($this->x_data_label_pos == 'plotup' || $this->x_data_label_pos == 'both')
            $this->DrawText('x_label', $this->x_data_label_angle,
                            $xpos, $this->plot_area[1] - $this->x_label_top_offset,
                            $this->ndx_datalabel_color, $xlab, 'center', 'bottom');

        if ($do_lines && $this->draw_x_data_label_lines)
            $this->DrawXDataLine($xpos, $row);
        return TRUE;
    }

    /**
     * Draws a Y axis data label, and optional data label line (used in horizontal plots)
     *
     * @param string $ylab  Text of the label to draw
     * @param int $ypos  Y position for the label, in device coordinates
     * @param int $row  Row index, 0 for the first Y, 1 for the second, etc.
     * @param bool $do_lines  True for plot types that support data label lines, False or omit if not
     * @return bool  True always
     * @since 5.1.2
     */
    protected function DrawYDataLabel($ylab, $ypos, $row, $do_lines=FALSE)
    {
        $ylab = $this->FormatLabel('yd', $ylab, $row);

        // Labels left of the plot area
        if ($this->y_data_label_pos == 'plotleft' || $this->y_data_label_pos == 'both')
            $this->DrawText('y_label', $this->y_data_label_angle,
                            $this->plot_area[0] - $this->y_label_left_offset, $ypos,
                            $this->ndx_datalabel_color, $ylab, 'right', 'center');

        // Labels right of the plot area
        if ($this->y_data_label_pos == 'plotright' || $this->y_data_label_pos == 'both')
            $this->DrawText('y_label', $this->y_data_label_angle,
                            $this->plot_area[2] + $this->y_label_right_offset, $ypos,
                            $this->ndx_datalabel_color, $ylab, 'left', 'center');

        if ($do_lines && $this->draw_y_data_label_lines)
            $this->DrawYDataLine($ypos, $row);
        return TRUE;
    }

    /**
     * Draws vertical data label lines (used in vertical plots)
     *
     * This draws vertical lines from a data point up and/or down.
     * Which lines are drawn depends on the value of x_data_label_pos.
     * Whether this is done not depends on draw_x_data_label_lines.
     *
     * @param int $xpos  X position in pixels of the line
     * @param int $row  Index of the data row being drawn
     * @return bool  True always
     */
    protected function DrawXDataLine($xpos, $row)
    {
        // Set color for solid, or flag for dashed line:
        $style = $this->SetDashedStyle($this->ndx_light_grid_color, $this->dashed_grid);

        if ($this->x_data_label_pos == 'both') {
            // Lines from the bottom up
            ImageLine($this->img, $xpos, $this->plot_area[3], $xpos, $this->plot_area[1], $style);
        } elseif ($this->x_data_label_pos == 'plotdown' && isset($this->data_max[$row])) {
            // Lines from the bottom of the plot up to the max Y value at this X:
            $ypos = $this->ytr($this->data_max[$row]);
            ImageLine($this->img, $xpos, $ypos, $xpos, $this->plot_area[3], $style);
        } elseif ($this->x_data_label_pos == 'plotup' && isset($this->data_min[$row])) {
            // Lines from the top of the plot down to the min Y value at this X:
            $ypos = $this->ytr($this->data_min[$row]);
            ImageLine($this->img, $xpos, $this->plot_area[1], $xpos, $ypos, $style);
        }
        return TRUE;
    }

    /**
     * Draws horizontal data label lines (used in horizontal plots)
     *
     * This draws horizontal lines from a data points left and/or right.
     * Which lines are drawn depends on the value of y_data_label_pos.
     * Whether this is done not depends on draw_y_data_label_lines.
     *
     * @param int $ypos  Y position in pixels of the line
     * @param int $row  Index of the data row being drawn
     * @return bool  True always
     * @since 6.0.0
     */
    protected function DrawYDataLine($ypos, $row)
    {
        // Set color for solid, or flag for dashed line:
        $style = $this->SetDashedStyle($this->ndx_light_grid_color, $this->dashed_grid);

        if ($this->y_data_label_pos == 'both') {
            // Lines from the left side to the right side
            ImageLine($this->img, $this->plot_area[0], $ypos, $this->plot_area[2], $ypos, $style);
        } elseif ($this->y_data_label_pos == 'plotleft' && isset($this->data_max[$row])) {
            // Lines from the left of the plot rightwards the max X value at this Y:
            $xpos = $this->xtr($this->data_max[$row]);
            ImageLine($this->img, $xpos, $ypos, $this->plot_area[0], $ypos, $style);
        } elseif ($this->y_data_label_pos == 'plotright' && isset($this->data_min[$row])) {
            // Lines from the right of the plot leftwards to the min X value at this Y:
            $xpos = $this->xtr($this->data_min[$row]);
            ImageLine($this->img, $this->plot_area[2], $ypos, $xpos, $ypos, $style);
        }
        return TRUE;
    }

    /**
     * Formats a pie chart label
     *
     * @param int $index  Pie slice number, starting with 0
     * @param string[] $pie_label_source  Label formatting mode(s). See CheckPieLabels() and SetPieLabelType()
     * @param float $arc_angle  Delta angle for this slice, in degrees
     * @param float $slice_weight Numeric value, or relative weight, of this slice
     * @return string  The formatted label value
     * @since 5.6.0
     */
    protected function FormatPieLabel($index, $pie_label_source, $arc_angle, $slice_weight)
    {
        $values = array(); // Builds up label value, one field at a time.
        foreach ($pie_label_source as $word) {
            switch ($word) {
            case 'label':    // Use label from data array, but only if data type is compatible
                $values[] = $this->datatype_pie_single ? $this->data[$index][0] : '';
                break;
            case 'value': // Use actual numeric value of the slice
                $values[] = $slice_weight;
                break;
            case 'index': // Use slice index: 0, 1, 2...
                $values[] = $index;
                break;
            default:        // Use percentage: 100% x arc_angle / (360 degrees) = arc_angle / 3.6
                $values[] = $arc_angle / 3.6;
            }
        }
        // Format the label and return the result. Note: The conditional avoids a number-to-string
        // conversion for the single-source case. This avoids a PHP issue with locale-based conversion.
        return $this->FormatLabel('p', count($values) == 1 ? $values[0] : implode(' ', $values));
    }

    /**
     * Draws a pie chart label
     *
     * This draws a single label for a pie chart.
     *
     * The $r parameter array is calculated by DrawPieChart() and contains
     * values that are constant for the chart, so do not need to be
     * recalculated for each slice. Array keys are 'x' 'y' and 'reverse'.
     * r[x], r[y] are the parameters of the ellipse:  ` x**2 / r[x]**2 + y**2 / r[y]**2 = 1 `
     * Also:  ` x = r[x] * cos(angle) ` and ` y = r[y] * sin(angle) ` (relative to pie center).
     * 'reverse' is a flag for text alignment (see GetTextAlignment()).
     *
     * @param string $label_txt  Pre-formatted label, from FormatPieLabel()
     * @param int $xc  X device coordinate of the pie center
     * @param int $yc  Y device coordinate of the pie center
     * @param float $start_angle  Slice starting angle in degrees
     * @param float $arc_angle  Slice angular width in degrees
     * @param mixed[] $r  Additional paramter array (from DrawPieChart, see comment above)
     * @return bool  True always
     * @since 5.6.0
     */
    protected function DrawPieLabel($label_txt, $xc, $yc, $start_angle, $arc_angle, $r)
    {
        $mid_angle = deg2rad($start_angle + $arc_angle / 2);
        $sin_mid = sin($mid_angle);
        $cos_mid = cos($mid_angle);
        // Calculate label reference point.
        $label_x = $xc + $cos_mid * $r['x'];
        $label_y = $yc - $sin_mid * $r['y'];
        // For labels in the lower half, outside the pie, offset it to account for shading.
        // But don't shift labels just below the horizontal, because the shading is too thin there,
        // and the label ends up too far from the slice. Make a smooth transition between label offsets on
        // shaded area and above. (This isn't perfect at all, but works for reasonably low shading.)
        if ($this->label_scale_position >= 0.5 && $this->shading > 0 && $sin_mid < 0) {
            $yoff = min($this->shading, -$sin_mid * $r['y']);
        } else $yoff = 0;

        // Calculate text alignment (h_align, v_align) based on angle:
        $this->GetTextAlignment($sin_mid, $cos_mid, $h_align, $v_align, $r['reverse']);
        // Draw the label:
        $this->DrawText('generic', 0, $label_x, $label_y + $yoff, $this->ndx_pielabel_color,
                        $label_txt, $h_align, $v_align);
        return TRUE;
    }

/////////////////////////////////////////////
///////////////                        LEGEND
/////////////////////////////////////////////

    /**
     * Adds text to a legend box
     *
     * The legend can be set up with a single call by passing an array of
     * strings (1 string per legend line/data set), or it can be built up
     * one line at a time with repeated calls passing a single string.
     * NULL (or an empty array) can be passed to cancel the legend.
     *
     * @param string|string[] $which_leg  Array of strings for the legend, or a single string to append
     * @return bool  True always
     */
    function SetLegend($which_leg)
    {
        if (is_array($which_leg)) {           // use array (or cancel, if empty array)
            $this->legend = $which_leg;
        } elseif (!is_null($which_leg)) {     // append string
            if (!isset($this->legend)) $this->legend = array(); // Seems unnecessary, but be safe.
            $this->legend[] = $which_leg;
        } else {
            $this->legend = NULL;  // Reset to no legend.
        }
        return TRUE;
    }

    /**
     * Positions the legend on the image, using device coordinates
     *
     * @param int $which_x  X coordinate in pixels of the upper left corner of the legend box
     * @param int $which_y  Y coordinate in pixels of the upper left corner of the legend box
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetLegendPixels($which_x=NULL, $which_y=NULL)
    {
        return $this->SetLegendPosition(0, 0, 'image', 0, 0, $which_x, $which_y);
    }

    /**
     * Positions the legend on the image, using world coordinates
     *
     * @param int $which_x  World coordinate X of the upper left corner of the legend box
     * @param int $which_y  World coordinate Y of the upper left corner of the legend box
     * @return bool  True (False on error if an error handler returns True)
     */
    function SetLegendWorld($which_x, $which_y)
    {
        return $this->SetLegendPosition(0, 0, 'world', $which_x, $which_y);
    }

    /**
     * Positions the legend
     *
     * This implements SetLegendWorld(), SetLegendPixels(), and also allows use
     * of relative coordinates, with optional pixel offset.
     *
     * 'Relative coordinates' means: (0,0) is the upper left corner, and (1,1)
     * is the lower right corner of the element (legend, image, plot, or title
     * area), regardless of its size. These are floating point values, each
     * usually in the range [0,1], but they can be negative or greater than 1.
     *
     * If any of x, y, x_offset, or y_offset are NULL, the default legend
     * positioning is restored.
     *
     * Note: This only stores the parameters. The real work is in GetLegendPosition().
     *
     * @param float $x  Relative coordinate X indicating an anchor point on the legend box
     * @param float $y  Relative coordinate X indicating an anchor point on the legend box
     * @param string $relative_to  Position is relative to: image | plot | world | title
     * @param float $x_base  Base point X for positioning to the anchor point
     * @param float $y_base  Base point Y for positioning to the anchor point
     * @param int $x_offset  Additional legend box offset X value in pixels
     * @param int $y_offset  Additional legend box offset Y value in pixels
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.4.0
     */
    function SetLegendPosition($x, $y, $relative_to, $x_base, $y_base, $x_offset = 0, $y_offset = 0)
    {
        // Special case: NULL means restore the default positioning.
        if (!isset($x, $y, $x_offset, $y_offset)) {
            $this->legend_pos = NULL;
        } else {
            $mode = $this->CheckOption($relative_to, 'image, plot, title, world', __FUNCTION__);
            if (empty($mode))
                return FALSE;
            // Save all values for use by GetLegendPosition()
            $this->legend_pos = compact('x', 'y', 'mode', 'x_base', 'y_base', 'x_offset', 'y_offset');
        }
        return TRUE;
    }

    /**
     * Controls the appearance of the legend
     *
     * @param string $text_align  How to align the text in the legend: left | right
     * @param string $colorbox_align  How to align the color boxes or shape markers: left | right | none | ''
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.0.4
     */
    function SetLegendStyle($text_align, $colorbox_align = '')
    {
        $this->legend_text_align = $this->CheckOption($text_align, 'left, right', __FUNCTION__);
        if (empty($colorbox_align))
            $this->legend_colorbox_align = $this->legend_text_align;
        else
            $this->legend_colorbox_align = $this->CheckOption($colorbox_align, 'left, right, none',
                                                              __FUNCTION__);
        return ($this->legend_text_align && $this->legend_colorbox_align);
    }

    /**
     * Selects use of color boxes or alternative shapes (point shapes or line segments) in the legend
     *
     * @param bool $use_shapes  True to use shapes or lines, false to use color boxes
     * @return bool  True always
     * @since 5.4.0
     */
    function SetLegendUseShapes($use_shapes)
    {
        $this->legend_use_shapes = (bool)$use_shapes;
        return TRUE;
    }

    /**
     * Controls the order of text lines in the legend (e.g. for Stackedbar plots)
     *
     * @param bool $reversal  True to reverse the order - bottom up; False for default top down
     * @return bool  True always
     * @since 5.5.0
     */
    function SetLegendReverse($reversal = False)
    {
        $this->legend_reverse_order = (bool)$reversal;
        return TRUE;
    }

    /**
     * Controls the borders around the color boxes in the legend
     *
     * @param string $cbbmode  Color box mode: none | textcolor | databordercolor
     * @return bool  True (False on error if an error handler returns True)
     * @since 6.0.0
     */
    function SetLegendColorboxBorders($cbbmode = 'textcolor')
    {
        $this->legend_colorbox_borders = $this->CheckOption($cbbmode, 'none, textcolor, databordercolor',
                                                            __FUNCTION__);
        return (boolean)$this->legend_colorbox_borders;
    }

    /**
     * Calculates legend sizing parameters
     *
     * Used by DrawLegend() and the public GetLegendSize().
     * It returns information based on any SetLegend*() calls already made. It does not use
     * legend position or data scaling, so it can be called before data scaling is set up.
     * It must not be called if $this->legend is empty.
     *
     * Returns an associative array with these entries describing legend sizing:
     *    'width', 'height' : Overall legend box size in pixels.
     *    'char_w', 'char_h' : Width and height of 'E' in legend text font. (Used to size color boxes)
     *    'v_margin' : Inside margin for legend
     *    'dot_height' : Height of color boxes (even if not drawn), for line spacing.
     *    'colorbox_mode', 'colorbox_width' : Colorbox/shape mode and width factor.
     *
     * @return array  Legend sizing parameter associative array
     * @since 5.4.0
     */
    protected function GetLegendSizeParams()
    {
        $font = &$this->fonts['legend']; // Shortcut to font info array

        // Find maximum legend label line width.
        $max_width = 0;
        foreach ($this->legend as $line) {
            list($width, $unused) = $this->SizeText('legend', 0, $line);
            if ($width > $max_width) $max_width = $width;
        }

        // Font parameters are used to size the color boxes:
        $char_w = $font['width'];
        $char_h = $font['height'];
        $line_spacing = $this->GetLineSpacing($font);

        // Get color-box mode. Note GetLegendSizeParams can be called from GetLegendSize, and not all
        // settings are defined then, but the colorbox_mode won't be used then so it need not be valid.
        if ($this->legend_colorbox_align == 'none') {
            $colorbox_mode = False; // Color boxes are off
        } elseif (!$this->legend_use_shapes || empty(self::$plots[$this->plot_type]['legend_alt_marker'])) {
            $colorbox_mode = 'box'; // Not using shapes, or plot type defines no shape, so use boxes.
        } else {
            $colorbox_mode = self::$plots[$this->plot_type]['legend_alt_marker']; // Shape from plot type
        }

        // Sizing parameters:
        $v_margin = $char_h / 2;                 // Between vertical borders and labels
        $dot_height = $char_h + $line_spacing;   // Height of the color boxes (even if not drawn)
        $colorbox_width = $char_w * $this->legend_colorbox_width; // Color box width, with adjustment

        // The 'line' style marker needs a wider colorbox than shape or box.
        if ($colorbox_mode == 'line')
            $colorbox_width *= 4;

        // Calculate overall legend box width and height.
        // Width is e.g.: "| space colorbox space text space |" where each space adds $char_w,
        // and colorbox (if drawn) adds $char_w * its width adjustment.
        if ($colorbox_mode) {
            $width = $max_width + 3 * $char_w + $colorbox_width;
        } else {
            $width = $max_width + 2 * $char_w;
        }
        $height = $dot_height * count($this->legend) + 2 * $v_margin;

        return compact('width', 'height', 'char_w', 'char_h', 'v_margin',
                       'colorbox_mode', 'dot_height', 'colorbox_width');
    }

    /**
     * Gets the legend box size (can be used to adjust the plot margins, for example)
     *
     * @return int[]  Legend box size as array of (width, height) in pixels, False if no legend defined.
     * @since 5.4.0
     */
    function GetLegendSize()
    {
        if (empty($this->legend))
            return FALSE;
        $params = $this->GetLegendSizeParams();
        return array($params['width'], $params['height']);
    }

    /**
     * Calculates the legend location in device coordinates
     *
     * This is a helper for DrawLegend, and is only called if there is a legend.
     * See SetLegendWorld(), SetLegendPixels(), SetLegendPosition().
     *
     * @param int $width  Width of the legend box
     * @param int $height  Height of the legend box
     * @return int[]  Coordinates of the upper left corner of the legend box as an array ($x, $y)
     * @since 5.4.0
     */
    protected function GetLegendPosition($width, $height)
    {
        // Extract variables set by SetLegend*(): $mode, $x, $y, $x_base, $y_base, $x_offset, $y_offset
        if (isset($this->legend_pos['mode']))
            extract($this->legend_pos);
        else
            $mode = ''; // Default legend position mode.

        switch ($mode) {

        case 'plot': // SetLegendPosition with mode='plot', relative coordinates over plot area.
            return array((int)($x_base * $this->plot_area_width - $x * $width)
                          + $this->plot_area[0] + $x_offset,
                         (int)($y_base * $this->plot_area_height - $y * $height)
                          + $this->plot_area[1] + $y_offset);

        case 'world': // User-defined position in world-coordinates (SetLegendWorld), using x_base, y_base
            return array($this->xtr($x_base) + $x_offset - (int)($x * $width),
                         $this->ytr($y_base) + $y_offset - (int)($y * $height));

        case 'image': // SetLegendPosition with mode='image', relative coordinates over image area.
                      // SetLegendPixels() uses this too, with x=y=0.
            return array((int)($x_base * $this->image_width - $x * $width) + $x_offset,
                         (int)($y_base * $this->image_height - $y * $height) + $y_offset);

        case 'title': // SetLegendPosition with mode='title', relative to main title.
            // Recalculate main title position/size, since CalcMargins does not save it. See DrawTitle()
            list($title_width, $title_height) = $this->SizeText('title', 0, $this->title_txt);
            $title_x = (int)(($this->image_width - $title_width) / 2);
            return array((int)($x_base * $title_width - $x * $width) + $title_x + $x_offset,
                         (int)($y_base * $title_height - $y * $height) + $this->title_offset + $y_offset);

        default: // If mode is unset (or invalid), use default position.
            return array ($this->plot_area[2] - $width - $this->safe_margin,
                          $this->plot_area[1] + $this->safe_margin);
        }
    }

    /**
     * Draws the plot legend - the outline box, text labels, and color boxes or shapes
     *
     * @return bool  True always
     */
    protected function DrawLegend()
    {
        // Calculate legend box sizing parameters:
        // See GetLegendSizeParams() to see what variables are set by this.
        extract($this->GetLegendSizeParams());

        // Get legend box position:
        list($box_start_x, $box_start_y) = $this->GetLegendPosition($width, $height);
        $box_end_y = $box_start_y + $height;
        $box_end_x = $box_start_x + $width;

        // Draw outer box
        ImageFilledRectangle($this->img, $box_start_x, $box_start_y, $box_end_x, $box_end_y,
                             $this->ndx_legend_bg_color);
        ImageRectangle($this->img, $box_start_x, $box_start_y, $box_end_x, $box_end_y,
                       $this->ndx_grid_color);

        // Calculate color box and text horizontal positions.
        if (!$colorbox_mode) {
            if ($this->legend_text_align == 'left')
                $x_pos = $box_start_x + $char_w;
            else
                $x_pos = $box_end_x - $char_w;
            $dot_left_x = 0; // Not used directly if color boxes/shapes are off, but referenced below.
        } elseif ($this->legend_colorbox_align == 'left') {
            $dot_left_x = $box_start_x + $char_w;
            $dot_right_x = $dot_left_x + $colorbox_width;
            if ($this->legend_text_align == 'left')
                $x_pos = $dot_right_x + $char_w;
            else
                $x_pos = $box_end_x - $char_w;
        } else {      // colorbox_align == 'right'
            $dot_right_x = $box_end_x - $char_w;
            $dot_left_x = $dot_right_x - $colorbox_width;
            if ($this->legend_text_align == 'left')
                $x_pos = $box_start_x + $char_w;
            else
                $x_pos = $dot_left_x - $char_w;
        }

        // $y_pos is the bottom of each color box. $yc is the vertical center of the color box or
        // the point shape (if drawn). The text is centered vertically on $yc.
        // For normal order (top-down), $y_pos starts at the top. For reversed order, at the bottom.
        if ($this->legend_reverse_order) {
            $y_pos = $box_end_y - $v_margin;
            $delta_y = -$dot_height;
        } else {
            $y_pos = $box_start_y + $v_margin + $dot_height;
            $delta_y = $dot_height;
        }
        $yc = (int)($y_pos - $dot_height / 2);
        $xc = (int)($dot_left_x + $colorbox_width / 2);   // Horizontal center for point shape if drawn

        // Colorbox color index, shape index, and line width/style index variables.
        // Note the arrays these are used to index have been padded to data_columns entries. The legend
        // can contain more than data_columns entries, though, but it only makes sense to be able
        // to index additional entries for the data color, due to the data_color callback.
        if ($colorbox_mode) {
            $color_index = 0;
            $max_color_index = count($this->ndx_data_colors) - 1;
            $lws_index = 0; // Line Width and Style index
            $shape_index = 0;
        }

        foreach ($this->legend as $leg) {
            // Draw text with requested alignment:
            $this->DrawText('legend', 0, $x_pos, $yc, $this->ndx_legend_text_color, $leg,
                            $this->legend_text_align, 'center');
            if ($colorbox_mode) {
                $y1 = $y_pos - $dot_height + 1;
                $y2 = $y_pos - 1;

                // If plot area background is on, draw a background for any non-box shapes:
                if ($this->draw_plot_area_background && $colorbox_mode != 'box') {
                    ImageFilledRectangle($this->img, $dot_left_x, $y1, $dot_right_x, $y2,
                                         $this->ndx_plot_bg_color);
                }

                switch ($colorbox_mode) {
                case 'shape':
                    // Draw the shape. DrawShape() takes shape_index modulo number of defined shapes.
                    $this->DrawShape($xc, $yc, $shape_index++, $this->ndx_data_colors[$color_index], FALSE);
                    break;

                case 'line':
                    // Draw a short line segment with proper color, width, and style
                    imagesetthickness($this->img, $this->line_widths[$lws_index]);
                    $style = $this->SetDashedStyle($this->ndx_data_colors[$color_index],
                                                   $this->line_styles[$lws_index] == 'dashed');
                    imageline($this->img, $dot_left_x, $yc, $dot_right_x, $yc, $style);
                    imagesetthickness($this->img, 1);
                    if (++$lws_index >= $this->data_columns) $lws_index = 0; // Wrap around
                    break;

                default:
                    // Draw color boxes:
                    ImageFilledRectangle($this->img, $dot_left_x, $y1, $dot_right_x, $y2,
                                         $this->ndx_data_colors[$color_index]);
                   // Draw a rectangle around the box, if enabled.
                   if ($this->legend_colorbox_borders != 'none') {
                       if ($this->legend_colorbox_borders == 'databordercolor')
                           $color = $this->ndx_data_border_colors[$color_index];
                       else
                           $color = $this->ndx_text_color;
                       ImageRectangle($this->img, $dot_left_x, $y1, $dot_right_x, $y2, $color);
                   }
                }
                if (++$color_index > $max_color_index) $color_index = 0;
            }
            $y_pos += $delta_y;
            $yc += $delta_y;
        }
        return TRUE;
    }

/////////////////////////////////////////////
////////////////////     PLOT DRAWING HELPERS
/////////////////////////////////////////////

    /**
     * Gets the color index to use for plotting a data element (point or line segment, for example)
     *
     * This is used to select data colors for plotting. Without a custom data
     * color callback, color selection is based on $idx, the column index in
     * the data array. So the first data set (Y) uses the first color, etc.
     * With a custom data color callback, both row and column index values
     * are passed to the callback so it can use them to select a color.
     *
     * @param int $row  Row index for the current data point (used only for a custom data color callback)
     * @param int $idx  Column index for the current data point (e.g. 0 for the first Y value for each X)
     * @param mixed[] $vars  Reference variable, array for local storage (caller makes an empty array)
     * @param int $data_color  Reference variable: returned color index to use for drawing
     * @param mixed $extra  Extra variable passed through to a data color callback
     * @since 5.2.0
     */
    protected function GetDataColor($row, $idx, &$vars, &$data_color, $extra = 0)
    {
        // Initialize or extract variables:
        if (empty($vars)) {
            $custom_color = (bool)$this->GetCallback('data_color');
            $num_data_colors = count($this->ndx_data_colors);
            $vars = compact('custom_color', 'num_data_colors');
        } else {
            extract($vars);
        }

        // Select the data color:
        if ($custom_color) {
            $idx = $this->DoCallback('data_color', $row, $idx, $extra) % $num_data_colors;
        }
        $data_color = $this->ndx_data_colors[$idx];
    }

    /**
     * Gets the color indexes to use for data element and error bar plotting
     *
     * @param int $row  Row index for the current data point (used only for a custom data color callback)
     * @param int $idx  Column index for the current data point (e.g. 0 for the first Y value for each X)
     * @param mixed[] $vars  Reference variable, array for local storage (caller makes an empty array)
     * @param int $data_color  Reference variable: returned color index to use for drawing
     * @param int error_color   Reference variable: returned color index to use for the error bars
     * @param mixed $extra  Extra variable passed through to a data color callback
     * @since 5.2.0
     */
    protected function GetDataErrorColors($row, $idx, &$vars, &$data_color, &$error_color, $extra = 0)
    {
        // Initialize or extract variables:
        if (empty($vars)) {
            $this->NeedErrorBarColors();   // This plot needs error bar colors.
            $custom_color = (bool)$this->GetCallback('data_color');
            $num_data_colors = count($this->ndx_data_colors);
            $num_error_colors = count($this->ndx_error_bar_colors);
            $vars = compact('custom_color', 'num_data_colors', 'num_error_colors');
        } else {
            extract($vars);
        }

        // Select the colors.
        if ($custom_color) {
            $col_i = $this->DoCallback('data_color', $row, $idx, $extra); // Custom color index
            $data_color = $this->ndx_data_colors[$col_i % $num_data_colors];
            $error_color = $this->ndx_error_bar_colors[$col_i % $num_error_colors];
        } else {
            $data_color = $this->ndx_data_colors[$idx];
            $error_color = $this->ndx_error_bar_colors[$idx];
        }
    }

    /**
     * Gets the color indexes to use for a bar chart (data color, border color, shading color)
     *
     * @param int $row  Row index for the current data point (used only for a custom data color callback)
     * @param int $idx  Column index for the current data point (e.g. 0 for the first Y value for each X)
     * @param mixed[] $vars  Reference variable, array for local storage (caller makes an empty array)
     * @param int $data_color  Returned color index to use for the bar fill
     * @param int $shade_color Returned color index for the shading, NULL if shading is off
     * @param int $border_color  Returned color index for the bar borders, NULL if borders are off
     * @since 5.2.0
     */
    protected function GetBarColors($row, $idx, &$vars, &$data_color, &$shade_color, &$border_color)
    {
        // Initialize or extract this functions persistant state variables:
        if (empty($vars)) {
            if (($shaded = ($this->shading > 0)))
                $this->NeedDataDarkColors();  // Plot needs dark colors for shading
            $custom_color = (bool)$this->GetCallback('data_color');
            $num_data_colors = count($this->ndx_data_colors);
            $num_border_colors = count($this->ndx_data_border_colors);
            // Are borders enabled? Default is true for unshaded plots, false for shaded.
            $borders = isset($this->draw_data_borders) ? $this->draw_data_borders : !$shaded;

            $vars = compact('borders', 'custom_color', 'num_data_colors', 'num_border_colors', 'shaded');
        } else {
            extract($vars);
        }

        // Select the colors.
        if ($custom_color) {
            $col_i = $this->DoCallback('data_color', $row, $idx); // Custom color index
            $i_data = $col_i % $num_data_colors; // Index for data colors and dark colors
            $i_border = $col_i % $num_border_colors; // Index for data borders (if used)
        } else {
            $i_data = $i_border = $idx;
        }
        $data_color = $this->ndx_data_colors[$i_data];
        $shade_color = $shaded ? $this->ndx_data_dark_colors[$i_data] : NULL;
        $border_color = $borders ? $this->ndx_data_border_colors[$i_border] : NULL;
    }

    /**
     * Gets the grid setting, on or off
     *
     * This function determines the dynamic defaults. The grid defaults on for
     * the dependent variable, off for the independent variable.
     *
     * @param string $xy  Which grid to check for: x | y
     * @return bool  True if the grid should be drawn, False if it should not be drawn
     * @since 6.0.0
     */
    protected function GetGridSetting($xy)
    {
        if ($xy == 'x')
            return isset($this->draw_x_grid) ? $this->draw_x_grid : $this->datatype_swapped_xy;
        // Assumed 'y'
        return isset($this->draw_y_grid) ? $this->draw_y_grid : !$this->datatype_swapped_xy;
    }

    /**
     * Draws a single marker shape (a dot or shape)
     *
     * This is used by points and linepoints plots to draw a point, and by the
     * legend.  Also see SetPointShapes() for the list of supported shapes.
     *
     * @param int $x  X device coordinate of the center of the shape
     * @param int $y  Y device coordinate of the center of the shape
     * @param int $record  Index into point_shapes[] and point_sizes[] arrays (taken modulo their sizes)
     * @param int $color  Color index to use for the point shape
     * @param bool $allow_none  True or omit allow 'none' as shape, False to substitute (for legend)
     * @return bool  True always
     * @since 5.4.0
     */
    protected function DrawShape($x, $y, $record, $color, $allow_none = TRUE)
    {
        $index = $record % $this->point_counts;
        $point_size = $this->point_sizes[$index];
        $half_point = (int)($point_size / 2);

        $x1 = $x - $half_point;
        $x2 = $x + $half_point;
        $y1 = $y - $half_point;
        $y2 = $y + $half_point;

        switch ($this->point_shapes[$index]) {
        case 'halfline':
            ImageLine($this->img, $x1, $y, $x, $y, $color);
            break;
        case 'none': /* Special case, no point shape here */
            if ($allow_none) break; // But fall throught to line if a shape is required
        case 'line':
            ImageLine($this->img, $x1, $y, $x2, $y, $color);
            break;
        case 'plus':
            ImageLine($this->img, $x1, $y, $x2, $y, $color);
            ImageLine($this->img, $x, $y1, $x, $y2, $color);
            break;
        case 'cross':
            ImageLine($this->img, $x1, $y1, $x2, $y2, $color);
            ImageLine($this->img, $x1, $y2, $x2, $y1, $color);
            break;
        case 'circle':
            ImageArc($this->img, $x, $y, $point_size, $point_size, 0, 360, $color);
            break;
        case 'dot':
            ImageFilledEllipse($this->img, $x, $y, $point_size, $point_size, $color);
            break;
        case 'diamond':
            $arrpoints = array($x1, $y, $x, $y1, $x2, $y, $x, $y2);
            ImageFilledPolygon($this->img, $arrpoints, 4, $color);
            break;
        case 'triangle':
            $arrpoints = array($x1, $y, $x2, $y, $x, $y2);
            ImageFilledPolygon($this->img, $arrpoints, 3, $color);
            break;
        case 'trianglemid':
            $arrpoints = array($x1, $y1, $x2, $y1, $x, $y);
            ImageFilledPolygon($this->img, $arrpoints, 3, $color);
            break;
        case 'yield':
            $arrpoints = array($x1, $y1, $x2, $y1, $x, $y2);
            ImageFilledPolygon($this->img, $arrpoints, 3, $color);
            break;
        case 'delta':
            $arrpoints = array($x1, $y2, $x2, $y2, $x, $y1);
            ImageFilledPolygon($this->img, $arrpoints, 3, $color);
            break;
        case 'star':
            ImageLine($this->img, $x1, $y, $x2, $y, $color);
            ImageLine($this->img, $x, $y1, $x, $y2, $color);
            ImageLine($this->img, $x1, $y1, $x2, $y2, $color);
            ImageLine($this->img, $x1, $y2, $x2, $y1, $color);
            break;
        case 'hourglass':
            $arrpoints = array($x1, $y1, $x2, $y1, $x1, $y2, $x2, $y2);
            ImageFilledPolygon($this->img, $arrpoints, 4, $color);
            break;
        case 'bowtie':
            $arrpoints = array($x1, $y1, $x1, $y2, $x2, $y1, $x2, $y2);
            ImageFilledPolygon($this->img, $arrpoints, 4, $color);
            break;
        case 'target':
            ImageFilledRectangle($this->img, $x1, $y1, $x, $y, $color);
            ImageFilledRectangle($this->img, $x, $y, $x2, $y2, $color);
            ImageRectangle($this->img, $x1, $y1, $x2, $y2, $color);
            break;
        case 'box':
            ImageRectangle($this->img, $x1, $y1, $x2, $y2, $color);
            break;
        case 'home': /* As in: "home plate" (baseball), also looks sort of like a house. */
            $arrpoints = array($x1, $y2, $x2, $y2, $x2, $y, $x, $y1, $x1, $y);
            ImageFilledPolygon($this->img, $arrpoints, 5, $color);
            break;
        case 'up':
            ImagePolygon($this->img, array($x, $y1, $x2, $y2, $x1, $y2), 3, $color);
            break;
        case 'down':
            ImagePolygon($this->img, array($x, $y2, $x1, $y1, $x2, $y1), 3, $color);
            break;
        default: /* Also 'rect' */
            ImageFilledRectangle($this->img, $x1, $y1, $x2, $y2, $color);
            break;
        }
        return TRUE;
    }

    /**
     * Draws a single marker point, using World Coordinates
     *
     * @param int $row  Row index of data point (only used for a data_points callback)
     * @param int $column  Column index of data point, used to select the marker shape and size
     * @param int $x_world  X world coordinate of the data point
     * @param int $y_world  Y world coordinate of the data point
     * @param int $color  Color to use for the data point
     * @return bool  True always (from DrawShape)
     */
    protected function DrawDot($row, $column, $x_world, $y_world, $color)
    {
        $x = $this->xtr($x_world);
        $y = $this->ytr($y_world);
        $result = $this->DrawShape($x, $y, $column, $color);
        $this->DoCallback('data_points', 'dot', $row, $column, $x, $y);
        return $result;
    }

    /**
     * Draws a single bar (or bar segment), with optional shading or border
     *
     * This draws a single bar (or bar segment), for bar and stackedbar plots,
     * both vertical and horizontal. The 3 color values come from GetBarColors.
     * Two flags (at most 1 of which can be false) are used to suppress shading
     * for some cases of stackedbar plots.
     *
     * @param int $row  Row index of data point (only used for a data_points callback)
     * @param int $column  Column index of data point (only used for a data_points callback)
     * @param int $x1  One corner of the bar X (device coordinates)
     * @param int $y1  One corner of the bar Y (device coordinates)
     * @param int $x2  Other corner of the bar X (device coordinates)
     * @param int $y2  Other corner of the bar Y (device coordinates)
     * @param int $data_color  Color index to use for the bar fill
     * @param int $shade_color  Color index to use for the shading (if shading is on, else NULL)
     * @param int $border_color  Color index to use for the bar outlines (borders), if enabled, else NULL
     * @param bool $shade_top  Shade the top? (Suppressed for downward stack segments except first)
     * @param bool $shade_side  Shade the right side? (Suppressed for leftward stack segments except first)
     * @return bool  True always
     * @since 5.2.0
     */
    protected function DrawBar($row, $column, $x1, $y1, $x2, $y2, $data_color, $shade_color, $border_color,
            $shade_top = TRUE, $shade_side = TRUE)
    {
        // Sort the points so x1,y1 is upper left and x2,y2 is lower right. This
        // is needed in order to get the shading right, and imagerectangle may require it.
        if ($x1 > $x2) {
            $t = $x1; $x1 = $x2; $x2 = $t;
        }
        if ($y1 > $y2) {
            $t = $y1; $y1 = $y2; $y2 = $t;
        }

        // Draw the bar
        ImageFilledRectangle($this->img, $x1, $y1, $x2, $y2, $data_color);

        // Draw a shade, if shading is on.
        if (isset($shade_color)) {
            $shade = $this->shading;
            if ($shade_top && $shade_side) {
                $pts = array($x1, $y1,  $x1 + $shade, $y1 - $shade, $x2 + $shade, $y1 - $shade,
                             $x2 + $shade, $y2 - $shade, $x2, $y2, $x2, $y1);
            } elseif ($shade_top) {   // Suppress side shading
                $pts = array($x1, $y1, $x1 + $shade, $y1 - $shade, $x2 + $shade, $y1 - $shade, $x2, $y1);
            } else { // Suppress top shading (Note shade_top==FALSE && shade_side==FALSE is not allowed)
                $pts = array($x2, $y2, $x2, $y1, $x2 + $shade, $y1 - $shade, $x2 + $shade, $y2 - $shade);
            }
            ImageFilledPolygon($this->img, $pts, count($pts) / 2, $shade_color);
        }

        // Draw a border around the bar, if enabled.
        if (isset($border_color)) {
            // Avoid a PHP/GD bug with zero-height ImageRectangle resulting in "T"-shaped ends.
            if ($y1 == $y2)
                imageline($this->img, $x1, $y1, $x2, $y2, $border_color);
            else
                imagerectangle($this->img, $x1, $y1, $x2, $y2, $border_color);
        }
        $this->DoCallback('data_points', 'rect', $row, $column, $x1, $y1, $x2, $y2);
        return TRUE;
    }

    /**
     * Draws an error bar set for horizontal plots, showing +/- error in X
     *
     * @param float $x  X world coordinate of the data point (dependent variable)
     * @param float $y  Y world coordinate of the data point (independent variable)
     * @param float $error_plus  X error offset above $x (world coordinates >= 0)
     * @param float $error_minus  X error offset below $x (world coordinates >= 0)
     * @param int $color  Color to use for the error bars
     * @return bool  True always
     * @since 6.1.0
     */
    protected function DrawXErrorBars($x, $y, $error_plus, $error_minus, $color)
    {
        $x1 = $this->xtr($x);
        $y1 = $this->ytr($y);
        $x2p = $this->xtr($x + $error_plus);
        $x2m = $this->xtr($x - $error_minus);

        imagesetthickness($this->img, $this->error_bar_line_width);
        imageline($this->img, $x2p, $y1 , $x2m, $y1, $color);
        if ($this->error_bar_shape == 'tee') {
            $e = $this->error_bar_size;
            imageline($this->img, $x2p, $y1 - $e, $x2p, $y1 + $e, $color);
            imageline($this->img, $x2m, $y1 - $e, $x2m, $y1 + $e, $color);
        }
        imagesetthickness($this->img, 1);
        return TRUE;
    }

    /**
     * Draws an error bar set for vertical plots, showing +/- error in Y
     *
     * @param float $x  X world coordinate of the data point (independent variable)
     * @param float $y  Y world coordinate of the data point (dependent variable)
     * @param float $error_plus  Y error offset above $y (world coordinates >= 0)
     * @param float $error_minus  Y error offset below $y (world coordinates >= 0)
     * @param int $color  Color to use for the error bars
     * @return bool  True always
     * @since 6.1.0
     */
    protected function DrawYErrorBars($x, $y, $error_plus, $error_minus, $color)
    {
        $x1 = $this->xtr($x);
        $y1 = $this->ytr($y);
        $y2p = $this->ytr($y + $error_plus);
        $y2m = $this->ytr($y - $error_minus);

        imagesetthickness($this->img, $this->error_bar_line_width);
        imageline($this->img, $x1, $y2p , $x1, $y2m, $color);
        if ($this->error_bar_shape == 'tee') {
            $e = $this->error_bar_size;
            imageline($this->img, $x1 - $e, $y2p, $x1 + $e, $y2p, $color);
            imageline($this->img, $x1 - $e, $y2m, $x1 + $e, $y2m, $color);
        }
        imagesetthickness($this->img, 1);
        return TRUE;
    }

    /**
     * Sets up the default pie chart label type and format
     *
     * If SetPieLabelType() was not called, this function set the default.
     * The default for pie chart labels is to show the slice percentage,
     * with fixed point precision.  For backward compatibility with
     * PHPlot <= 5.5.0, the Y label data precision (if set) is the default
     * precision used.
     *
     * @return string[]  A value to use as pie_label_source in FormatPieLabel()
     * @since 5.6.0
     */
    protected function CheckPieLabels()
    {
        if (empty($this->pie_label_source)) { // SetPieLabelType() was not called, or was reset to default
            $prec = isset($this->label_format['y']['precision']) ?  $this->label_format['y']['precision'] : 1;
            $this->SetLabelType('p', array('data', $prec, '', '%'));
            return array('percent'); // Default to 'percent' labels (leaving this->pie_label_source empty)
        }
        return $this->pie_label_source; // Use label type set set with SetPieLabelType()
    }

    /**
     * Sets up for an area plot, calculating a points list and drawing data labels
     *
     * This is used for area fill plots: [stacked]area and [stacked]squaredarea.
     * It converts the data array to device coordinate arrays. This also
     * draws the axis data labels (if enabled).  Caller ensures there are at
     * least 2 rows (X), and all rows have same number of columns (Y).
     * Note that the returned $yd array has an extra column for points along
     * the X axis. See comment below on 'artifical Y value'.
     * This does not support missing points or data value labels.
     *
     * @param bool $stacked  True for a stacked plot (cumulative Y), false if not
     * @param int[] $xd  Reference variable - returned array with X device coordinates
     * @param int[] $yd  Reference variable - returned 2D array with Y device coordinates
     * @return int  Number of columns in yd[][], which is $this->data_columns + 1
     * @since 6.2.0
     */
    protected function SetupAreaPlot($stacked, &$xd, &$yd)
    {
        $xd = array();
        $yd = array();

        // Outer loop over rows (X); inner over columns (Y):
        for ($row = 0; $row < $this->num_data_rows; $row++) {
            $rec = 1;                                       // Skip record #0 (data label)

            if ($this->datatype_implied)                    // Implied X values?
                $x_now = 0.5 + $row;                        // Place text-data at X = 0.5, 1.5, 2.5, etc...
            else
                $x_now = $this->data[$row][$rec++];         // Read it, advance record index

            $xd[$row] = $x_now_pixels = $this->xtr($x_now); // Save in device coordinates

            if ($this->x_data_label_pos != 'none')          // Draw X Data labels?
                $this->DrawXDataLabel($this->data[$row][0], $x_now_pixels, $row);

            // There is an artificial Y value at the X axis. For stacked plots, it goes before the
            // first real Y, so the first area fill is from the axis to the first Y data set.
            // For non-stacked plots, it goes after the last Y, so the last area fill is from axis
            // to the last Y data set.
            if ($stacked)
                $yd[$row] = array($this->x_axis_y_pixels);
            else
                $yd[$row] = array();

            // Store the Y values for this X. Missing Y values are not supported, and are replaced with 0.
            // Negative numbers are not supported, and are replaced with absolute values.
            // The resulting numbers are also clipped to the X axis' Y value (which can be > 0).
            $y = 0; // Accumulate (if not reset below) the Y values
            for ($idx = 0; $rec < $this->records_per_group; $rec++, $idx++) {
                if (is_numeric($y_now = $this->data[$row][$rec]))
                    $y += abs($y_now);
                $yd[$row][] = $this->ytr(max($this->x_axis_position, $y));
                if (!$stacked) $y = 0; // For non-stacked plots, reset Y in each loop.
            }
            // See above: For non-stacked plots, the Y value for X axis goes at the end.
            if (!$stacked)
                $yd[$row][] = $this->x_axis_y_pixels;
        }
        return ($this->data_columns + 1); // This is the size of each yd[][]
    }

    /**
     * Draws the data borders for an area fill plot
     *
     * This is used by area fill plots (area, squaredarea, and their stacked
     * variants) to draw the data borders, if enabled.
     *
     * @param int $n_columns  Number of columns in $yd, returned by SetupAreaPlot()
     * @param int[] $xd  X device coordinate array from SetupAreaPlot()
     * @param int[] $yd  Y device coordinate array from SetupAreaPlot()
     * @param bool $stacked  True for a stacked plot (cumulative Y), false if not
     * @param bool $stepped  True for a stepped (squared) plot, false for a regular area plot
     * @return bool  True always
     * @since 6.2.0
     */
     function DrawAreaFillBorders($n_columns, $xd, $yd, $stacked, $stepped)
     {
        for ($col = 1; $col < $n_columns; $col++) {
            $color = $this->ndx_data_border_colors[$col-1];
            // This is due to the difference in the $yd array for stacked and unstacked.
            if ($stacked) {
                $this_col = $col;         // Border follows column = 1 to N-1
                $other_col = $col - 1;    // Left and right edges use the previous column
            } else {
                $this_col = $col - 1;     // Border follows column = 0 to N-2
                $other_col = $col;        // Left and right edges use the next column
            }

            // Left edge:
            $x = $xd[0];
            $y = $yd[0][$this_col];
            ImageLine($this->img, $x, $yd[0][$other_col], $x, $y, $color);

            // Across the top, with an 'X then Y' step at each point:
            for ($row = 1; $row < $this->num_data_rows; $row++) {
                $prev_x = $x;
                $prev_y = $y;
                $x = $xd[$row];
                $y = $yd[$row][$this_col];
                if ($stepped) {
                    ImageLine($this->img, $prev_x, $prev_y, $x, $prev_y, $color);
                    ImageLine($this->img, $x, $prev_y, $x, $y, $color);
                } else {
                    ImageLine($this->img, $prev_x, $prev_y, $x, $y, $color);
                }
            }

            // Right edge:
            ImageLine($this->img, $x, $y, $x, $yd[$this->num_data_rows - 1][$other_col], $color);
        }
        return TRUE;
     }

/////////////////////////////////////////////
////////////////////             PLOT DRAWING
/////////////////////////////////////////////

    /**
     * Draws a pie plot (Pie chart)
     *
     * This is the main function for drawing a pie chart.  Supported data
     * types are 'text-data', 'data-data', and 'text-data-single'.
     *
     * For text-data-single, the data array contains records with a label and
     * one Y value.  Each record defines a sector of the pie, as a portion of
     * the sum of all Y values.  Data labels are ignored by default, but can
     * be selected for display with SetPieLabelType().
     *
     * For text-data and data-data, the data array contains records with an
     * ignored label, an ignored X value for data-data only, and N (N>=1) Y
     * values per record.  The pie chart will be produced with N segments. The
     * relative size of the first sector of the pie is the sum of the first Y
     * data value in each record, etc.  The data labels cannot be used, since
     * they don't map to specific pie sectors.
     *
     * If there are no valid positive data points at all, just draw nothing.
     * It may seem more correct to raise an error, but all of the other plot
     * types handle it this way implicitly. DrawGraph() checks for an empty
     * data array, but this handles a non-empty data array with no Y values,
     * or all Y=0.
     *
     * @return bool  True (False on error if an error handler returns True)
     *
     */
    protected function DrawPieChart()
    {
        // Early checks and initialization:
        if (!$this->CheckDataType('text-data, text-data-single, data-data'))
            return FALSE;

        // SetLabelScalePosition(0 or FALSE) means no labels.
        $do_labels = !empty($this->label_scale_position);
        if ($do_labels) {
            // Validate and get default for pie chart label source and format:
            $pie_label_source = $this->CheckPieLabels();
            // Labels outside (vs inside) the pie? If so, pie size will need adjusting.
            $labels_outside = $this->label_scale_position >= 0.5;  // Only defined if ($do_labels)
        }

        // Draw segment borders? Default is True for unshaded, False for shaded
        $do_borders = isset($this->draw_pie_borders) ? $this->draw_pie_borders : ($this->shading == 0);

        $max_data_colors = count($this->ndx_data_colors); // Number of colors available

        // Check shading. Diameter factor $diam_factor is (height / width)
        if ($this->shading > 0) {
            $diam_factor = $this->pie_diam_factor;
            $this->NeedDataDarkColors(); // Dark colors are needed for shading
        } else {
            $diam_factor = 1.0; // Unshaded pies are always round, width == height
        }

        // Pie center point is always the center of the plot area, regardless of label sizes.
        $xpos = $this->plot_area[0] + $this->plot_area_width/2;
        $ypos = $this->plot_area[1] + $this->plot_area_height/2;

        // Reduce the data array into sumarr[], accounting for the data type:
        $num_slices = $this->data_columns;  // See CheckDataArray which calculates this for us.
        if ($num_slices < 1) return TRUE;   // Give up early if there is no data at all.
        $sumarr = array_fill(0, $num_slices, 0); // Initialize array of per-sector sums.

        if ($this->datatype_pie_single) {
            // text-data-single: One data column per row, one pie slice per row.
            for ($i = 0; $i < $num_slices; $i++) {
                if (is_numeric($val = $this->data[$i][1]))
                    $sumarr[$i] = abs($val);
            }
        } else {
            // text-data: Sum each column (skipping label), one pie slice per column.
            // data-data: Sum each column (skipping X value and label), one pie slice per column.
            $skip = ($this->datatype_implied) ? 1 : 2; // Leading values to skip in each row.
            for ($i = 0; $i < $this->num_data_rows; $i++) {
                for ($j = $skip; $j < $this->num_recs[$i]; $j++) {
                    if (is_numeric($val = $this->data[$i][$j]))
                        $sumarr[$j-$skip] += abs($val);
                }
            }
        }

        $total = array_sum($sumarr);
        if ($total == 0) {
            // There are either no valid data points, or all are 0.
            // See top comment about why not to make this an error.
            return TRUE;
        }

        // Pre-calculate the label strings, if labels are on. Also get the maximum height and width
        // of the labels, to use in sizing the pie chart (if the labels are outside the pie).
        // This is an overly pessimistic approach - assumes the widest label is at 0 or 180 degrees - but
        // is much easier than calculating the exact space needed for all labels around the pie.
        // For more detailed comments on the in-loop calculations, see the second loop below where
        // the features are actually drawn.
        // Note this is going around the pie, with angles specified, but we do not yet know the pie size.

        $label_max_width = 0;  // Widest label width, in pixels
        $label_max_height = 0; // Tallest label height, in pixels
        if ($do_labels) {
            $labels = array(); // Array to store the formatted label strings
            $end_angle = $start_angle = $this->pie_start_angle;
            for ($j = 0; $j < $num_slices; $j++) {
                $slice_weight = $sumarr[$j];
                $arc_angle = 360 * $slice_weight / $total;
                if ($this->pie_direction_cw) {
                    $end_angle = $start_angle;
                    $start_angle -= $arc_angle;
                } else {
                    $start_angle = $end_angle;
                    $end_angle += $arc_angle;
                }
                $arc_start_angle = (int)(360 - $start_angle);
                $arc_end_angle = (int)(360 - $end_angle);
                if ($arc_start_angle > $arc_end_angle) { // Skip segments with angle < 1 degree
                    $labels[$j] = $this->FormatPieLabel($j, $pie_label_source, $arc_angle, $slice_weight);
                    if ($labels_outside) {   // Labels are outside the pie chart
                        list($width, $height) = $this->SizeText('generic', 0, $labels[$j]);
                        if ($width > $label_max_width) $label_max_width = $width;
                        if ($height > $label_max_height) $label_max_height = $height;
                    }
                }
            }
        }

        // Calculate the maximum available area for the pie, leaving room for labels (if outside the pie):
        // This can be overridden by using SetPieAutoSize(FALSE), which sets the flag: pie_full_size=TRUE.
        if ($do_labels && $labels_outside && !$this->pie_full_size) {
            // There needs to be safe_margin between the labels and the plot area margins, and at least
            // safe_margin between the labels and the pie edge (this is LR_marg and TB_marg below).
            //    plot_area_width = avail_width + 2 * (LR_marg + label_width + safe_margin)
            //        Where LR_marg = max(safe_margin, avail_width * label_scale_position - avail_width/2)
            //    plot_area_height = avail_height + 2 * (TB_marg + label_height + safe_margin + shading)
            //        Where TB_marg = max(safe_margin, avail_height * label_scale_position - avail_height/2)
            //        Note shading is on bottom only, but since center is fixed, it is counted on top too.
            // Note (avail_width * label_scale_position) is the distance from the pie center to the label
            // text base point. Subtract avail_width/2 to get the inner margin (unless it is too small).
            // Similar for Y: avail_height * label_scale_position - avail_height/2 is the distance from
            // the pie center up to the label text base point.

            // Calculate available space for both values of LR_marg, TB_marg and take the smaller ones.
            $avail_width = min(
                ($this->plot_area_width / 2 - $label_max_width - $this->safe_margin) /
                    $this->label_scale_position,
                 $this->plot_area_width - 4 * $this->safe_margin - 2 * $label_max_width);

            $avail_height = min(
                 ($this->plot_area_height / 2 - $label_max_height - $this->safe_margin - $this->shading) /
                     $this->label_scale_position,
                  $this->plot_area_height - 4*$this->safe_margin - 2*($label_max_height + $this->shading));

            // Sanity check - don't let large labels shrink the pie too much.
            $avail_width = max($avail_width, $this->pie_min_size_factor * $this->plot_area_width);
            $avail_height = max($avail_height, $this->pie_min_size_factor * $this->plot_area_height);
        } else {     // No adjustment needed for labels
            $avail_width = $this->plot_area_width - 2 * $this->safe_margin;
            // Note shading is only on bottom, but need to subtract 2x because center does not move.
            $avail_height = $this->plot_area_height - 2 * ($this->safe_margin + $this->shading);
        }

        // Calculate the pie width and height for the best fit, given diam_factor and available space:
        if ($avail_height / $avail_width > $diam_factor) {
            $pie_width = $avail_width;
            $pie_height = $pie_width * $diam_factor;
        } else {
            $pie_height = $avail_height;
            $pie_width = $pie_height / $diam_factor;
        }

        // Factors used to calculate label positions by DrawPieLabel(). See there for explanation.
        if ($do_labels) {
            $r['reverse'] =  0.25 < $this->label_scale_position && $this->label_scale_position < 0.5;
            $r['x'] = $pie_width * $this->label_scale_position;
            $r['y'] = $pie_height * $this->label_scale_position;
            if ($labels_outside) {
                // Don't let outside labels touch the pie edge - move them out a bit:
                $r['x'] = max($r['x'], $pie_width / 2 + $this->safe_margin);
                $r['y'] = max($r['y'], $pie_height / 2 + $this->safe_margin);
            } else {
                // Don't let inside labels touch the pie edge - move them in a bit:
                $r['x'] = min($r['x'], $pie_width / 2 - $this->safe_margin);
                $r['y'] = min($r['y'], $pie_height / 2 - $this->safe_margin);
            }
        }

        // Draw the pie. For shaded pies, draw one set for each shading level ($h).
        for ($h = $this->shading; $h >= 0; $h--) {
            $color_index = 0;

            // Initialize the start angle (for clockwise) or end angle (for counter-clockwise).
            // See "Calculate the two angles" below to make sense of this.
            $end_angle = $start_angle = $this->pie_start_angle;

            // Loop over all pie segments:
            for ($j = 0; $j < $num_slices; $j++) {
                $slice_weight = $sumarr[$j];
                $arc_angle = 360 * $slice_weight / $total;

                // For shaded pies: the last one (at the top of the "stack") has a brighter color:
                if ($h == 0)
                    $slicecol = $this->ndx_data_colors[$color_index];
                else
                    $slicecol = $this->ndx_data_dark_colors[$color_index];

                // Calculate the two angles that define this pie segment.
                // Note that regardless of the direction (CW or CCW), start_angle < end_angle.
                if ($this->pie_direction_cw) {
                    $end_angle = $start_angle;
                    $start_angle -= $arc_angle;
                } else {
                    $start_angle = $end_angle;
                    $end_angle += $arc_angle;
                }

                // Calculate the arc angles for ImageFilledArc(), which measures angles in the opposite
                // direction (counter-clockwise), and only takes integer values.
                $arc_start_angle = (int)(360 - $start_angle);
                $arc_end_angle = (int)(360 - $end_angle);
                // Don't try to draw a 0 degree slice - it would make a full circle.
                if ($arc_start_angle > $arc_end_angle) {
                    // Draw the slice
                    ImageFilledArc($this->img, $xpos, $ypos+$h, $pie_width, $pie_height,
                                   $arc_end_angle, $arc_start_angle, $slicecol, IMG_ARC_PIE);

                    // Processing to do only for the last (if shaded) or only (if unshaded) loop:
                    if ($h == 0) {
                        // Draw the pie segment outline (if enabled):
                        if ($do_borders) {
                            ImageFilledArc($this->img, $xpos, $ypos, $pie_width, $pie_height,
                                           $arc_end_angle, $arc_start_angle, $this->ndx_pieborder_color,
                                           IMG_ARC_PIE | IMG_ARC_EDGED |IMG_ARC_NOFILL);
                        }

                        // Draw the label:
                        if ($do_labels)
                            $this->DrawPieLabel($labels[$j], $xpos, $ypos, $start_angle, $arc_angle, $r);
                        // Trigger a data points callback; note it gets the calculated (reversed) angles:
                        $this->DoCallback('data_points', 'pie', $j, 0, $xpos, $ypos, $pie_width,
                                          $pie_height, $arc_start_angle, $arc_end_angle);
                    }
                }
                if (++$color_index >= $max_data_colors)
                    $color_index = 0;
            }   // end loop for each slice
        }   // end loop for each level of shading
        return TRUE;
    }

    /**
     * Draws a points plot, or the points for a linepoints plot
     *
     * This is the main function for drawing a points plot, and is also used
     * for a linepoints plot. Vertical and Horizontal plots, and error plots,
     * are all supported. "iv" is used for the independent variable (X for
     * vertical plots, Y for horizontal) and "dv" is used for the dependent
     * variable (Y or X respectively).
     *
     * When $paired is true, a linepoints plot is being drawn, and some
     * elements are suppressed here because they are done elsewhere. See
     * DrawLinePoints() for details.
     *
     * @param bool $paired  True if doing a linepoints plot, False or omit for points plot
     * @return bool  True (False on error if an error handler returns True)
     */
    protected function DrawDots($paired = FALSE)
    {
        if (!$this->CheckDataType('text-data, data-data, text-data-yx, data-data-yx, '
                                . 'data-data-error, data-data-yx-error'))
            return FALSE;

        // Adjust the point shapes and point sizes arrays:
        $this->CheckPointParams();

        $gcvars = array(); // For GetDataColor, which initializes and uses this.
        // Special flag for data color callback to indicate the 'points' part of 'linepoints':
        $alt_flag = $paired ? 1 : 0;

        // Data labels, Data Value Labels? (Skip if doing the points from a linepoints plot)
        if ($this->datatype_swapped_xy) {
            // Horizontal plots can have X Data Value Labels, Y Axis Data Labels
            $do_x_axis_labels = FALSE;
            $do_x_valu_labels = !$paired && $this->CheckDataValueLabels($this->x_data_label_pos, $dvl);
            $do_y_axis_labels = !$paired && $this->y_data_label_pos != 'none';
            $do_y_valu_labels = FALSE;
        } else {
            // Vertical plots can have X Axis Data Labels, Y Data Value Labels
            $do_x_axis_labels = !$paired && $this->x_data_label_pos != 'none';
            $do_x_valu_labels = FALSE;
            $do_y_axis_labels = FALSE;
            $do_y_valu_labels = !$paired && $this->CheckDataValueLabels($this->y_data_label_pos, $dvl);
        }

        for ($row = 0; $row < $this->num_data_rows; $row++) {
            $rec = 1;                    // Skip record #0 (data label)

            if ($this->datatype_implied)                // Implied independent variable values?
                $iv = 0.5 + $row;                       // Place text-data at 0.5, 1.5, 2.5, etc...
            else
                $iv = $this->data[$row][$rec++];        // Read it, advance record index

            // Axis data label?
            if ($do_x_axis_labels)
                $this->DrawXDataLabel($this->data[$row][0], $this->xtr($iv), $row, TRUE);
            elseif ($do_y_axis_labels)
                $this->DrawYDataLabel($this->data[$row][0], $this->ytr($iv), $row, TRUE);

            // Proceed with dependent values
            for ($idx = 0; $rec < $this->num_recs[$row]; $idx++) {
                if (is_numeric($dv = $this->data[$row][$rec++])) {      // Allow for missing data

                    // Select the color(s):
                    if ($this->datatype_error_bars) {
                        $this->GetDataErrorColors($row, $idx, $gcvars, $data_color, $error_color, $alt_flag);
                    } else {
                        $this->GetDataColor($row, $idx, $gcvars, $data_color, $alt_flag);
                    }

                    // Draw the marker, and error bar (if enabled):
                    if ($this->datatype_swapped_xy) {
                        $this->DrawDot($row, $idx, $dv, $iv, $data_color);
                        if ($this->datatype_error_bars) {
                            $this->DrawXErrorBars($dv, $iv, $this->data[$row][$rec],
                                                  $this->data[$row][$rec+1], $error_color);
                        }
                    } else {
                        $this->DrawDot($row, $idx, $iv, $dv, $data_color);
                        if ($this->datatype_error_bars) {
                            $this->DrawYErrorBars($iv, $dv, $this->data[$row][$rec],
                                                  $this->data[$row][$rec+1], $error_color);
                        }
                    }

                    // Draw data value labels?
                    if ($do_y_valu_labels) { // Vertical plot
                        $this->DrawDataValueLabel('y', $row, $idx, $iv, $dv, $dv, $dvl);
                    } elseif ($do_x_valu_labels) { // Horizontal plot
                        $this->DrawDataValueLabel('x', $row, $idx, $dv, $iv, $dv, $dvl);
                    }
                }
                if ($this->datatype_error_bars) {
                    $rec += 2; // Skip over error bar values, even in missing data case.
                }
            }
        }
        return TRUE;
    }

    /**
     * Draws a thinbarline plot (Thin Bar Line)
     *
     * This is the main function for drawing a thinbarline plot, which
     * is also known as an Impulse plot. Supported data types are
     * data-data and text-data for vertical plots, and data-data-yx and
     * text-data-yx for horizontal plots. "iv" is used for the independent
     * variable (X for vertical plots, Y for horizontal) and "dv" is used
     * for the dependent variable (Y or X respectively).
     *
     * Although this plot type supports multiple data sets, it rarely makes
     * sense to have more than one, because the lines will overlay.
     *
     * @return bool  True (False on error if an error handler returns True)
     */
    protected function DrawThinBarLines()
    {
        if (!$this->CheckDataType('text-data, data-data, text-data-yx, data-data-yx'))
            return FALSE;

        $gcvars = array(); // For GetDataColor, which initializes and uses this.

        for ($row = 0; $row < $this->num_data_rows; $row++) {
            $rec = 1;                    // Skip record #0 (data label)

            if ($this->datatype_implied)                    // Implied independent variable values?
                $iv_now = 0.5 + $row;                       // Place text-data at 0.5, 1.5, 2.5, etc...
            else
                $iv_now = $this->data[$row][$rec++];        // Read it, advance record index

            if ($this->datatype_swapped_xy) {
                $y_now_pixels = $this->ytr($iv_now);
                // Draw Y Data labels?
                if ($this->y_data_label_pos != 'none')
                    $this->DrawYDataLabel($this->data[$row][0], $y_now_pixels, $row);
            } else {
                $x_now_pixels = $this->xtr($iv_now);
                // Draw X Data labels?
                if ($this->x_data_label_pos != 'none')
                    $this->DrawXDataLabel($this->data[$row][0], $x_now_pixels, $row);
            }

            // Proceed with dependent values
            for ($idx = 0; $rec < $this->num_recs[$row]; $rec++, $idx++) {
                if (is_numeric($dv = $this->data[$row][$rec])) {          // Allow for missing data
                    ImageSetThickness($this->img, $this->line_widths[$idx]);

                    // Select the color:
                    $this->GetDataColor($row, $idx, $gcvars, $data_color);

                    if ($this->datatype_swapped_xy) {
                        // Draw a line from user defined y axis position right (or left) to xtr($dv)
                        ImageLine($this->img, $this->y_axis_x_pixels, $y_now_pixels,
                                              $this->xtr($dv), $y_now_pixels, $data_color);
                    } else {
                        // Draw a line from user defined x axis position up (or down) to ytr($dv)
                        ImageLine($this->img, $x_now_pixels, $this->x_axis_y_pixels,
                                              $x_now_pixels, $this->ytr($dv), $data_color);
                   }
                }
            }
        }

        ImageSetThickness($this->img, 1);
        return TRUE;
    }

    /**
     * Draws an area or stackedarea plot
     *
     * This is the main function for drawing area and stackedarea plots.  Both
     * of these fill the area between lines, but 'stackedarea' is cumulative (like
     * stackedbars), and 'area' is not. Also 'area' fills from the last data set to
     * the X axis, and 'stackedarea' fills from the X axis to the first data set.
     * 'area' and 'stackedarea' plots are identical when there is only one data set.
     *
     * Supported data types are data-data and text-data.  All Y values must be
     * >= 0 (with absolute value used if any negative values are found).
     * Missing data points are not supported (any missing points are set to
     * 0).  All rows must have the same number of Y points, or an error will
     * be produced.
     *
     * @param bool $do_stacked  True for stackedarea plot, false or omit for area plot
     * @return bool  True (False on error if an error handler returns True)
     */
    protected function DrawArea($do_stacked = FALSE)
    {
        if (!$this->CheckDataType('text-data, data-data'))
            return FALSE;

        // Validation: Need at least 2 rows; all rows must have same number of columns.
        if (($n_rows = $this->num_data_rows) < 2) return TRUE;
        if ($this->records_per_group != min($this->num_recs)) {
            return $this->PrintError("DrawArea(): Data array must contain the same number"
                      . " of Y values for each X");
        }

		// Calculate and store device coordinates xd[] and yd[][], and draw the data labels.
        $n_columns = $this->SetupAreaPlot($do_stacked, $xd, $yd);

        // Draw the filled polygons.
        // Note data_columns is the number of Y points (columns excluding label and X), and the
        // number of entries in the yd[] arrays is data_columns+1.
        $prev_col = 0;
        for ($col = 1; $col < $n_columns; $col++) { // 1 extra for X axis artificial column
            $pts = array();
            // Previous data set forms top (for area) or bottom (for stackedarea):
            for ($row = 0; $row < $n_rows; $row++) {
                array_push($pts, $xd[$row], $yd[$row][$prev_col]);
            }
            // Current data set forms bottom (for area) or top (for stackedarea):
            for ($row = $n_rows - 1; $row >= 0; $row--) {
                array_push($pts, $xd[$row], $yd[$row][$col]);
            }
            // Draw it:
            ImageFilledPolygon($this->img, $pts, $n_rows * 2, $this->ndx_data_colors[$prev_col]);

            $prev_col = $col;
        }

        // Draw the data borders, if enabled. (After, else the area fills cover parts of it.)
        if (!empty($this->draw_data_borders))
            $this->DrawAreaFillBorders($n_columns, $xd, $yd, $do_stacked, FALSE);

        return TRUE;
    }

    /**
     * Draws a lines plot, or the lines for a linepoints plot
     *
     * This is the main function for drawing a lines plot, and is also used
     * for a linepoints plot. Vertical and Horizontal plots, and error plots,
     * are all supported. "iv" is used for the independent variable (X for
     * vertical plots, Y for horizontal) and "dv" is used for the dependent
     * variable (Y or X respectively).
     *
     * When $paired is true, a linepoints plot is being drawn, and some
     * elements are suppressed here because they are done elsewhere. See
     * DrawLinePoints() for details.
     *
     * @param bool $paired  True if doing a linepoints plots, False or omit for lines plot
     * @return bool  True (False on error if an error handler returns True)
     */
    protected function DrawLines($paired = FALSE)
    {
        if (!$this->CheckDataType('text-data, data-data, text-data-yx, data-data-yx, '
                                . 'data-data-error, data-data-yx-error'))
            return FALSE;

        // Flag array telling if the current point is valid, one element per plot line.
        // If start_lines[i] is true, then (lastx[i], lasty[i]) is the previous point.
        if ($this->data_columns > 0)
            $start_lines = array_fill(0, $this->data_columns, FALSE);

        $gcvars = array(); // For GetDataColor, which initializes and uses this.

        // Data labels, Data Value Labels?
        if ($this->datatype_swapped_xy) {
            // Horizontal plots can have X Data Value Labels, Y Axis Data Labels
            $do_x_axis_labels = FALSE;
            $do_x_valu_labels = $this->CheckDataValueLabels($this->x_data_label_pos, $dvl);
            $do_y_axis_labels = $this->y_data_label_pos != 'none';
            $do_y_valu_labels = FALSE;
        } else {
            // Vertical plots can have X Axis Data Labels, Y Data Value Labels
            $do_x_axis_labels = $this->x_data_label_pos != 'none';
            $do_x_valu_labels = FALSE;
            $do_y_axis_labels = FALSE;
            $do_y_valu_labels = $this->CheckDataValueLabels($this->y_data_label_pos, $dvl);
        }

        for ($row = 0; $row < $this->num_data_rows; $row++) {
            $rec = 1;                                   // Skip record #0 (data label)

            if ($this->datatype_implied)                // Implied X values?
                $iv = 0.5 + $row;                       // Place text-data at X = 0.5, 1.5, 2.5, etc...
            else
                $iv = $this->data[$row][$rec++];        // Get actual X value from array

            // Convert independent variable to device coordinates
            if ($this->datatype_swapped_xy) {
                $y_now_pixels = $this->ytr($iv);
            } else {
                $x_now_pixels = $this->xtr($iv);
            }

            // Axis data label?
            if ($do_x_axis_labels)
                $this->DrawXDataLabel($this->data[$row][0], $x_now_pixels, $row, TRUE);
            elseif ($do_y_axis_labels)
                $this->DrawYDataLabel($this->data[$row][0], $y_now_pixels, $row, TRUE);

            // Proceed with dependent values
            for ($idx = 0; $rec < $this->num_recs[$row]; $idx++) {
                $line_style = $this->line_styles[$idx];

                // Skip point if data value is missing. Also skip if the whole line is suppressed
                // with style='none' (useful with linepoints plots)
                if (is_numeric($dv = $this->data[$row][$rec++]) && $line_style != 'none') {

                    // Convert dependent variable to device coordinates
                    if ($this->datatype_swapped_xy) {
                        $x_now_pixels = $this->xtr($dv);
                    } else {
                        $y_now_pixels = $this->ytr($dv);
                    }

                    // Select the color(s):
                    if ($this->datatype_error_bars) {
                        $this->GetDataErrorColors($row, $idx, $gcvars, $data_color, $error_color);
                    } else {
                        $this->GetDataColor($row, $idx, $gcvars, $data_color);
                    }

                    if ($start_lines[$idx]) {
                        // Set line width, revert it to normal at the end
                        ImageSetThickness($this->img, $this->line_widths[$idx]);

                        // Select solid color or dashed line
                        $style = $this->SetDashedStyle($data_color, $line_style == 'dashed');

                        // Draw the line segment:
                        ImageLine($this->img, $x_now_pixels, $y_now_pixels,
                                  $lastx[$idx], $lasty[$idx], $style);
                    }

                    // Draw error bars, but not for linepoints plots, because DrawPoints() does it.
                    if ($this->datatype_error_bars && !$paired) {
                        if ($this->datatype_swapped_xy) {
                            $this->DrawXErrorBars($dv, $iv, $this->data[$row][$rec],
                                                  $this->data[$row][$rec+1], $error_color);
                        } else {
                            $this->DrawYErrorBars($iv, $dv, $this->data[$row][$rec],
                                                  $this->data[$row][$rec+1], $error_color);
                        }
                    }

                    // Draw data value labels?
                    if ($do_y_valu_labels) // Vertical plot
                        $this->DrawDataValueLabel('y', $row, $idx, $iv, $dv, $dv, $dvl);
                    elseif ($do_x_valu_labels) // Horizontal plot
                        $this->DrawDataValueLabel('x', $row, $idx, $dv, $iv, $dv, $dvl);

                    $lastx[$idx] = $x_now_pixels;
                    $lasty[$idx] = $y_now_pixels;
                    $start_lines[$idx] = TRUE;
                } elseif ($this->draw_broken_lines) {
                    $start_lines[$idx] = FALSE; // Missing point value or line style suppression
                }
                if ($this->datatype_error_bars)
                    $rec += 2; // Skip over error bar values, even in missing data case.
            }
        }

        ImageSetThickness($this->img, 1);       // Revert to original state for lines to be drawn later.
        return TRUE;
    }

    /**
     * Draws a linepoints plot (Lines and Points)
     *
     * This is the main function for drawing a linepoints plot. This just uses
     * DrawLines() to draw the lines, and DrawDots() to draw the points, so it
     * supports the same data types and variations as they do.
     *
     * The argument passed to the two drawing functions tells them not to
     * duplicate elements, as follows: DrawLines() draws the lines, not the
     * error bars (even if applicable), and the data labels.  DrawDots() draws
     * the points, the error bars (if applicable), and not the data labels.
     *
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.1.3
     */
    protected function DrawLinePoints()
    {
        return $this->DrawLines(TRUE) && $this->DrawDots(TRUE);
    }

    /**
     * Draws a squared plot (Squared Line, Stepped Line)
     *
     * This is the main function for drawing a squared plot.  Supported data
     * types are data-data and text-data.  This is based on DrawLines(), with
     * two line segments drawn for each point.
     *
     * @return bool  True (False on error if an error handler returns True)
     */
    protected function DrawSquared()
    {
        if (!$this->CheckDataType('text-data, data-data'))
            return FALSE;

        // Flag array telling if the current point is valid, one element per plot line.
        // If start_lines[i] is true, then (lastx[i], lasty[i]) is the previous point.
        if ($this->data_columns > 0)
            $start_lines = array_fill(0, $this->data_columns, FALSE);

        $gcvars = array(); // For GetDataColor, which initializes and uses this.

        // Data Value Labels?
        $do_dvls = $this->CheckDataValueLabels($this->y_data_label_pos, $dvl);

        for ($row = 0; $row < $this->num_data_rows; $row++) {
            $record = 1;                                    // Skip record #0 (data label)

            if ($this->datatype_implied)                    // Implied X values?
                $x_now = 0.5 + $row;                        // Place text-data at X = 0.5, 1.5, 2.5, etc...
            else
                $x_now = $this->data[$row][$record++];      // Read it, advance record index

            $x_now_pixels = $this->xtr($x_now);             // Absolute coordinates

            if ($this->x_data_label_pos != 'none')          // Draw X Data labels?
                $this->DrawXDataLabel($this->data[$row][0], $x_now_pixels, $row);

            // Draw Lines
            for ($idx = 0; $record < $this->num_recs[$row]; $record++, $idx++) {
                if (is_numeric($y_now = $this->data[$row][$record])) {         // Allow for missing Y data
                    $y_now_pixels = $this->ytr($y_now);

                    if ($start_lines[$idx]) {
                        // Set line width, revert it to normal at the end
                        ImageSetThickness($this->img, $this->line_widths[$idx]);

                        // Select the color:
                        $this->GetDataColor($row, $idx, $gcvars, $data_color);

                        // Select solid color or dashed line
                        $style = $this->SetDashedStyle($data_color, $this->line_styles[$idx] == 'dashed');

                        // Draw the step:
                        $y_mid = $lasty[$idx];
                        ImageLine($this->img, $lastx[$idx], $y_mid, $x_now_pixels, $y_mid, $style);
                        ImageLine($this->img, $x_now_pixels, $y_mid, $x_now_pixels, $y_now_pixels, $style);
                    }

                    // Draw data value labels?
                    if ($do_dvls)
                        $this->DrawDataValueLabel('y', $row, $idx, $x_now, $y_now, $y_now, $dvl);

                    $lastx[$idx] = $x_now_pixels;
                    $lasty[$idx] = $y_now_pixels;
                    $start_lines[$idx] = TRUE;
                } elseif ($this->draw_broken_lines) {  // Y data missing, leave a gap.
                    $start_lines[$idx] = FALSE;
                }
            }
        }

        ImageSetThickness($this->img, 1);
        return TRUE;
    }

    /**
     * Draws a squaredarea or stackedsquaredarea plot (Squared Area)
     *
     * This is the main function for drawing squaredarea and stackedsquaredarea plots,
     * which area a blend of 'squared' plus either 'area' or 'stackedarea'. Supported
     * data types are data-data and text-data.  Missing points are not allowed,
     * and all data sets must have the same number of points.
     *
     * @param bool $do_stacked  True for cumulative (stacked), false or omit for unstacked.
     * @return bool  True (False on error if an error handler returns True)
     */
    protected function DrawSquaredArea($do_stacked = FALSE)
    {
        if (!$this->CheckDataType('text-data, data-data'))
            return FALSE;

        // Validation: Need at least 2 rows; all rows must have same number of columns.
        if (($n_rows = $this->num_data_rows) < 2) return TRUE;
        if ($this->records_per_group != min($this->num_recs)) {
            return $this->PrintError("DrawSquaredArea(): Data array must contain the same number"
                      . " of Y values for each X");
        }

		// Calculate and store device coordinates xd[] and yd[][], and draw the data labels.
        $n_columns = $this->SetupAreaPlot($do_stacked, $xd, $yd);

        // Draw a filled polygon for each Y column
        $prev_col = 0;
        for ($col = 1; $col < $n_columns; $col++) { // 1 extra for X axis artificial column

            // Current data set forms the top. For each point after the first, add 2 points.
            $x_prev = $xd[0];
            $y_prev = $yd[0][$col];
            $pts = array($x_prev, $y_prev);  // Bottom left point
            for ($row = 1; $row < $n_rows; $row++) {
                $x = $xd[$row];
                $y = $yd[$row][$col];
                array_push($pts, $x, $y_prev, $x, $y);
                $x_prev = $x;
                $y_prev = $y;
            }

            // Previous data set forms the bottom. Process right to left.
            // Note $row is now $n_rows, and it will be stepped back to 0.
            $row--;
            $x_prev = $xd[$row];
            $y_prev = $yd[$row][$prev_col];
            array_push($pts, $x_prev, $y_prev); // Bottom right point
            while (--$row >= 0) {
                $x = $xd[$row];
                $y = $yd[$row][$prev_col];
                array_push($pts, $x_prev, $y, $x, $y);
                $x_prev = $x;
                $y_prev = $y;
            }

            // Draw the resulting polygon, which has (2 * (1 + 2*(n_rows-1))) points:
            ImageFilledPolygon($this->img, $pts, 4 * $n_rows - 2, $this->ndx_data_colors[$prev_col]);
            $prev_col = $col;
        }

        // Draw the data borders, if enabled. (After, else the area fills cover parts of it.)
        if (!empty($this->draw_data_borders))
            $this->DrawAreaFillBorders($n_columns, $xd, $yd, $do_stacked, TRUE);

        return TRUE;
    }

    /**
     * Draws a bars plot (Bar chart)
     *
     * This is the main function for drawing a bars plot.  Supported data
     * types are text-data, for vertical plots, and text-data-yx, for
     * horizontal plots (for which it calls DrawHorizBars()).
     *
     * @return bool  True (False on error if an error handler returns True)
     */
    protected function DrawBars()
    {
        if (!$this->CheckDataType('text-data, text-data-yx'))
            return FALSE;
        if ($this->datatype_swapped_xy)
            return $this->DrawHorizBars();
        $this->CalcBarWidths(FALSE, TRUE); // Calculate bar widths for unstacked, vertical

        // This is the X offset from the bar group's label center point to the left side of the first bar
        // in the group. See also CalcBarWidths above.
        $x_first_bar = ($this->data_columns * $this->record_bar_width) / 2 - $this->bar_adjust_gap;

        $gcvars = array(); // For GetBarColors, which initializes and uses this.

        for ($row = 0; $row < $this->num_data_rows; $row++) {
            $record = 1;                                    // Skip record #0 (data label)

            $x_now_pixels = $this->xtr(0.5 + $row);         // Place text-data at X = 0.5, 1.5, 2.5, etc...

            if ($this->x_data_label_pos != 'none')          // Draw X Data labels?
                $this->DrawXDataLabel($this->data[$row][0], $x_now_pixels, $row);

            // Lower left X of first bar in the group:
            $x1 = $x_now_pixels - $x_first_bar;

            // Draw the bars in the group:
            for ($idx = 0; $record < $this->num_recs[$row]; $record++, $idx++) {
                if (is_numeric($y = $this->data[$row][$record])) {    // Allow for missing Y data
                    $x2 = $x1 + $this->actual_bar_width;

                    if (($upgoing_bar = $y >= $this->x_axis_position)) {
                        $y1 = $this->ytr($y);
                        $y2 = $this->x_axis_y_pixels;
                    } else {
                        $y1 = $this->x_axis_y_pixels;
                        $y2 = $this->ytr($y);
                    }

                    // Select the colors:
                    $this->GetBarColors($row, $idx, $gcvars, $data_color, $shade_color, $border_color);

                    // Draw the bar, and the shade or border:
                    $this->DrawBar($row, $idx, $x1, $y1, $x2, $y2, $data_color, $shade_color, $border_color);

                    // Draw optional data value label above or below the bar:
                    if ($this->y_data_label_pos == 'plotin') {
                        $dvl['x_offset'] = ($idx + 0.5) * $this->record_bar_width - $x_first_bar;
                        if ($upgoing_bar) {
                            $dvl['v_align'] = 'bottom';
                            $dvl['y_offset'] = -5 - $this->shading;
                        } else {
                            $dvl['v_align'] = 'top';
                            $dvl['y_offset'] = 2;
                        }
                        $this->DrawDataValueLabel('y', $row, $idx, $row+0.5, $y, $y, $dvl);
                    }
                }
                // Step to next bar in group:
                $x1 += $this->record_bar_width;
            }
        }
        return TRUE;
    }

    /**
     * Draws a Horizontal Bar chart
     *
     * This is called from DrawBars() when the data type indicates a
     * horizontal plot.
     *
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.1.2
     */
    protected function DrawHorizBars()
    {
        $this->CalcBarWidths(FALSE, FALSE); // Calculate bar widths for unstacked, vertical

        // This is the Y offset from the bar group's label center point to the bottom of the first bar
        // in the group. See also CalcBarWidths above.
        $y_first_bar = ($this->data_columns * $this->record_bar_width) / 2 - $this->bar_adjust_gap;

        $gcvars = array(); // For GetBarColors, which initializes and uses this.

        for ($row = 0; $row < $this->num_data_rows; $row++) {
            $record = 1;                                    // Skip record #0 (data label)

            $y_now_pixels = $this->ytr(0.5 + $row);         // Place bars at Y=0.5, 1.5, 2.5, etc...

            if ($this->y_data_label_pos != 'none')          // Draw Y Data Labels?
                $this->DrawYDataLabel($this->data[$row][0], $y_now_pixels, $row);

            // Lower left Y of first bar in the group:
            $y1 = $y_now_pixels + $y_first_bar;

            // Draw the bars in the group:
            for ($idx = 0; $record < $this->num_recs[$row]; $record++, $idx++) {
                if (is_numeric($x = $this->data[$row][$record])) {    // Allow for missing X data
                    $y2 = $y1 - $this->actual_bar_width;

                    if (($rightwards_bar = $x >= $this->y_axis_position)) {
                        $x1 = $this->xtr($x);
                        $x2 = $this->y_axis_x_pixels;
                    } else {
                        $x1 = $this->y_axis_x_pixels;
                        $x2 = $this->xtr($x);
                    }

                    // Select the colors:
                    $this->GetBarColors($row, $idx, $gcvars, $data_color, $shade_color, $border_color);

                    // Draw the bar, and the shade or border:
                    $this->DrawBar($row, $idx, $x1, $y1, $x2, $y2, $data_color, $shade_color, $border_color);

                    // Draw optional data value label to the right or left of the bar:
                    if ($this->x_data_label_pos == 'plotin') {
                        $dvl['y_offset'] = $y_first_bar - ($idx + 0.5) * $this->record_bar_width;
                        if ($rightwards_bar) {
                            $dvl['h_align'] = 'left';
                            $dvl['x_offset'] = 5 + $this->shading;
                        } else {
                            $dvl['h_align'] = 'right';
                            $dvl['x_offset'] = -2;
                        }
                        $this->DrawDataValueLabel('x', $row, $idx, $x, $row+0.5, $x, $dvl);
                    }
                }
                // Step to next bar in group:
                $y1 -= $this->record_bar_width;
            }
        }
        return TRUE;
    }

    /**
     * Draws a stackedbars plot (Stacked Bar chart)
     *
     * This is the main function for drawing a stackedbars plot.  Supported
     * data types are text-data, for vertical plots, and text-data-yx, for
     * horizontal plots (for which it calls DrawHorizStackedBars()).
     * Original stacked bars idea by Laurent Kruk < lolok at users.sourceforge.net >
     *
     * @return bool  True (False on error if an error handler returns True)
     */
    protected function DrawStackedBars()
    {
        if (!$this->CheckDataType('text-data, text-data-yx'))
            return FALSE;
        if ($this->datatype_swapped_xy)
            return $this->DrawHorizStackedBars();
        $this->CalcBarWidths(TRUE, TRUE); // Calculate bar widths for stacked, vertical

        // This is the X offset from the bar's label center point to the left side of the bar.
        $x_first_bar = $this->record_bar_width / 2 - $this->bar_adjust_gap;

        $gcvars = array(); // For GetBarColors, which initializes and uses this.

        // Determine if any data labels are on:
        $data_labels_within = ($this->y_data_label_pos == 'plotstack');
        $data_labels_end = $data_labels_within || ($this->y_data_label_pos == 'plotin');
        $data_label_y_offset = -5 - $this->shading; // For upward labels only.

        for ($row = 0; $row < $this->num_data_rows; $row++) {
            $record = 1;                                    // Skip record #0 (data label)

            $x_now_pixels = $this->xtr(0.5 + $row);         // Place text-data at X = 0.5, 1.5, 2.5, etc...

            if ($this->x_data_label_pos != 'none')          // Draw X Data labels?
                $this->DrawXDataLabel($this->data[$row][0], $x_now_pixels, $row);

            // Determine bar direction based on 1st non-zero value. Note the bar direction is
            // based on zero, not the axis value.
            $n_recs = $this->num_recs[$row];
            $upward = TRUE; // Initialize this for the case of all segments = 0
            for ($i = $record; $i < $n_recs; $i++) {
                if (is_numeric($this_y = $this->data[$row][$i]) && $this_y != 0) {
                    $upward = ($this_y > 0);
                    break;
                }
            }

            $x1 = $x_now_pixels - $x_first_bar;  // Left X of bars in this stack
            $x2 = $x1 + $this->actual_bar_width; // Right X of bars in this stack
            $wy1 = 0;                            // World coordinates Y1, current sum of values
            $wy2 = $this->x_axis_position;       // World coordinates Y2, last drawn value

            // Draw bar segments and labels in this stack.
            $first = TRUE;
            for ($idx = 0; $record < $n_recs; $record++, $idx++) {

                // Skip missing Y values. Process Y=0 values due to special case of moved axis.
                if (is_numeric($this_y = $this->data[$row][$record])) {

                    $wy1 += $this_y;    // Keep the running total for this bar stack

                    // Draw the segment only if it will increase the stack height (ignore if wrong direction):
                    if (($upward && $wy1 > $wy2) || (!$upward && $wy2 > $wy1)) {

                        $y1 = $this->ytr($wy1); // Convert to device coordinates. $y1 is outermost value.
                        $y2 = $this->ytr($wy2); // $y2 is innermost (closest to axis).

                        // Select the colors:
                        $this->GetBarColors($row, $idx, $gcvars, $data_color, $shade_color, $border_color);

                        // Draw the bar, and the shade or border:
                        $this->DrawBar($row, $idx, $x1, $y1, $x2, $y2,
                            $data_color, $shade_color, $border_color,
                            // Only shade the top for upward bars, or the first segment of downward bars:
                            $upward || $first, TRUE);

                        // Draw optional data label for this bar segment just inside the end.
                        // Text value is the current Y, but position is the cumulative Y.
                        // The label is only drawn if it fits in the segment height |y2-y1|.
                        if ($data_labels_within) {
                            $dvl['min_height'] = abs($y1 - $y2);
                            if ($upward) {
                                $dvl['v_align'] = 'top';
                                $dvl['y_offset'] = 3;
                            } else {
                                $dvl['v_align'] = 'bottom';
                                $dvl['y_offset'] = -3;
                            }
                            $this->DrawDataValueLabel('y', $row, $idx, $row+0.5, $wy1, $this_y, $dvl);
                        }
                        // Mark the new end of the bar, conditional on segment height > 0.
                        $wy2 = $wy1;
                        $first = FALSE;
                    }
                }
            }   // end for

            // Draw optional data label above the bar with the total value.
            // Value is wy1 (total value), but position is wy2 (end of the bar stack).
            // These differ only with wrong-direction segments, or a stack completely clipped by the axis.
            if ($data_labels_end) {
                $dvl['min_height'] = NULL; // Might be set above, but the whole array might not exist.
                if ($upward) {
                    $dvl['v_align'] = 'bottom';
                    $dvl['y_offset'] = $data_label_y_offset;
                } else {
                    $dvl['v_align'] = 'top';
                    $dvl['y_offset'] = 5;
                }
                $this->DrawDataValueLabel('y', $row, NULL, $row+0.5, $wy2, $wy1, $dvl);
            }
        }   // end for
        return TRUE;
    }

    /**
     * Draws a Horizontal Stacked Bar chart
     *
     * This is called from DrawStackedBars() when the data type indicates a
     * horizontal plot.
     *
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.1.3
     */
    protected function DrawHorizStackedBars()
    {
        $this->CalcBarWidths(TRUE, FALSE); // Calculate bar widths for stacked, horizontal

        // This is the Y offset from the bar's label center point to the bottom of the bar
        $y_first_bar = $this->record_bar_width / 2 - $this->bar_adjust_gap;

        $gcvars = array(); // For GetBarColors, which initializes and uses this.

        // Determine if any data labels are on:
        $data_labels_within = ($this->x_data_label_pos == 'plotstack');
        $data_labels_end = $data_labels_within || ($this->x_data_label_pos == 'plotin');
        $data_label_x_offset = 5 + $this->shading; // For rightward labels only

        for ($row = 0; $row < $this->num_data_rows; $row++) {
            $record = 1;                                    // Skip record #0 (data label)

            $y_now_pixels = $this->ytr(0.5 + $row);         // Place bars at Y=0.5, 1.5, 2.5, etc...

            if ($this->y_data_label_pos != 'none')          // Draw Y Data labels?
                $this->DrawYDataLabel($this->data[$row][0], $y_now_pixels, $row);

            // Determine bar direction based on 1st non-zero value. Note the bar direction is
            // based on zero, not the axis value.
            $n_recs = $this->num_recs[$row];
            $rightward = TRUE; // Initialize this for the case of all segments = 0
            for ($i = $record; $i < $n_recs; $i++) {
                if (is_numeric($this_x = $this->data[$row][$i]) && $this_x != 0) {
                    $rightward = ($this_x > 0);
                    break;
                }
            }

            // Lower left and upper left Y of the bars in this stack:
            $y1 = $y_now_pixels + $y_first_bar;  // Lower Y of bars in this stack
            $y2 = $y1 - $this->actual_bar_width; // Upper Y of bars in this stack
            $wx1 = 0;                            // World coordinates X1, current sum of values
            $wx2 = $this->y_axis_position;       // World coordinates X2, last drawn value

            // Draw bar segments and labels in this stack.
            $first = TRUE;
            for ($idx = 0; $record < $this->num_recs[$row]; $record++, $idx++) {

                // Skip missing X values. Process X=0 values due to special case of moved axis.
                if (is_numeric($this_x = $this->data[$row][$record])) {

                    $wx1 += $this_x;  // Keep the running total for this bar stack

                    // Draw the segment only if it will increase the stack length (ignore if wrong direction):
                    if (($rightward && $wx1 > $wx2) || (!$rightward && $wx2 > $wx1)) {

                        $x1 = $this->xtr($wx1); // Convert to device coordinates. $x1 is outermost value.
                        $x2 = $this->xtr($wx2); // $x2 is innermost (closest to axis).

                        // Select the colors:
                        $this->GetBarColors($row, $idx, $gcvars, $data_color, $shade_color, $border_color);

                        // Draw the bar, and the shade or border:
                        $this->DrawBar($row, $idx, $x1, $y1, $x2, $y2,
                            $data_color, $shade_color, $border_color,
                            // Only shade the side for rightward bars, or the first segment of leftward bars:
                            TRUE, $rightward || $first);

                        // Draw optional data label for this bar segment just inside the end.
                        // Text value is the current X, but position is the cumulative X.
                        // The label is only drawn if it fits in the segment width |x2-x1|.
                        if ($data_labels_within) {
                            $dvl['min_width'] = abs($x1 - $x2);
                            if ($rightward) {
                                $dvl['h_align'] = 'right';
                                $dvl['x_offset'] = -3;
                            } else {
                                $dvl['h_align'] = 'left';
                                $dvl['x_offset'] = 3;
                            }
                            $this->DrawDataValueLabel('x', $row, $idx, $wx1, $row+0.5, $this_x, $dvl);
                        }
                        // Mark the new end of the bar, conditional on segment width > 0.
                        $wx2 = $wx1;
                        $first = FALSE;
                    }
                }
            }   // end for

            // Draw optional data label right of the bar with the total value.
            // Value is wx1 (total value), but position is wx2 (end of the bar stack).
            // These differ only with wrong-direction segments, or a stack completely clipped by the axis.
            if ($data_labels_end) {
                $dvl['min_width'] = NULL; // Might be set above, but the whole array might not exist.
                if ($rightward) {
                    $dvl['h_align'] = 'left';
                    $dvl['x_offset'] = $data_label_x_offset;
                } else {
                    $dvl['h_align'] = 'right';
                    $dvl['x_offset'] = -5;
                }
                $this->DrawDataValueLabel('x', $row, NULL, $wx2, $row+0.5, $wx1, $dvl);
            }
        }   // end for
        return TRUE;
    }

    /**
     * Draws an ohlc, candlesticks, or candlesticks2 plot ("Open/High/Low/Close" OHLC plot)
     *
     * This is the main function for drawing an ohlc, candlesticks, or
     * candlesticks2 plot, which are typically used to show price changes in
     * financial instruments.  Supported data types are text-data and
     * data-data, each with exactly 4 Y values per row: Open, High, Low, and
     * Close. The 2 parameters select one of the 3 plot subtypes.
     *
     * @param bool $draw_candles  True to draw a candlestick plot, False to draw an ohlc plot
     * @param bool $always_fill  True to always fill, False or omit to fill only when closing down
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.3.0
     */
    protected function DrawOHLC($draw_candles, $always_fill = FALSE)
    {
        if (!$this->CheckDataType('text-data, data-data'))
            return FALSE;
        if ($this->data_columns != 4) // early error check (more inside the loop)
            return $this->PrintError("DrawOHLC(): rows must have 4 values.");

        // Assign name of GD function to draw candlestick bodies for stocks that close up.
        $draw_body_close_up = $always_fill ? 'imagefilledrectangle' : 'imagerectangle';

        // Calculate the half-width of the candle body, or length of the tick marks.
        // This is scaled based on the plot density, but within tight limits.
        $dw = max($this->ohlc_min_width, min($this->ohlc_max_width,
                     (int)($this->ohlc_frac_width * $this->plot_area_width / $this->num_data_rows)));

        // Get line widths to use: index 0 for body/stroke, 1 for wick/tick.
        list($body_thickness, $wick_thickness) = $this->line_widths;

        $gcvars = array(); // For GetDataColor, which initializes and uses this.

        for ($row = 0; $row < $this->num_data_rows; $row++) {
            $record = 1;                                    // Skip record #0 (data label)

            if ($this->datatype_implied)                    // Implied X values?
                $x_now = 0.5 + $row;                        // Place text-data at X = 0.5, 1.5, 2.5, etc...
            else
                $x_now = $this->data[$row][$record++];      // Read it, advance record index

            $x_now_pixels = $this->xtr($x_now);             // Convert X to device coordinates
            $x_left = $x_now_pixels - $dw;
            $x_right = $x_now_pixels + $dw;

            if ($this->x_data_label_pos != 'none')          // Draw X Data labels?
                $this->DrawXDataLabel($this->data[$row][0], $x_now_pixels, $row);

            // Each row must have 4 values, but skip rows with non-numeric entries.
            if ($this->num_recs[$row] - $record != 4) {
                return $this->PrintError("DrawOHLC(): row $row must have 4 values.");
            }
            if (!is_numeric($yo = $this->data[$row][$record++])
             || !is_numeric($yh = $this->data[$row][$record++])
             || !is_numeric($yl = $this->data[$row][$record++])
             || !is_numeric($yc = $this->data[$row][$record++])) {
                continue;
            }

            // Set device coordinates for each value and direction flag:
            $yh_pixels = $this->ytr($yh);
            $yl_pixels = $this->ytr($yl);
            $yc_pixels = $this->ytr($yc);
            $yo_pixels = $this->ytr($yo);
            $closed_up = $yc >= $yo;

            // Get data colors and line thicknesses:
            if ($closed_up) {
                $this->GetDataColor($row, 1, $gcvars, $body_color); // Color 1 for body, closing up
                $this->GetDataColor($row, 3, $gcvars, $ext_color);  // Color 3 for wicks/ticks
            } else {
                $this->GetDataColor($row, 0, $gcvars, $body_color); // Color 0 for body, closing down
                $this->GetDataColor($row, 2, $gcvars, $ext_color);  // Color 2 for wicks/ticks
            }
            imagesetthickness($this->img, $body_thickness);

            if ($draw_candles) {
                // Note: Unlike ImageFilledRectangle, ImageRectangle 'requires' its arguments in
                // order with upper left corner first.
                if ($closed_up) {
                    $yb1_pixels = $yc_pixels; // Upper body Y
                    $yb2_pixels = $yo_pixels; // Lower body Y
                    $draw_body = $draw_body_close_up;
                    // Avoid a PHP/GD bug resulting in "T"-shaped ends to zero height unfilled rectangle:
                    if ($yb1_pixels == $yb2_pixels)
                        $draw_body = 'imagefilledrectangle';
                } else {
                    $yb1_pixels = $yo_pixels;
                    $yb2_pixels = $yc_pixels;
                    $draw_body = 'imagefilledrectangle';
                }

                // Draw candle body
                $draw_body($this->img, $x_left, $yb1_pixels, $x_right, $yb2_pixels, $body_color);

                // Draw upper and lower wicks, if they have height. (In device coords, that's dY<0)
                imagesetthickness($this->img, $wick_thickness);
                if ($yh_pixels < $yb1_pixels) {
                    imageline($this->img, $x_now_pixels, $yb1_pixels, $x_now_pixels, $yh_pixels, $ext_color);
                }
                if ($yl_pixels > $yb2_pixels) {
                    imageline($this->img, $x_now_pixels, $yb2_pixels, $x_now_pixels, $yl_pixels, $ext_color);
                }
            } else {
                // Basic OHLC
                imageline($this->img, $x_now_pixels, $yl_pixels, $x_now_pixels, $yh_pixels, $body_color);
                imagesetthickness($this->img, $wick_thickness);
                imageline($this->img, $x_left, $yo_pixels, $x_now_pixels, $yo_pixels, $ext_color);
                imageline($this->img, $x_right, $yc_pixels, $x_now_pixels, $yc_pixels, $ext_color);
            }
            imagesetthickness($this->img, 1);
            $this->DoCallback('data_points', 'rect', $row, 0, $x_left, $yh_pixels, $x_right, $yl_pixels);
        }
        return TRUE;
    }

    /**
     * Draws a bubbles plot (Bubble chart)
     *
     * This is the main function for drawing a bubbles plot, which is a
     * scatter plot with bubble size showing the Z value.
     * Supported data type is data-data-xyz with rows of (label, X, Y1, Z1, ...)
     * with multiple data sets (Y, Z pairs) supported.
     *
     * @return bool  True (False on error if an error handler returns True)
     * @since 5.5.0
     */
    protected function DrawBubbles()
    {
        if (!$this->CheckDataType('data-data-xyz'))
            return FALSE;

        $gcvars = array(); // For GetDataColor, which initializes and uses this.

        // Calculate or use supplied maximum bubble size:
        if (isset($this->bubbles_max_size)) {
            $bubbles_max_size = $this->bubbles_max_size;
        } else {
            $bubbles_max_size = min($this->plot_area_width, $this->plot_area_height) / 12;
        }

        // Calculate bubble scale parameters. Bubble_size(z) = $f_size * $z + $b_size
        if ($this->max_z <= $this->min_z) {   // Regressive case, no Z range.
            $f_size = 0;
            $b_size = ($bubbles_max_size + $this->bubbles_min_size) / 2; // Use average size of all bubbles
        } else {
            $f_size = ($bubbles_max_size - $this->bubbles_min_size) / ($this->max_z - $this->min_z);
            $b_size = $bubbles_max_size - $f_size * $this->max_z;
        }

        for ($row = 0; $row < $this->num_data_rows; $row++) {
            $rec = 1;                    // Skip record #0 (data label)
            $x = $this->xtr($this->data[$row][$rec++]); // Get X value from data array.

            // Draw X Data labels?
            if ($this->x_data_label_pos != 'none')
                $this->DrawXDataLabel($this->data[$row][0], $x, $row, TRUE);

            // Proceed with Y,Z values
            for ($idx = 0; $rec < $this->num_recs[$row]; $rec += 2, $idx++) {

                if (is_numeric($y_now = $this->data[$row][$rec])) {      //Allow for missing Y data
                    $y = $this->ytr($y_now);
                    $z = (double)$this->data[$row][$rec+1]; // Z is required if Y is present.
                    $size = (int)($f_size * $z + $b_size);  // Calculate bubble size

                    // Select the color:
                    $this->GetDataColor($row, $idx, $gcvars, $data_color);

                    // Draw the bubble:
                    ImageFilledEllipse($this->img, $x, $y, $size, $size, $data_color);
                    $this->DoCallback('data_points', 'circle', $row, $idx, $x, $y, $size);
                }
            }
        }
        return TRUE;
    }

    /**
     * Draws a boxes plot (Box Plot or Box and Whisker plot)
     *
     * This is the main function for drawing a boxes plot.  Supported data
     * types are text-data and data-data, each with 5 or more Y values per
     * row. The first 5 values are Ymin, YQ1, Ymid, YQ3, Ymax. Any additional
     * values are outliers. PHPlot requires Ymin <= YQ1 <= Ymin <= YQ3 <= Ymax
     * but does not assume anything about specific values (quartile, median).
     *
     * @return bool  True (False on error if an error handler returns True)
     * @since 6.1.0
     */
    protected function DrawBoxes()
    {
        if (!$this->CheckDataType('text-data, data-data'))
            return FALSE;
        if ($this->data_columns < 5)   // early error check (more inside the loop)
            return $this->PrintError("DrawBoxes(): rows must have 5 or more values.");

        // Set up the point shapes/sizes arrays - needed for outliers:
        $this->CheckPointParams();

        // Calculate the half-width of the boxes.
        // This is scaled based on the plot density, but within tight limits.
        $width1 = max($this->boxes_min_width, min($this->boxes_max_width,
                     (int)($this->boxes_frac_width * $this->plot_area_width / $this->num_data_rows)));
        // This is the half-width of the upper and lower T's and the ends of the whiskers:
        $width2 = $this->boxes_t_width * $width1;

        // A box plot can use up to 3 different line widths:
        list($box_thickness, $belt_thickness, $whisker_thickness) = $this->line_widths;

        $gcvars = array(); // For GetDataColor, which initializes and uses this.

        for ($row = 0; $row < $this->num_data_rows; $row++) {
            $record = 1;                                    // Skip record #0 (data label)

            if ($this->datatype_implied)                    // Implied X values?
                $xw = 0.5 + $row;                           // Place text-data at X = 0.5, 1.5, 2.5, etc...
            else
                $xw = $this->data[$row][$record++];         // Read it, advance record index

            $xd = $this->xtr($xw);       // Convert X to device coordinates
            $x_left = $xd - $width1;
            $x_right = $xd + $width1;

            if ($this->x_data_label_pos != 'none')          // Draw X Data labels?
                $this->DrawXDataLabel($this->data[$row][0], $xd, $row);

            // Each row must have at least 5 values:
            $num_y = $this->num_recs[$row] - $record;
            if ($num_y < 5) {
                return $this->PrintError("DrawBoxes(): row $row must have at least 5 values.");
            }

            // Collect the 5 primary Y values, plus any outliers:
            $yd = array(); // Device coords
            for ($i = 0; $i < $num_y; $i++) {
                $yd[$i] = is_numeric($y = $this->data[$row][$record++]) ? $this->ytr($y) : NULL;
            }

            // Skip the row if either YQ1 or YQ3 is missing:
            if (!isset($yd[1], $yd[3])) continue;

            // Box plot uses 4 colors, and 1 dashed line style for the whiskers:
            $this->GetDataColor($row, 0, $gcvars, $box_color);
            $this->GetDataColor($row, 1, $gcvars, $belt_color);
            $this->GetDataColor($row, 2, $gcvars, $outlier_color);
            $this->GetDataColor($row, 3, $gcvars, $whisker_color);
            $whisker_style = $this->SetDashedStyle($whisker_color, $this->line_styles[0] == 'dashed');

            // Draw the lower whisker and T
            if (isset($yd[0]) && $yd[0] > $yd[1]) {   // Note device Y coordinates are inverted (*-1)
                imagesetthickness($this->img, $whisker_thickness);
                imageline($this->img, $xd, $yd[0], $xd, $yd[1], $whisker_style);
                imageline($this->img, $xd - $width2, $yd[0], $xd + $width2, $yd[0], $whisker_color);
            }

            // Draw the upper whisker and T
            if (isset($yd[4]) && $yd[3] > $yd[4]) {   // Meaning: Yworld[3] < Yworld[4]
                imagesetthickness($this->img, $whisker_thickness);
                imageline($this->img, $xd, $yd[3], $xd, $yd[4], $whisker_style);
                imageline($this->img, $xd - $width2, $yd[4], $xd + $width2, $yd[4], $whisker_color);
            }

            // Draw the median belt (before the box, so the ends of the belt don't break up the box.)
            if (isset($yd[2])) {
                imagesetthickness($this->img, $belt_thickness);
                imageline($this->img, $x_left, $yd[2], $x_right, $yd[2], $belt_color);
             }

            // Draw the box
            imagesetthickness($this->img, $box_thickness);
            imagerectangle($this->img, $x_left, $yd[3], $x_right, $yd[1], $box_color);
            imagesetthickness($this->img, 1);

            // Draw any outliers, all using the same shape marker (index 0) and color:
            for ($i = 5; $i < $num_y; $i++) {
                if (isset($yd[$i]))
                    $this->DrawShape($xd, $yd[$i], 0, $outlier_color);
            }

            $this->DoCallback('data_points', 'rect', $row, 0, $x_left, $yd[4], $x_right, $yd[0]);
        }
        return TRUE;
    }

    /**
     * Draws the current graph onto the image
     *
     * This is the function that performs the actual drawing, after all the
     * parameters and data are set up. It also outputs the finished image,
     * unless told not to with SetPrintImage(False).
     * Note: It is possible for this to be called multiple times (multi-plot).
     *
     * @return bool  True (False on error if an error handler returns True)
     */
    function DrawGraph()
    {
        // Test for missing image, missing data, empty data:
        if (!$this->CheckDataArray())
            return FALSE; // Error message already reported.

        // Load some configuration values from the array of plot types:
        $pt = &self::$plots[$this->plot_type]; // Use reference for shortcut
        $draw_method = $pt['draw_method'];
        $draw_arg = isset($pt['draw_arg']) ? $pt['draw_arg'] : array();
        $draw_axes = empty($pt['suppress_axes']);

        // Allocate colors for the plot:
        $this->SetColorIndexes();

        // Calculate scaling, but only for plots with axes (excludes pie charts).
        if ($draw_axes) {

            // Get maxima and minima for scaling:
            if (!$this->FindDataLimits())
                return FALSE;

            // Set plot area world values (plot_max_x, etc.):
            if (!$this->CalcPlotAreaWorld())
                return FALSE;

            // Calculate X and Y axis positions in World Coordinates:
            $this->CalcAxisPositions();

            // Process label-related parameters:
            $this->CheckLabels();
        }

        // Calculate the plot margins, if needed.
        // For pie charts, set the $maximize argument to maximize space usage.
        $this->CalcMargins(!$draw_axes);

        // Calculate the actual plot area in device coordinates:
        $this->CalcPlotAreaPixels();

        // Calculate the mapping between world and device coordinates:
        if ($draw_axes) $this->CalcTranslation();

        // Pad color and style arrays to fit records per group:
        $this->PadArrays();
        $this->DoCallback('draw_setup');

        $this->DrawBackground();
        $this->DrawImageBorder();
        $this->DoCallback('draw_image_background');

        $this->DrawPlotAreaBackground();
        $this->DoCallback('draw_plotarea_background', $this->plot_area);

        $this->DrawTitle();
        if ($draw_axes) {  // If no axes (pie chart), no axis titles either
            $this->DrawXTitle();
            $this->DrawYTitle();
        }
        $this->DoCallback('draw_titles');

        // grid_at_foreground flag allows grid behind or in front of the plot
        if ($draw_axes && !$this->grid_at_foreground) {
            $this->DrawYAxis();     // Y axis must be drawn before X axis (see DrawYAxis())
            $this->DrawXAxis();
            $this->DoCallback('draw_axes');
        }

        // Call the plot-type drawing method:
        call_user_func_array(array($this, $draw_method), $draw_arg);
        $this->DoCallback('draw_graph', $this->plot_area);

        if ($draw_axes && $this->grid_at_foreground) {
            $this->DrawYAxis();     // Y axis must be drawn before X axis (see DrawYAxis())
            $this->DrawXAxis();
            $this->DoCallback('draw_axes');
        }

        $this->DrawPlotBorder($draw_axes); // Flag controls default for plot area borders
        $this->DoCallback('draw_border');

        if (!empty($this->legend)) {
            $this->DrawLegend();
            $this->DoCallback('draw_legend');
        }
        $this->DoCallback('draw_all', $this->plot_area);

        if ($this->print_image && !$this->PrintImage())
            return FALSE;

        return TRUE;
    }

/////////////////////////////////////////////
//////////////////         DEPRECATED METHODS
/////////////////////////////////////////////

    /*
     * Note on deprecated methods - as these pre-date the PHPlot Reference
     * Manual, and there is minimal documentation about them, I have neither
     * removed them nor changed them. They are not tested or documented, and
     * should not be used.
     */

    /**
     * @deprecated  Use SetYTickPos() instead
     */
    function SetDrawVertTicks($which_dvt)
    {
        if ($which_dvt != 1)
            $this->SetYTickPos('none');
        return TRUE;
    }

    /**
     * @deprecated  Use SetXTickPos() instead
     */
    function SetDrawHorizTicks($which_dht)
    {
        if ($which_dht != 1)
           $this->SetXTickPos('none');
        return TRUE;
    }

    /**
     * @deprecated  Use SetNumXTicks() instead
     */
    function SetNumHorizTicks($n)
    {
        return $this->SetNumXTicks($n);
    }

    /**
     * @deprecated  Use SetNumYTicks() instead
     */
    function SetNumVertTicks($n)
    {
        return $this->SetNumYTicks($n);
    }

    /**
     * @deprecated  Use SetXTickIncrement() instead
     */
    function SetHorizTickIncrement($inc)
    {
        return $this->SetXTickIncrement($inc);
    }

    /**
     * @deprecated  Use SetYTickIncrement() instead
     */
    function SetVertTickIncrement($inc)
    {
        return $this->SetYTickIncrement($inc);
    }

    /**
     * @deprecated  Use SetYTickPos() instead
     */
    function SetVertTickPosition($which_tp)
    {
        return $this->SetYTickPos($which_tp);
    }

    /**
     * @deprecated  Use SetXTickPos() instead
     */
    function SetHorizTickPosition($which_tp)
    {
        return $this->SetXTickPos($which_tp);
    }

    /**
     * @deprecated  Use SetFont() instead
     */
    function SetTitleFontSize($which_size)
    {
        return $this->SetFont('title', $which_size);
    }

    /**
     * @deprecated  Use SetFont() instead
     */
    function SetAxisFontSize($which_size)
    {
        $this->SetFont('x_label', $which_size);
        $this->SetFont('y_label', $which_size);
    }

    /**
     * @deprecated  Use SetFont() instead
     */
    function SetSmallFontSize($which_size)
    {
        return $this->SetFont('generic', $which_size);
    }

    /**
     * @deprecated  Use SetFont() instead
     */
    function SetXLabelFontSize($which_size)
    {
        return $this->SetFont('x_title', $which_size);
    }

    /**
     * @deprecated  Use SetFont() instead
     */
    function SetYLabelFontSize($which_size)
    {
        return $this->SetFont('y_title', $which_size);
    }

    /**
     * @deprecated  Use SetXTitle() instead
     */
    function SetXLabel($which_xlab)
    {
        return $this->SetXTitle($which_xlab);
    }

    /**
     * @deprecated  Use SetYTitle() instead
     */
    function SetYLabel($which_ylab)
    {
        return $this->SetYTitle($which_ylab);
    }

    /**
     * @deprecated  Use SetXTickLength() and SetYTickLength() instead
     */
    function SetTickLength($which_tl)
    {
        $this->SetXTickLength($which_tl);
        $this->SetYTickLength($which_tl);
        return TRUE;
    }

    /**
     * @deprecated  Use SetYLabelType() instead
     */
    function SetYGridLabelType($which_yglt)
    {
        return $this->SetYLabelType($which_yglt);
    }

    /**
     * @deprecated  Use SetXLabelType() instead
     */
    function SetXGridLabelType($which_xglt)
    {
        return $this->SetXLabelType($which_xglt);
    }

    /**
     * @deprecated  Use SetYTickLabelPos() instead
     */
    function SetYGridLabelPos($which_yglp)
    {
        return $this->SetYTickLabelPos($which_yglp);
    }

    /**
     * @deprecated  Use SetXTickLabelPos() instead
     */
    function SetXGridLabelPos($which_xglp)
    {
        return $this->SetXTickLabelPos($which_xglp);
    }

    /**
     * @deprecated  Use SetXtitle() instead
     */
    function SetXTitlePos($xpos)
    {
        $this->x_title_pos = $xpos;
        return TRUE;
    }

    /**
     * @deprecated  Use SetYTitle() instead
     */
    function SetYTitlePos($xpos)
    {
        $this->y_title_pos = $xpos;
        return TRUE;
    }

    /**
     * @deprecated  Use SetXDataLabelPos() instead
     */
    function SetDrawXDataLabels($which_dxdl)
    {
        if ($which_dxdl == '1' )
            $this->SetXDataLabelPos('plotdown');
        else
            $this->SetXDataLabelPos('none');
    }

    /**
     * @deprecated  Use SetPlotAreaPixels() instead
     */
    function SetNewPlotAreaPixels($x1, $y1, $x2, $y2)
    {
        return $this->SetPlotAreaPixels($x1, $y1, $x2, $y2);
    }

    /**
     * @deprecated  Use SetLineWidths() instead
     */
    function SetLineWidth($which_lw)
    {

        $this->SetLineWidths($which_lw);

        if (!$this->error_bar_line_width) {
            $this->SetErrorBarLineWidth($which_lw);
        }
        return TRUE;
    }

    /**
     * @deprecated  Use SetPointShapes() instead
     */
    function SetPointShape($which_pt)
    {
        $this->SetPointShapes($which_pt);
        return TRUE;
    }

    /**
     * @deprecated  Use SetPointSizes() instead
     */
    function SetPointSize($which_ps)
    {
        $this->SetPointSizes($which_ps);
        return TRUE;
    }

    /**
     * @deprecated  Use PrintError() instead
     */
    protected function DrawError($error_message, $where_x = NULL, $where_y = NULL)
    {
        return $this->PrintError($error_message);
    }

}

/**
 * Class for creating a plot using a truecolor (24-bit R,G,B) image
 *
 * The PHPlot_truecolor class extends the PHPlot class to use GD truecolor
 * images. Unlike PHPlot which usually creates indexed RGB files limited to
 * 256 total colors, PHPlot_truecolor objects use images which do not have a
 * limit on the number of colors.
 *
 * Note: Without a background image, the PHPlot class creates a palette
 * (indexed) color image, and the PHPlot_truecolor class creates a truecolor
 * image. If a background image is used with the constructor of either class,
 * the type of image produced matches the type of the background image.
 *
 */
class PHPlot_truecolor extends PHPlot
{
    /**
     * Constructor: Sets up GD truecolor image resource, and initializes plot style controls
     *
     * @param int $width  Image width in pixels
     * @param int $height  Image height in pixels
     * @param string $output_file  Path for output file. Omit, or NULL, or '' to mean no output file
     * @param string $input_file   Path to a file to be used as background. Omit, NULL, or '' for none
     */
    function __construct($width=600, $height=400, $output_file=NULL, $input_file=NULL)
    {
        $this->initialize('imagecreatetruecolor', $width, $height, $output_file, $input_file);
    }
}