File: Plot.java

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package ij.gui;
import java.awt.*;
import java.util.*;
import java.io.*;
import java.lang.reflect.Method;
import java.awt.geom.Point2D;
import ij.*;
import ij.process.*;
import ij.util.*;
import ij.plugin.Colors;
import ij.plugin.filter.Analyzer;
import ij.macro.Interpreter;
import ij.measure.Calibration;
import ij.measure.Measurements;
import ij.measure.ResultsTable;

/** This class creates an image that line graphs, scatter plots and plots of vector fields
 *	(arrows) can be drawn on and displayed.
 *
 *	Note that the clone() operation is a shallow clone: objects like arrays, the PlotProperties,
 *	PlotObjects, the ImagePlus etc. of the clone remain the same as those of the original.
 *
 * @author Wayne Rasband
 * @author Philippe CARL, CNRS, philippe.carl (AT) unistra.fr (log axes, arrows, ArrayList data)
 * @author Norbert Vischer (overlay range arrows, 'R'eset range, filled plots, dynamic plots, boxes and whiskers, superscript)
 * @author Michael Schmid (axis grid/ticks, resizing/panning/changing range, high-resolution, serialization)
 */
public class Plot implements Cloneable {

	/** Text justification. */
	public static final int LEFT=ImageProcessor.LEFT_JUSTIFY, CENTER=ImageProcessor.CENTER_JUSTIFY, RIGHT=ImageProcessor.RIGHT_JUSTIFY;
	/** Legend positions */
	//NOTE: These have only bits of LEGEND_POSITION_MASK set. The flags of the legend are stored as flags of the legend PlotObject.
	//These are saved in the flags of the PlotObject class; thus bits up to 0x0f are reserved
	public static final int TOP_LEFT=0x90, TOP_RIGHT=0xA0, BOTTOM_LEFT=0xB0, BOTTOM_RIGHT=0xC0, AUTO_POSITION=0x80;
	/** Masks out bits for legend positions; if all these bits are off, the legend is turned off */
	static final int LEGEND_POSITION_MASK = 0xf0;
	/** Legend has its curves in bottom-to-top sequence (otherwise top to bottom) */
	public static final int LEGEND_BOTTOM_UP = 0x100;
	/** Legend erases background (otherwise transparent) */
	public static final int LEGEND_TRANSPARENT = 0x200;
	/** Display points using a circle (5 pixels in diameter if line thickness<=1, otherwise 7). */
	public static final int CIRCLE = 0;
	/** Display points using an X-shaped mark. */
	public static final int X = 1;
	/** Connect points with solid lines. */
	public static final int LINE = 2;
	/** Display points using a square box-shaped mark. */
	public static final int BOX = 3;
	/** Display points using an tiangular mark. */
	public static final int TRIANGLE = 4;
	/** Display points using an cross-shaped mark. */
	public static final int CROSS = 5;
	/** Display points using a single pixel. */
	public static final int DOT = 6;
	/** Draw black lines between the dots and a circle with the given color at each dot */
	public static final int CONNECTED_CIRCLES = 7;
	/** Display points using an diamond-shaped mark. */
	public static final int DIAMOND = 8;
	/** Draw shape using macro code */
	public static final int CUSTOM = 9;
	/** Fill area between line plot and x-axis at y=0. */
	public static final int FILLED = 10;
	/** Draw a histogram bar for each point (bars touch each other unless the x axis has categories set via the axis label.
	 *  x values should be sorted (ascending or descending) */
	public static final int BAR = 11;
	/** Draw a free-standing bar for each point. x values should be equidistant and sorted (ascending or descending) */
	public static final int SEPARATED_BAR = 12;

	/** Names for the shapes as an array */
	final static String[] SHAPE_NAMES = new String[] {
			"Circle", "X", "Line", "Box", "Triangle", "+", "Dot", "Connected Circles", "Diamond",
			"Custom", "Filled", "Bar", "Separated Bars"};
	/** Names in nicely sorting order for menus */
	final static String[] SORTED_SHAPES = new String[] {
			SHAPE_NAMES[LINE], SHAPE_NAMES[CONNECTED_CIRCLES], SHAPE_NAMES[FILLED], SHAPE_NAMES[BAR], SHAPE_NAMES[SEPARATED_BAR],
			SHAPE_NAMES[CIRCLE], SHAPE_NAMES[BOX], SHAPE_NAMES[TRIANGLE], SHAPE_NAMES[CROSS],
			SHAPE_NAMES[DIAMOND], SHAPE_NAMES[X], SHAPE_NAMES[DOT]};
	/** flag for numeric labels of x-axis ticks */
	public static final int X_NUMBERS = 0x1;
	/** flag for numeric labels of x-axis ticks */
	public static final int Y_NUMBERS = 0x2;
	/** flag for drawing major ticks on linear (non-logarithmic) x axis */
	public static final int X_TICKS = 0x4;
	/** flag for drawing major ticks on linear (non-logarithmic) y axis */
	public static final int Y_TICKS = 0x8;
	/** flag for drawing vertical grid lines for x axis */
	public static final int X_GRID = 0x10;
	/** flag for drawing horizontal grid lines for y axis */
	public static final int Y_GRID = 0x20;
	/** flag for forcing frame to coincide with the grid/ticks in x direction (results in unused space) */
	public static final int X_FORCE2GRID = 0x40;
	/** flag for forcing frame to coincide with the grid/ticks in y direction (results in unused space) */
	public static final int Y_FORCE2GRID = 0x80;
	/** flag for drawing minor ticks on linear (non-logarithmic) x axis */
	public static final int X_MINOR_TICKS = 0x100;
	/** flag for drawing minor ticks on linear (non-logarithmic) y axis */
	public static final int Y_MINOR_TICKS = 0x200;
	/** flag for logarithmic x-axis */
	public static final int X_LOG_NUMBERS = 0x400;
	/** flag for logarithmic y axis */
	public static final int Y_LOG_NUMBERS = 0x800;
	/** flag for ticks (major and minor, if space) on logarithmic x axis */
	public static final int X_LOG_TICKS = 0x1000;
	/** flag for ticks (major and minor, if space) on logarithmic y axis */
	public static final int Y_LOG_TICKS = 0x2000;
	//leave 0x4000, 0x8000 reserved for broken axes?
	/** The default axisFlags, will be modified by PlotWindow.noGridLines and PlotWindow.noTicks (see getDefaultFlags) */
	public static final int DEFAULT_FLAGS =	 X_NUMBERS + Y_NUMBERS + /*X_TICKS + Y_TICKS +*/
			X_GRID + Y_GRID + X_LOG_TICKS + Y_LOG_TICKS;

	/** Flag for addressing the x axis, for copying from a template: copy/write x axis range. */
	// This must be 0x1 because bit shift operations are used for the other axes
	public static final int X_RANGE = 0x1;
	/** Flag for addressing the y axis, for copying from a template: copy/write y axis range */
	public static final int Y_RANGE = 0x2;
	/** Flags for modifying the range of all axes */
	static final int ALL_AXES_RANGE = X_RANGE | Y_RANGE;
	//0x4, 0x8 reserved for secondary axes
	/** Flag for copying from a template: copy plot size */
	public static final int COPY_SIZE = 0x10;
	/** Flag for copying from a template: copy style & text of axis labels */
	public static final int COPY_LABELS = 0x20;
	/** Flag for copying from a template: copy legend */
	public static final int COPY_LEGEND = 0x40;
	/** Flag for copying from a template: copy axis style */
	public static final int COPY_AXIS_STYLE = 0x80;
	/** Flag for copying from a template: copy contents style */
	public static final int COPY_CONTENTS_STYLE = 0x100;
	/** Flag for copying PlotObjects (curves...) from a template if the template has more PlotObjects than the Plot to copy to. */
	public static final int COPY_EXTRA_OBJECTS = 0x200;

	/** The default margin width left of the plot frame (enough for 5-digit numbers such as unscaled 16-bit
	 *	@deprecated Not a fixed value any more, use getDrawingFrame() to get the drawing area */
	public static final int LEFT_MARGIN = 65;
	/** The default margin width right of the plot frame
	 *	@deprecated Not a fixed value any more, use getDrawingFrame() to get the drawing area */
	public static final int RIGHT_MARGIN = 18;
	/** The default margin width above the plot frame
	 *	@deprecated Not a fixed value any more, use getDrawingFrame() to get the drawing area */
	public static final int TOP_MARGIN = 15;
	/** The default margin width below the plot frame
	 *	@deprecated Not a fixed value any more, use getDrawingFrame() to get the drawing area */
	public static final int BOTTOM_MARGIN = 40;
	/** minimum width of frame area in plot */
	public static final int MIN_FRAMEWIDTH = 160;
	/** minimum width of frame area in plot */
	public static final int MIN_FRAMEHEIGHT = 90;
	/** key in ImagePlus properties to access the plot behind an ImagePlus */
	public static final String PROPERTY_KEY = "thePlot";

	static final float DEFAULT_FRAME_LINE_WIDTH = 1.0001f; //Frame thickness
	private static final int MIN_X_GRIDSPACING = 45;	//minimum distance between grid lines or ticks along x at plot width 0
	private static final int MIN_Y_GRIDSPACING = 30;	//minimum distance between grid lines or ticks along y at plot height 0
	private final double MIN_LOG_RATIO = 3;				//If max/min ratio is less than this, force linear axis even if log required. should be >2
	private static final int LEGEND_PADDING = 4;		//pixels around legend text etc
	private static final int LEGEND_LINELENGTH = 20;	//length of lines in legend
	private static final int USUALLY_ENLARGE = 1, ALWAYS_ENLARGE = 2; //enlargeRange settings
	private static final double RELATIVE_ARROWHEAD_SIZE = 0.2; //arrow heads have 1/5 of vector length
	private static final int MIN_ARROWHEAD_LENGTH = 3;
	private static final int MAX_ARROWHEAD_LENGTH = 20;
	private static final String MULTIPLY_SYMBOL = "\u00B7"; //middot, default multiplication symbol for scientific notation. Use setOptions("msymbol=\\u00d7") for '×'

	PlotProperties pp = new PlotProperties();		//size, range, formatting etc, for easy serialization
	PlotProperties ppSnapshot;						//copy for reverting
	Vector<PlotObject> allPlotObjects = new Vector<PlotObject>();	//all curves, labels etc., also serialized for saving/reading
	Vector<PlotObject> allPlotObjectsSnapshot;      //copy for reverting
	private PlotVirtualStack stack;
	/** For high-resolution plots, everything will be scaled with this number. Otherwise, must be 1.0.
	 *  (creating margins, saving PlotProperties etc only supports scale=1.0) */
	float scale = 1.0f;
	Rectangle frame = null;							//the clip frame, do not use for image scale
	//The following are the margin sizes actually used. They are modified for font size and also scaled for high-resolution plots
	int leftMargin = LEFT_MARGIN, rightMargin = RIGHT_MARGIN, topMargin = TOP_MARGIN, bottomMargin = BOTTOM_MARGIN;
	int frameWidth;									//width corresponding to plot range; frame.width is larger by 1
	int frameHeight;								//height corresponding to plot range; frame.height is larger by 1
	int preferredPlotWidth = PlotWindow.plotWidth;  //default size of plot frame (not taking 'High-Resolution' scale factor into account)
	int preferredPlotHeight = PlotWindow.plotHeight;

	double xMin = Double.NaN, xMax, yMin, yMax;		//current plot range, logarithm if log axis
	double[] currentMinMax = new double[]{Double.NaN, 0, Double.NaN, 0}; //current plot range, xMin, xMax, yMin, yMax (values, not logarithm if log axis)
	double[] defaultMinMax = new double[]{Double.NaN, 0, Double.NaN, 0}; //default plot range
	double[] savedMinMax = new double[]{Double.NaN, 0, Double.NaN, 0};	//keeps previous range for revert
	int[] enlargeRange;                             // whether to enlarge the range slightly to avoid values at the border (0=off, USUALLY_ENLARGE, ALWAYS_ENLARGE)
	boolean logXAxis, logYAxis;                     // whether to really use log axis (never for small relative range)
	//for passing on what should be kept when 'live' plotting (PlotMaker), but note that 'COPY_EXTRA_OBJECTS' is also on for live plotting:
	int templateFlags = COPY_SIZE | COPY_LABELS | COPY_AXIS_STYLE | COPY_CONTENTS_STYLE | COPY_LEGEND;
	private int dsize = PlotWindow.getDefaultFontSize();
	Font defaultFont = FontUtil.getFont("Arial",Font.PLAIN,dsize); //default font for labels, axis, etc.
	Font currentFont = defaultFont;                 // font as changed by setFont or setFontSize, must never be null
	private double xScale, yScale;                  // pixels per data unit
	private int xBasePxl, yBasePxl;                 // pixel coordinates corresponding to 0
	private int maxIntervals = 12;                  // maximum number of intervals between ticks or grid lines
	private int tickLength = 7;                     // length of major ticks
	private int minorTickLength = 3;                // length of minor ticks
	private Color gridColor = new Color(0xc0c0c0);  // light gray
	private ImageProcessor ip;
	private ImagePlus imp;                          // if we have an ImagePlus, updateAndDraw on changes
	private String title;
	private boolean invertedLut;                    // grayscale plots only, set in Edit>Options>Appearance
	private boolean plotDrawn;
	PlotMaker plotMaker;                            // for PlotMaker interface, handled by PlotWindow
	private Color currentColor;						// for next objects added
	private Color currentColor2;					// 2nd color for next object added (e.g. line for CONNECTED_CIRCLES)
	float currentLineWidth;
	private int currentJustification = LEFT;
	private boolean ignoreForce2Grid;               // after explicit setting of range (limits), ignore 'FORCE2GRID' flags
	//private boolean snapToMinorGrid;  			// snap to grid when zooming to selection
	private static double SEPARATED_BAR_WIDTH=0.5;  // for plots with separate bars (e.g. categories), fraction of space, 0.1-1.0
	double[] steps;                                 // x & y interval between numbers, major ticks & grid lines, remembered for redrawing the grid
	private int objectToReplace = -1;               // index in allPlotObjects, for replace
	private Point2D.Double textLoc;                 // remembers position of previous addLabel call (replaces text if at the same position)
	private int textIndex;                          // remembers index of previous addLabel call (for replacing if at the same position)

	/** Constructs a new Plot with the default options.
	 * Use add(shape,xvalues,yvalues) to add curves.
	 * @param title the window title
	 * @param xLabel	the x-axis label; see setXYLabels for seting categories on an axis via the label
	 * @param yLabel	the y-axis label; see setXYLabels for seting categories on an axis via the label
	 * @see #add(String,double[],double[])
	 * @see #add(String,double[])
	 */
	public Plot(String title, String xLabel, String yLabel) {
		this(title, xLabel, yLabel, (float[])null, (float[])null, getDefaultFlags());
	}

	/** Obsolete, replaced by "new Plot(title,xLabel,yLabel); add(shape,x,y);".
	 * @deprecated
	*/
	public Plot(String title, String xLabel, String yLabel, float[] x, float[] y) {
		this(title, xLabel, yLabel, x, y, getDefaultFlags());
	}

	/** Obsolete, replaced by "new Plot(title,xLabel,yLabel); add(shape,x,y);".
	 * @deprecated
	*/
	public Plot(String title, String xLabel, String yLabel, double[] x, double[] y) {
		this(title, xLabel, yLabel, x!=null?Tools.toFloat(x):null, y!=null?Tools.toFloat(y):null, getDefaultFlags());
	}

	/** This version of the constructor has a 'flags' argument for
		controlling whether ticks, grid, etc. are present and whether
		the axes are logarithmic */
	public Plot(String title, String xLabel, String yLabel, int flags) {
		this(title, xLabel, yLabel, (float[])null, (float[])null, flags);
	}

	/** Obsolete, replaced by "new Plot(title,xLabel,yLabel,flags); add(shape,x,y);".
	 * @deprecated
	*/
	public Plot(String title, String xLabel, String yLabel, float[] xValues, float[] yValues, int flags) {
		this.title = title;
		pp.axisFlags = flags;
		setXYLabels(xLabel, yLabel);
		if (yValues != null && yValues.length>0) {
			addPoints(xValues, yValues, /*yErrorBars=*/null, LINE, /*label=*/null);
			allPlotObjects.get(0).flags = PlotObject.CONSTRUCTOR_DATA;
		}
	}

	/** Obsolete, replaced by "new Plot(title,xLabel,yLabel,flags); add(shape,x,y);".
	 * @deprecated
	*/
	public Plot(String title, String xLabel, String yLabel, double[] x, double[] y, int flags) {
		this(title, xLabel, yLabel, x!=null?Tools.toFloat(x):null, y!=null?Tools.toFloat(y):null, flags);
	}

	/** Constructs a new plot from an InputStream and closes the stream. If the ImagePlus is
	 *  non-null, its title and ImageProcessor are used, but the image displayed is not modified.
	*/
	public Plot(ImagePlus imp, InputStream is) throws IOException, ClassNotFoundException {
		ObjectInputStream in = new ObjectInputStream(is);
		pp = (PlotProperties)in.readObject();
		allPlotObjects = (Vector<PlotObject>)in.readObject();
		in.close();
		if (pp.xLabel.type==8) {
			pp.xLabel.updateType();	//convert old (pre-1.52i) type codes for the PlotObjects
			pp.yLabel.updateType();
			pp.frame.updateType();
			if (pp.legend != null) pp.legend.updateType();
			for (PlotObject plotObject : allPlotObjects)
				plotObject.updateType();
		}

		defaultMinMax = pp.rangeMinMax;
		currentFont = nonNullFont(pp.frame.getFont(), currentFont); // best guess in case we want to add a legend
		getProcessor();     //prepares scale, calibration etc, but does not plot it yet
		this.title = imp != null ? imp.getTitle() : "Untitled Plot";
		if (imp != null) {
			this.imp = imp;
			ip = imp.getProcessor();
			imp.setIgnoreGlobalCalibration(true);
			adjustCalibration(imp.getCalibration());
			imp.setProperty(PROPERTY_KEY, this);
		}
	}

	/** Obsolete, replaced by "new Plot(title,xLabel,yLabel); add(shape,x,y);".
	 * @deprecated
	*/
	public Plot(String dummy, String title, String xLabel, String yLabel, float[] x, float[] y) {
		this(title, xLabel, yLabel, x, y, getDefaultFlags());
	}

	/** Writes this plot into an OutputStream containing (1) the serialized PlotProperties and
	 *	(2) the serialized Vector of all 'added' PlotObjects. The stream is NOT closed.
	 *	The plot should have been drawn already.
	 */
	 //	 Conversion to Streams can be also used to clone plots (not a shallow clone), but this is rather slow.
	 //	 Sample code:
	 //	  try {
	 //		final PipedOutputStream pos = new PipedOutputStream();
	 //		final PipedInputStream pis = new PipedInputStream(pos);
	 //		new Thread(new Runnable() {
	 //		  final public void run() {
	 //			try {
	 //			  Plot p = new Plot(null, pis);
	 //			  pis.close();
	 //			  pos.close();
	 //			  p.show();
	 //			} catch(Exception e) {IJ.handleException(e);};
	 //		  }
	 //		}, "threadMakingPlotFromStream").start();
	 //		toStream(pos);
	 //	  } catch(Exception e) {IJ.handleException(e);}
	void toStream(OutputStream os) throws IOException {
		//prepare
		for (PlotObject plotObject : pp.getAllPlotObjects())		//make sure all fonts are set properly
			if (plotObject != null)
				plotObject.setFont(nonNullFont(plotObject.getFont(), currentFont));
		pp.rangeMinMax = currentMinMax;
		//write
		ObjectOutputStream out = new ObjectOutputStream(os);
		out.writeObject(pp);
		out.writeObject(allPlotObjects);
	}

	/** Writes this plot into a byte array containing (1) the serialized PlotProperties and
	 *	(2) the serialized Vector of all 'added' PlotObjects.
	 *	The plot should have been drawn already. Returns null on error (which should never happen). */
	public byte[] toByteArray() {
		try {
			ByteArrayOutputStream bos = new ByteArrayOutputStream();
			toStream(bos);
			bos.close();
			return bos.toByteArray();
		} catch (Exception e) {
			IJ.handleException(e);
			return null;
		}
	}

	/** Returns the title of the image showing the plot (if any) or title of the plot */
	public String getTitle() {
		return imp == null ? title : imp.getTitle();
	}

	/** Sets the x-axis and y-axis range. Saves the new limits as default (so the 'R' field sets the limits to these).
	 *  Updates the image if existing.
	 *  Accepts NaN values to indicate auto-range. */
	public void setLimits(double xMin, double xMax, double yMin, double yMax) {
		setLimitsNoUpdate(xMin, xMax, yMin, yMax);
		makeLimitsDefault();
		ignoreForce2Grid = true;
		if (plotDrawn)
			setLimitsToDefaults(true);
	}

	/** Sets the x-axis and y-axis range. Accepts NaN values to indicate auto range.
	 *  Does not update the image and leaves the default limits (for reset via the 'R' field) untouched. */
	void setLimitsNoUpdate(double xMin, double xMax, double yMin, double yMax) {
		boolean containsNaN = (Double.isNaN(xMin + xMax + yMin + yMax));
		if (containsNaN && getNumPlotObjects(PlotObject.XY_DATA|PlotObject.ARROWS, false)==0)//can't apply auto-range without data
			return;
		double[] range = {xMin, xMax, yMin, yMax};
		if (containsNaN) {                          //auto range for at least one limit
			double[] extrema = getMinAndMax(true, ALL_AXES_RANGE);
			boolean[] auto = new boolean[range.length];
			for (int i = 0; i < range.length; i++)
				if (Double.isNaN(range[i])) {
					auto[i] = true;
					range[i] = extrema[i];
				}
			for (int a = 0; a<range.length; a+=2) { //for all axes (0 for x, 2 for y): would semi-auto reverse the axis?
				if (auto[a] == auto[a+1]) continue; //ignore if not semi-auto
				boolean currentAxisReverse = defaultMinMax[a+1] < defaultMinMax[a];
				if ((!currentAxisReverse && range[a+1] <= range[a]) || (currentAxisReverse && range[a] <= range[a+1])) {
					auto[a] = true;					//semi-auto to full-auto
					auto[a+1] = true;
					range[a] = extrema[a];
					range[a+1] = extrema[a+1];
				}
			}
			for (int i = 0; i < range.length; i++)
				if (!auto[i])       // don't modify for limits that were set manually
					enlargeRange[i] = 0;
			enlargeRange(range);    // for automatic limits, avoid points exactly at the border
		}
		System.arraycopy(range, 0, currentMinMax, 0, Math.min(range.length, currentMinMax.length));
		ignoreForce2Grid = true;
	}

	/** Takes over the current limits as the default ones (i.e., the limits set by clicking at the 'R' field in the bottom-left corner) */
	void makeLimitsDefault() {
		System.arraycopy(currentMinMax, 0, defaultMinMax, 0, Math.min(currentMinMax.length, defaultMinMax.length));
	}

	/** Returns the current limits as an array xMin, xMax, yMin, yMax.
	 *  (note that ImageJ versions before to 1.52i have returned incorrect values in case of log axes)
	 *	Note that future versions might return a longer array (e.g. for y2 axis limits) */
	public double[] getLimits() {
		return currentMinMax.clone();//new double[] {xMin, xMax, yMin, yMax};
	}

	/** Sets the current limits from an array xMin, xMax, yMin, yMax
	 *  The array may be also longer or shorter, but should not contain NaN values.
	 *  This method should be used after the plot has been displayed.
	 *  Does not update the plot; use updateImage() thereafter.
	 *  Does not save the previous limits, i.e., leaves the default limits (for reset via the 'R' field) untouched.
	*/
	public void setLimits(double[] limits) {
		System.arraycopy(limits, 0, currentMinMax, 0, Math.min(limits.length, defaultMinMax.length));
	}

	/** Sets options for the plot. Multiple options may be separated by whitespace or commas.
	 *  Note that whitespace surrounding the '=' characters is not allowed.
	 *  Currently recognized options are:
	 *  "addhspace=10 addvspace=5" Increases the left&right or top&bottom margins by the given number of pixels.
	 *  "xinterval=30 yinterval=90" Sets interval between numbers, major ticks & grid lines
	 *    (default intervals are used if the custom intervals would be too dense or too sparse)
	 *  "xdecimals=2 ydecimals=-1" Sets the minimum number of decimals; use negative numbers for scientific notation.
	 *  "msymbol=' \\u00d7 '" Sets multiplication symbol for scientific notation, here a cross with spaces.
	 *  */
	public void setOptions(String options) {
		pp.frame.options = options.toLowerCase();
	}

	/** Sets the canvas size in (unscaled) pixels and sets the scale to 1.0.
	 * If the scale remains 1.0, this will be the size of the resulting ImageProcessor.
	 * When not called, the canvas size is adjusted for the plot size specified
	 * by setFrameSize() or setWindowSize(), or otherwise in Edit>Options>Plots.
	 * @see #setFrameSize(int,int)
	 * @see #setWindowSize(int,int)
	*/
	public void setSize(int width, int height) {
		if (ip != null && width == ip.getWidth() && height == ip.getHeight())
			return;
		Dimension minSize = getMinimumSize();
		pp.width = Math.max(width, minSize.width);
		pp.height = Math.max(height, minSize.height);
		scale = 1.0f;
		ip = null;
		if (plotDrawn) updateImage();
	}

	/** The size of the plot including borders with axis labels etc., in pixels */
	public Dimension getSize() {
		if (ip == null)
			getBlankProcessor();
		return new Dimension(ip.getWidth(), ip.getHeight());
	}

	/** Sets the plot frame size in (unscaled) pixels. This size does not include the
	 *	borders with the axis labels. Also sets the scale to 1.0.
	 *	This frame size in pixels divided by the data range defines the image scale.
	 *	This method does not check for the minimum size MIN_FRAMEWIDTH, MIN_FRAMEHEIGHT.
	 *	Note that the black frame will have an outer size that is one pixel larger
	 *	(when plotted with a linewidth of one pixel).
	 * @see #setWindowSize(int,int)
	*/
	public void setFrameSize(int width, int height) {
		if (pp.width <= 0) {                //plot not drawn yet? Just remember as preferred size
			preferredPlotWidth = width;
			preferredPlotHeight = height;
			scale = 1.0f;
		} else {
			makeMarginValues();
			width += leftMargin+rightMargin;
			height += topMargin+bottomMargin;
			setSize(width, height);
		}
	}

	/** Sets the plot window size in pixels.
	 * @see #setFrameSize(int,int)
	*/
	public void setWindowSize(int width, int height) {
		scale = 1.0f;
		makeMarginValues();
		int titleBarHeight = 22;
		int infoHeight = 11;
		double scale = Prefs.getGuiScale();
		if (scale>1.0)
			infoHeight = (int)(infoHeight*scale);
		int buttonPanelHeight = 45;
		if (pp.width <= 0) {     //plot not drawn yet?
			int extraWidth = leftMargin+rightMargin+ImageWindow.HGAP*2;
			int extraHeight = topMargin+bottomMargin+titleBarHeight+infoHeight+buttonPanelHeight;
			if (extraWidth<width)
				width -= extraWidth;
			if (extraHeight<height)
				height -= extraHeight;
			preferredPlotWidth = width;
			preferredPlotHeight = height;
		} else {
			int extraWidth = ImageWindow.HGAP*2;
			int extraHeight = titleBarHeight+infoHeight+buttonPanelHeight;
			if (extraWidth<width)
				width -= extraWidth;
			if (extraHeight<height)
				height -= extraHeight;
			setSize(width, height);
		}
	}

	/** The minimum plot size including borders, in pixels (at scale=1) */
	public Dimension getMinimumSize() {
		return new Dimension(MIN_FRAMEWIDTH + leftMargin + rightMargin,
				MIN_FRAMEHEIGHT + topMargin + bottomMargin);
	}

	/** Adjusts the format with another plot as a template, using the current
	 *  (usually default) templateFlags of this plot.
	 *  <code>plot</code> may be null; then the call has no effect. */
	public void useTemplate(Plot plot) {
		useTemplate(plot, templateFlags);
	}

	/** Adjusts the format (style) with another plot as a template. Flags determine what to
	 *	copy from the template; these can be X_RANGE, Y_RANGE, COPY_SIZE, COPY_LABELS, COPY_AXIS_STYLE,
	 *  COPY_CONTENTS_STYLE (hidden items are ignored), and COPY_LEGEND.
	 *	<code>plot</code> may be null; then the call has no effect. */
	public void useTemplate(Plot plot, int templateFlags) {
		if (plot == null) return;
		this.defaultFont = plot.defaultFont;
		this.currentFont = plot.currentFont;
		this.currentLineWidth = plot.currentLineWidth;
		this.currentColor = plot.currentColor;
		if ((templateFlags & COPY_AXIS_STYLE) != 0) {
			this.pp.axisFlags = plot.pp.axisFlags;
			this.pp.frame = plot.pp.frame.deepClone();
		}
		if ((templateFlags & COPY_LABELS) != 0) {
			this.pp.xLabel.label = plot.pp.xLabel.label;
			this.pp.yLabel.label = plot.pp.yLabel.label;
			this.pp.xLabel.setFont(plot.pp.xLabel.getFont());
			this.pp.yLabel.setFont(plot.pp.yLabel.getFont());
		}
		for (int i=0; i<currentMinMax.length; i++)
			if ((templateFlags>>(i/2)&0x1) != 0) {
				currentMinMax[i] = plot.currentMinMax[i];
				if (!plotDrawn) defaultMinMax[i] = plot.currentMinMax[i];
			}
		if ((templateFlags & COPY_LEGEND) != 0 && plot.pp.legend != null)
			this.pp.legend = plot.pp.legend.deepClone();
		if ((templateFlags & (COPY_LEGEND | COPY_CONTENTS_STYLE)) != 0) {
			int plotPObjectIndex = 0;  //points to PlotObjects of the templatePlot
			int plotPObjectsSize = plot.allPlotObjects.size();
			for (PlotObject plotObject : allPlotObjects) {
				if (plotObject.type == PlotObject.XY_DATA && !plotObject.hasFlag(PlotObject.HIDDEN)) {
					while(plotPObjectIndex<plotPObjectsSize &&
							(plot.allPlotObjects.get(plotPObjectIndex).type != PlotObject.XY_DATA ||
							 plot.allPlotObjects.get(plotPObjectIndex).hasFlag(PlotObject.HIDDEN)))
						plotPObjectIndex++; //skip everything that is invisible or has no label
					if (plotPObjectIndex>=plotPObjectsSize) break;
					if ((templateFlags & COPY_LEGEND) != 0)
						plotObject.label = plot.allPlotObjects.get(plotPObjectIndex).label;
					if ((templateFlags & COPY_CONTENTS_STYLE) != 0)
						setPlotObjectStyle(plotObject, getPlotObjectStyle(plot.allPlotObjects.get(plotPObjectIndex)));
					plotPObjectIndex++;
				}
			}
		}
		if ((templateFlags & COPY_SIZE) != 0)
			setSize(plot.pp.width, plot.pp.height);

		if ((templateFlags & COPY_EXTRA_OBJECTS) != 0)
			for (int p = allPlotObjects.size(); p < plot.allPlotObjects.size(); p++)
				allPlotObjects.add(plot.allPlotObjects.get(p));
		this.templateFlags = templateFlags;
	}

	/** Sets the scale. Everything, including labels, line thicknesses, etc will be scaled by this factor.
	 *  Also multiplies the plot size by this value. Used for 'Create high-resolution plot'.
	 *	Should be called before creating the plot.
	 *  Note that plots with a scale different from 1.0 must not be shown in a PlotWindow, but only as
	 *  simple image in a normal ImageWindow. */
	public void setScale(float scale) {
		this.scale = scale;
		if (scale > 20f) scale = 20f;
		if (scale < 0.7f) scale = 0.7f;
		pp.width = sc(pp.width);
		pp.height = sc(pp.height);
		plotDrawn = false;
	}

	/** Sets the labels of the x and y axes. 'xLabel', 'yLabel' may be null.
	 *  If a label has the form {txt1,txt2,txt3}, the corresponding axis will be labeled
	 *  not by numbers but rather with the texts "txt1", "txt2" ... instead of 0, 1, ...
	 *  In this special case, there will be no label for the axis on the plot.
	 *	Call update() thereafter to make the change visible (if it is shown already). */
	public void setXYLabels(String xLabel, String yLabel) {
		pp.xLabel.label = xLabel!=null ? xLabel : "";
		pp.yLabel.label = yLabel!=null ? yLabel : "";
	}

	/** Sets the maximum number of intervals in a plot.
	 *	Call update() thereafter to make the change visible (if the image is shown already). */
	public void setMaxIntervals(int intervals) {
			maxIntervals = intervals;
	}

	/** Sets the length of the major tick in pixels.
	 *	Call update() thereafter to make the change visible (if the image is shown already). */
	public void setTickLength(int tickLength) {
			this.tickLength = tickLength;
	}

	/** Sets the length of the minor tick in pixels. */
	public void setMinorTickLength(int minorTickLength) {
			this.minorTickLength = minorTickLength;
	}

	/** Sets the flags that control the axes format.
	 *	Does not modify the flags for logarithmic axes on/off and the FORCE2GRID flags.
	 *	Call update() thereafter to make the change visible (if it is shown already). */
	public void setFormatFlags(int flags) {
		int unchangedFlags = X_LOG_NUMBERS | Y_LOG_NUMBERS | X_FORCE2GRID | Y_FORCE2GRID;
		flags = flags & (~unchangedFlags);	  //remove flags that should not be affected
		pp.axisFlags = (pp.axisFlags & unchangedFlags) | flags;
	}

	/** Returns the flags that control the axes */
	public int getFlags() {
		return pp.axisFlags;
	}

	/** Sets the X Axis format to Log or Linear.
	 *	Call update() thereafter to make the change visible (if it is shown already). */
	public void setAxisXLog(boolean axisXLog) {
		pp.axisFlags = axisXLog ? pp.axisFlags | X_LOG_NUMBERS : pp.axisFlags & (~X_LOG_NUMBERS);
	}

	/** Sets the Y Axis format to Log or Linear.
	 *	Call update() thereafter to make the change visible (if it is shown already). */
	public void setAxisYLog(boolean axisYLog) {
		pp.axisFlags = axisYLog ? pp.axisFlags | Y_LOG_NUMBERS : pp.axisFlags & (~Y_LOG_NUMBERS);
	}

	/** Sets whether to show major ticks at the x axis.
	 *	Call update() thereafter to make the change visible (if the image is shown already). */

	public void setXTicks(boolean xTicks) {
		pp.axisFlags = xTicks ? pp.axisFlags | X_TICKS : pp.axisFlags & (~X_TICKS);
	}

	/** Sets whether to show major ticks at the y axis.
	 *	Call update() thereafter to make the change visible (if the image is shown already). */
	public void setYTicks(boolean yTicks) {
		pp.axisFlags = yTicks ? pp.axisFlags | Y_TICKS : pp.axisFlags & (~Y_TICKS);
	}

	/** Sets whether to show minor ticks on the x axis (if linear). Also sets major ticks if true and no grid is set.
	 *	Call update() thereafter to make the change visible (if the image is shown already). */
	public void setXMinorTicks(boolean xMinorTicks) {
		pp.axisFlags = xMinorTicks ? pp.axisFlags | X_MINOR_TICKS : pp.axisFlags & (~X_MINOR_TICKS);
		if (xMinorTicks && !hasFlag(X_GRID))
			pp.axisFlags |= X_TICKS;
	}

	/** Sets whether to show minor ticks on the y axis (if linear). Also sets major ticks if true and no grid is set.
	 *	Call update() thereafter to make the change visible (if the image is shown already). */
	public void setYMinorTicks(boolean yMinorTicks) {
		pp.axisFlags = yMinorTicks ? pp.axisFlags | Y_MINOR_TICKS : pp.axisFlags & (~Y_MINOR_TICKS);
		if (yMinorTicks && !hasFlag(Y_GRID))
			pp.axisFlags |= Y_TICKS;
	}

	/** Sets the properties of the axes. Call update() thereafter to make the change visible
	 *	(if the image is shown already). */
	public void setAxes(boolean xLog, boolean yLog, boolean xTicks, boolean yTicks, boolean xMinorTicks, boolean yMinorTicks,
			int tickLenght, int minorTickLenght) {
		setAxisXLog		  (xLog);
		setAxisYLog		  (yLog);
		setXMinorTicks	  (xMinorTicks);
		setYMinorTicks	  (yMinorTicks);
		setXTicks		  (xTicks);
		setYTicks		  (yTicks);
		setTickLength	  (tickLenght);
		setMinorTickLength(minorTickLenght);
	}

	/** Sets log scale in x. Call update() thereafter to make the change visible
	 *	(if the image is shown already). */

	public void setLogScaleX() {
		setAxisXLog(true);
	}

	public void setLogScaleY() {
		setAxisYLog(true);
	}

	/** The default flags, taking PlotWindow.noGridLines, PlotWindow.noTicks into account */
	public static int getDefaultFlags() {
		int defaultFlags = 0;
		if (!PlotWindow.noGridLines) //note that log ticks are also needed because the range may span less than a decade, then no grid is visible
			defaultFlags |= X_GRID | Y_GRID | X_NUMBERS | Y_NUMBERS | X_LOG_TICKS | Y_LOG_TICKS;
		if (!PlotWindow.noTicks)
			defaultFlags |= X_TICKS | Y_TICKS | X_MINOR_TICKS | Y_MINOR_TICKS | X_NUMBERS | Y_NUMBERS | X_LOG_TICKS | Y_LOG_TICKS;
		return defaultFlags;
	}

	/** Adds a curve or set of points to this plot, where 'type' is
	 * "line", "connected circle", "filled", "bar", "separated bar", "circle", "box", "triangle", "diamond", "cross",
	 * "x" or "dot". Run <i>Help&gt;Examples&gt;JavaScript&gt;Graph Types</i> to see examples.
	 * If 'type' is in the form "code: <macroCode>", the macro given is executed to draw the symbol;
	 * macro variables 'x' and 'y' are the pixel coordinates of the point, 'xval' and 'yval' are the plot data
	 * and 'i' is the index of the data point (starting with 0 for the first point in the array).
	 * The drawing including line thickness, font size, etc. be scaled by scale factor 's' (to make high-resolution plots work).
	 * Example: "code: setFont('sanserif',12*s,'bold anti');drawString(d2s(yval,1),x-14*s,y-4*s);"
	 * writes the y value for each point above the point.
	*/
	public void add(String type, double[] xvalues, double[] yvalues) {
		int iShape = toShape(type);
		addPoints(Tools.toFloat(xvalues), Tools.toFloat(yvalues), null, iShape, iShape==CUSTOM?type.substring(5, type.length()):null);
	}

	/** Replaces the specified plot object (curve or set of points).
		 Equivalent to add() if there are no plot objects. */
	public void replace(int index, String type, double[] xvalues, double[] yvalues) {
		if (index>=0 && index<allPlotObjects.size()) {
			objectToReplace = allPlotObjects.size()>0?index:-1;
			add(type, xvalues, yvalues);
		}
	}

	/** Adds a curve, set of points or error bars to this plot, where 'type' is
	 * "line", "connected circle", "filled", "bar", "separated bar", "circle", "box",
	 * "triangle", "diamond", "cross", "x", "dot", "error bars" or "xerror bars".
	*/
	public void add(String type, double[] yvalues) {
		int iShape = toShape(type);
		if (iShape==-1)
			addErrorBars(yvalues);
		else if (iShape==-2)
			addHorizontalErrorBars(yvalues);
		else
			addPoints(null, Tools.toFloat(yvalues), null, iShape, iShape==CUSTOM?type.substring(5, type.length()):null);
	}

	/** Adds a set of points to the plot or adds a curve if shape is set to LINE.
	 * @param xValues	the x coordinates, or null. If null, integers starting at 0 will be used for x.
	 * @param yValues	the y coordinates (must not be null)
	 * @param yErrorBars error bars in y, may be null
	 * @param shape		CIRCLE, X, BOX, TRIANGLE, CROSS, DIAMOND, DOT, LINE, CONNECTED_CIRCLES
	 * @param label		Label for this curve or set of points, used for a legend and for listing the plots
	 */
	public void addPoints(float[] xValues, float[] yValues, float[] yErrorBars, int shape, String label) {
		if (xValues==null || xValues.length==0) {
			xValues = new float[yValues.length];
			for (int i=0; i<yValues.length; i++)
				xValues[i] = i;
		}
		if (objectToReplace>=0)
			allPlotObjects.set(objectToReplace, new PlotObject(xValues, yValues, yErrorBars, shape, currentLineWidth, currentColor, currentColor2, label));
		else
			allPlotObjects.add(new PlotObject(xValues, yValues, yErrorBars, shape, currentLineWidth, currentColor, currentColor2, label));
		objectToReplace = -1;
		if (plotDrawn) updateImage();
	}

	/** Adds a set of points to the plot or adds a curve if shape is set to LINE.
	 * @param x			the x coordinates
	 * @param y			the y coordinates
	 * @param shape		CIRCLE, X, BOX, TRIANGLE, CROSS, DIAMOND, DOT, LINE, CONNECTED_CIRCLES
	 */
	public void addPoints(float[] x, float[] y, int shape) {
		addPoints(x, y, null, shape, null);
	}

	/** Adds a set of points to the plot using double arrays. */
	public void addPoints(double[] x, double[] y, int shape) {
		addPoints(Tools.toFloat(x), Tools.toFloat(y), shape);
	}

	/** Returns the number for a given plot symbol shape, -1 for xError and -2 for yError (all case-insensitive) */
	public static int toShape(String str) {
		str = str.toLowerCase(Locale.US);
		int shape = Plot.CIRCLE;
		if (str.contains("curve") || str.contains("line"))
			shape = Plot.LINE;
		else if (str.contains("connected"))
			shape = Plot.CONNECTED_CIRCLES;
		else if (str.contains("filled"))
			shape = Plot.FILLED;
		else if (str.contains("circle"))
			shape = Plot.CIRCLE;
		else if (str.contains("box"))
			shape = Plot.BOX;
		else if (str.contains("triangle"))
			shape = Plot.TRIANGLE;
		else if (str.contains("cross") || str.contains("+"))
			shape = Plot.CROSS;
		else if (str.contains("diamond"))
			shape = Plot.DIAMOND;
		else if (str.contains("dot"))
			shape = Plot.DOT;
		else if (str.contains("xerror"))
			shape = -2;
		else if (str.contains("error"))
			shape = -1;
		else if (str.contains("x"))
			shape = Plot.X;
		else if (str.contains("separate"))
			shape = Plot.SEPARATED_BAR;
		else if (str.contains("bar"))
			shape = Plot.BAR;
		if (str.startsWith("code:"))
			shape = CUSTOM;
		return shape;
	}

	/** Adds a set of points to the plot using double ArrayLists.
	 * Must be called before the plot is displayed. */
	public void addPoints(ArrayList x, ArrayList y, int shape) {
		addPoints(getDoubleFromArrayList(x), getDoubleFromArrayList(y), shape);
	}

	/** Adds a set of points to the plot or adds a curve if shape is set to LINE.
	 * @param x			the x-coodinates
	 * @param y			the y-coodinates
	 * @param errorBars	half-lengths of the vertical error bars, may be null
	 * @param shape		CIRCLE, X, BOX, TRIANGLE, CROSS, DIAMOND, DOT or LINE
	 */
	public void addPoints(double[] x, double[] y, double[] errorBars, int shape) {
		addPoints(Tools.toFloat(x), Tools.toFloat(y), Tools.toFloat(errorBars), shape, null);
	}

	/** Adds a set of points to the plot using double ArrayLists.
	 * Must be called before the plot is displayed. */
	public void addPoints(ArrayList x, ArrayList y, ArrayList errorBars, int shape) {
		addPoints(getDoubleFromArrayList(x), getDoubleFromArrayList(y), getDoubleFromArrayList(errorBars), shape);
	}

	public double[] getDoubleFromArrayList(ArrayList list) {
		if (list == null) return null;
		double[] targ = new double[list.size()];
		for (int i = 0; i < list.size(); i++)
			targ[i] = ((Double) list.get(i)).doubleValue();
		return targ;
	}

	/** Adds a set of points that will be drawn as ARROWs.
	 * @param x1		the x-coodinates of the beginning of the arrow
	 * @param y1		the y-coodinates of the beginning of the arrow
	 * @param x2		the x-coodinates of the end		  of the arrow
	 * @param y2		the y-coodinates of the end		  of the arrow
	 */
	public void drawVectors(double[] x1, double[] y1, double[] x2, double[] y2) {
		allPlotObjects.add(new PlotObject(Tools.toFloat(x1), Tools.toFloat(y1),
				Tools.toFloat(x2), Tools.toFloat(y2), currentLineWidth, currentColor));
	}

	/**
	 * Adds a set of 'shapes' such as boxes and whiskers
	 *
	 * @param shapeType e.g. "boxes width=20"
	 * @param floatCoords eg[6][3] holding 1 Xval + 5 Yvals for 3 boxes
	 */
	public void drawShapes(String shapeType, ArrayList floatCoords) {
		allPlotObjects.add(new PlotObject(shapeType, floatCoords, currentLineWidth, currentColor, currentColor2));
	}

	public static double calculateDistance(int x1, int y1, int x2, int y2) {
		return java.lang.Math.sqrt((x2 - x1)*(double)(x2 - x1) + (y2 - y1)*(double)(y2 - y1));
	}

	/** Adds a set of vectors to the plot using double ArrayLists.
	 *	Does not support logarithmic axes.
	 *	Must be called before the plot is displayed. */
	public void drawVectors(ArrayList x1, ArrayList y1, ArrayList x2, ArrayList y2) {
		drawVectors(getDoubleFromArrayList(x1), getDoubleFromArrayList(y1), getDoubleFromArrayList(x2), getDoubleFromArrayList(y2));
	}

	/** Adds vertical error bars to the last data passed to the plot (via the constructor or addPoints). */
	public void addErrorBars(float[] errorBars) {
		PlotObject mainObject = getLastCurveObject();
		if (mainObject != null)
			mainObject.yEValues = errorBars;
		else throw new RuntimeException("Plot can't add y error bars without data");
	}

	/** Adds vertical error bars to the last data passed to the plot (via the constructor or addPoints). */
	public void addErrorBars(double[] errorBars) {
		addErrorBars(Tools.toFloat(errorBars));
	}

	/** Adds horizontal error bars to the last data passed to the plot (via the constructor or addPoints). */
	public void addHorizontalErrorBars(float[] xErrorBars) {
		PlotObject mainObject = getLastCurveObject();
		if (mainObject != null)
			mainObject.xEValues = xErrorBars;
		else throw new RuntimeException("Plot can't add x error bars without data");
	}

	/** Adds horizontal error bars to the last data passed to the plot (via the constructor or addPoints). */
	public void addHorizontalErrorBars(double[] xErrorBars) {
		addHorizontalErrorBars(Tools.toFloat(xErrorBars));
	}

	/** Draws text at the specified location, where (0,0)
	 *  is the upper left corner of the the plot frame and (1,1) is
	 *  the lower right corner. Uses the justification specified by setJustification().
	 *  When called with the same position as the previous addLabel call, the text of that previous call is replaced */
	public void addLabel(double x, double y, String label) {
		if (textLoc!=null && x==textLoc.getX() && y==textLoc.getY())
			allPlotObjects.set(textIndex, new PlotObject(label, x, y, currentJustification, currentFont, currentColor, PlotObject.NORMALIZED_LABEL));
		else {
			allPlotObjects.add(new PlotObject(label, x, y, currentJustification, currentFont, currentColor, PlotObject.NORMALIZED_LABEL));
			textLoc = new Point2D.Double(x,y);
			textIndex = allPlotObjects.size()-1;
		}
	}

	/* Draws text at the specified location, using the coordinate system defined
	 * by setLimits() and the justification specified by setJustification(). */
	public void addText(String label, double x, double y) {
		allPlotObjects.add(new PlotObject(label, x, y, currentJustification, currentFont, currentColor, PlotObject.LABEL));
	}

	/** Adds an automatically positioned legend, where 'labels' can be a tab-delimited or
		newline-delimited list of curve or point labels in the sequence these data were added.
		Hidden data sets are ignored.
		If 'labels' is null or empty, the labels of the data set previously (if any) are used.
		To modify the legend's style, call 'setFont' and 'setLineWidth' before 'addLegend'. */
	public void addLegend(String labels) {
		addLegend(labels, "auto");
	}

	/** Adds a legend at the position given in 'options', where 'labels' can be tab-delimited or
	 *  newline-delimited list of curve or point labels in the sequence these data were added.
	 *  Hidden data sets are ignored; no labels (and no delimiters) should be provided for these.
	 *  Apart from top to bottom and bottom to top (controlled by "bottom-to-top" in the options),
	 *  the sequence may be altered by preceding numbers followed by double underscores, such as
	 *  "1__Other Data Set\t0__First Data Set" (the number and double underscore won't be displayed).
	 *  When this possibility is used, only items with double underscores will be shown in the legend
	 *  (preceding double underscores without a number make the item appear in the legend without altering the sequence).
	 * 	If 'labels' is null or empty, the labels of the data set previously (if any) are used.
		To modify the legend's style, call 'setFont' and 'setLineWidth' before 'addLegend'. */
	public void addLegend(String labels, String options) {
		int flags = 0;
		if (options!=null) {
			options = options.toLowerCase();
			if (options.contains("top-left"))
				flags |= Plot.TOP_LEFT;
			else if (options.contains("top-right"))
				flags |= Plot.TOP_RIGHT;
			else if (options.contains("bottom-left"))
				flags |= Plot.BOTTOM_LEFT;
			else if (options.contains("bottom-right"))
				flags |= Plot.BOTTOM_RIGHT;
			else if (!options.contains("off") && !options.contains("no"))
				flags |= Plot.AUTO_POSITION;
			if (options.contains("bottom-to-top"))
				flags |= Plot.LEGEND_BOTTOM_UP;
			if (options.contains("transparent"))
				flags |= Plot.LEGEND_TRANSPARENT;
		}
		setLegend(labels, flags);
	}

	/** Adds a legend. The legend will be always drawn last (on top of everything).
	 *	To modify the legend's style, call 'setFont' and 'setLineWidth' before 'addLegend'
	 *	@param labels labels of the points or curves in the sequence of the data were added, tab-delimited or linefeed-delimited.
	 *	The labels of the datasets will be set to these values. If null or not given, the labels set
	 *	previously (if any) will be used.
	 *	Hidden data sets are ignored; no labels (and no delimiters) should be provided for these.
	 *	Apart from top to bottom and bottom to top (controlled by the LEGEND_BOTTOM_UP flag),
	 *  the sequence may be altered by preceding numbers followed by double underscores, such as
	 *  "1__Other Data Set\t0__First Data Set" (the number and double underscore won't be displayed).
	 *  When this possibility is used, only items with double underscores will be shown in the legend
	 *  (preceding double underscores without a number make the item appear in the legend without altering the sequence).
	 *	@param flags  Bitwise or of position (AUTO_POSITION, TOP_LEFT etc.), LEGEND_TRANSPARENT, and LEGEND_BOTTOM_UP if desired.
	 *	Updates the image (if it is shown already). */
	public void setLegend(String labels, int flags) {
		if (labels != null && labels.length()>0) {
			String[] allLabels = labels.split("[\n\t]");
			int iPart = 0;
			for (PlotObject plotObject : allPlotObjects)
				if (plotObject.type == PlotObject.XY_DATA && !plotObject.hasFlag(PlotObject.HIDDEN))
					if (iPart < allLabels.length) {
						String label = allLabels[iPart++];
						if (label!=null && label.length()>0)
							plotObject.label = label;
					}
		}
		pp.legend = new PlotObject(currentLineWidth == 0 ? 1 : currentLineWidth,
				currentFont, currentColor == null ? Color.black : currentColor, flags);
		if (plotDrawn) updateImage();
	}

	/** Sets the label for the plot object number 'index' in the sequence they were added.
	 *  With index=-1, sets the label for the last object added.
	 *  For x/y data, the label is used for the legend and as header in getResultsTableWithLabels.
	 *  For Text/Label objects, it affects the label shown (but the plot is not redisplayed).
	*/
	public void setLabel(int index, String label) {
		if (index < 0) index = allPlotObjects.size() + index;
		allPlotObjects.get(index).label = label;
	}

	/** Removes NaNs from the xValues and yValues arrays of all plot objects. */ 
	public void removeNaNs() {
		for (PlotObject plotObj : allPlotObjects){
			if(plotObj != null && plotObj.xValues!= null && plotObj.yValues != null ){
				int oldSize = plotObj.xValues.length;
				float[] xVals = new float[oldSize];
				float[] yVals = new float[oldSize];
				int newSize = 0;
				for (int kk = 0; kk < oldSize; kk++) {
					if (!Float.isNaN(plotObj.xValues[kk] + plotObj.yValues[kk])) {
						xVals[newSize] = plotObj.xValues[kk];
						yVals[newSize] = plotObj.yValues[kk];
						newSize++;
					}
				}
				if (newSize < oldSize) {
					plotObj.xValues = new float[newSize];
					plotObj.yValues = new float[newSize];
					System.arraycopy(xVals, 0, plotObj.xValues, 0, newSize);
					System.arraycopy(yVals, 0, plotObj.yValues, 0, newSize);
				}
			}
		}
	}

	/** Returns an array of the available curve types ("Line", "Bar", "Circle", etc). */
	public String[] getTypes() {
		return SORTED_SHAPES;
	}

	/** Sets the justification used by addLabel(), where <code>justification</code>
	 * is Plot.LEFT, Plot.CENTER or Plot.RIGHT. Default is LEFT. */
	public void setJustification(int justification) {
		currentJustification = justification;
	}

	/** Changes the drawing color for the next objects that will be added to the plot.
	 *	For selecting the color of the curve passed with the constructor,
	 *	use <code>setColor</code> before <code>draw</code>.
	 *	The frame and labels are always drawn in black. */
	public void setColor(Color c) {
		currentColor = c;
		currentColor2 = null;
	}

	public void setColor(String color) {
		setColor(Colors.decode(color, Color.black));
	}

	/** Changes the drawing color for the next objects that will be added to the plot.
	 *	It also sets secondary color: This is the color of the line for CONNECTED_CIRCLES,
	 *	and the color for filling open symbols (CIRCLE, BOX, TRIANGLE).
	 *	Set it to null or use the one-argument call setColor(color) to disable filling.
	 *	For selecting the color of the curve passed with the constructor,
	 *	use <code>setColor</code> before <code>draw</code>.
	 *	The frame and labels are always drawn in black. */
	public void setColor(Color c, Color c2) {
		currentColor = c;
		currentColor2 = c2;
	}

	/** Sets the drawing colors for the next objects that will be added to the plot. */
	public void setColor(String c1, String c2) {
		setColor(Colors.decode(c1, Color.black), Colors.decode(c2, null));
	}

	/** Set the plot frame background color. */
	public void setBackgroundColor(Color c) {
		pp.frame.color2 = c;
	}

	/** Set the plot frame background color. */
	public void setBackgroundColor(String c) {
		setBackgroundColor(Colors.decode(c,Color.white));
	}

	/** Changes the line width for the next objects that will be added to the plot. */
	public void setLineWidth(int lineWidth) {
		currentLineWidth = lineWidth > 0 ? lineWidth : 0.01f;
	}

	/** Changes the line width for the next objects that will be added to the plot.
	 *  After all objects have been added, set the line width to the width desired
	 *  for the frame around the plot (max. 3) */
	public void setLineWidth(float lineWidth) {
		currentLineWidth = lineWidth > 0.01 ? lineWidth : 0.01f;
	}

	/** Draws a line using the coordinate system defined by setLimits(). */
	public void drawLine(double x1, double y1, double x2, double y2) {
		allPlotObjects.add(new PlotObject(x1, y1, x2, y2, currentLineWidth, 0, currentColor, PlotObject.LINE));
	}

	/** Draws a line using a normalized 0-1, 0-1 coordinate system,
	 * with (0,0) at the top left and (1,1) at the lower right corner.
	 * This is the same coordinate system used by addLabel(x,y,label).
	 */
	public void drawNormalizedLine(double x1, double y1, double x2, double y2) {
		allPlotObjects.add(new PlotObject(x1, y1, x2, y2, currentLineWidth, 0, currentColor, PlotObject.NORMALIZED_LINE));
	}

	/** Draws a line using the coordinate system defined by setLimits(). */
	public void drawDottedLine(double x1, double y1, double x2, double y2, int step) {
		allPlotObjects.add(new PlotObject(x1, y1, x2, y2, currentLineWidth, step, currentColor, PlotObject.DOTTED_LINE));
	}

	/** Sets the font size for all following addLabel() etc. operations. The currently set font when
	 *	displaying the plot determines the font of all labels & numbers.
	 *  After the plot has been shown, sets the font for the numbers and the legend (if present).
	 *	If the plot is hown already, call update() thereafter to make the change visible. */
	public void setFontSize(int size) {
		setFont(-1, (float)size);
	}

	/** Sets the font for all following addLabel() etc. operations. The currently set font when
	 *	displaying the plot determines the font of all labels & numbers.
	 *  After the plot has been shown, sets the font for the numbers and the legend (if present);
	 *  use setFont(char, Font) to set these fonts individually.
	 *	If the plot is hown already, call update() thereafter to make the change visible. */
	public void setFont(Font font) {
		if (font == null) font = defaultFont;
		currentFont = font;
		if (plotDrawn) {
			pp.frame.setFont(font);
			if (pp.legend != null)
				pp.legend.setFont(font);
		}
	}

	/** Sets the font size and style for all following addLabel() etc. operations. This leaves
	 *	the font name and style of the previously used fonts unchanged. The currently set font
	 *	when displaying the plot determines the font of the numbers at the axes.
	 *	That font also sets the default label font size, which may be overridden by
	 *	setAxisLabelFontSize or setXLabelFont, setYLabelFont.
	 *  After the plot has been shown, sets the font for the numbers and the legend (if present);
	 *  use setFont(char, Font) to set these fonts individually.
	 *	Styles are defined in the Font class, e.g. Font.PLAIN, Font.BOLD.
	 *	Set <code>style</code> to -1 to leave the style unchanged.
	 *	Call update() thereafter to make the change visible (if the image is shown already). */
	public void setFont(int style, float size) {
		if (size < 9) size = 9f;
		if (size > 36) size = 36f;
		Font previousFont = nonNullFont(pp.frame.getFont(), currentFont);
		if (style < 0) style = previousFont.getStyle();
		setFont(previousFont.deriveFont(style, size));
	}

	/** Sets the x and y label font size and style. Styles are defined
	 *	in the Font class, e.g. Font.PLAIN, Font.BOLD.
	 *	Set <code>style</code> to -1 to leave the style unchanged.
	 *	Call update() thereafter to make the change visible (if the image is shown already). */
	public void setAxisLabelFont(int style, float size) {
		if (size < 9) size = 9f;
		if (size > 33) size = 33f;
		pp.xLabel.setFont(nonNullFont(pp.xLabel.getFont(), currentFont));
		pp.yLabel.setFont(nonNullFont(pp.yLabel.getFont(), currentFont));
		setXLabelFont(pp.xLabel.getFont().deriveFont(style < 0 ? pp.xLabel.getFont().getStyle() : style, size));
		setYLabelFont(pp.xLabel.getFont().deriveFont(style < 0 ? pp.yLabel.getFont().getStyle() : style, size));
	}

	/** Sets the xLabelFont; must not be null. If this method is not used, the last setFont
	 *	of setFontSize call before displaying the plot determines the font, or if neither
	 *	was called, the font size of the Plot Options is used. */
	public void setXLabelFont(Font font) {
		pp.xLabel.setFont(font);
	}

	/** Sets the yLabelFont; must not be null. */
	public void setYLabelFont(Font font) {
		pp.yLabel.setFont(font);
	}

	/** Determines whether to use antialiased text (default true) */
	public void setAntialiasedText(boolean antialiasedText) {
		pp.antialiasedText = antialiasedText;
	}

	/** Returns the font currently used (e.g. for the next 'addLabel') */
	public Font getCurrentFont() {
		return currentFont != null ? currentFont : defaultFont;
	}

	/** Returns the default font for the plot */
	public Font getDefaultFont() {
		return defaultFont;
	}

	/** Gets the font for xLabel ('x'), yLabel('y'), numbers ('f' for 'frame') or the legend ('l').
	 *	Returns null if the given PlotObject does not exist or its font is null */
	public Font getFont(char c) {
		PlotObject plotObject = pp.getPlotObject(c);
		if (plotObject != null)
			return plotObject.getFont();
		else
			return null;
	}

	/** Sets the font for xLabel ('x'), yLabel('y'), numbers ('f' for 'frame') or the legend ('l') */
	public void setFont(char c, Font font) {
		PlotObject plotObject = pp.getPlotObject(c);
		if (plotObject != null)
			plotObject.setFont(font);
	}

	/** Gets the label String of the xLabel ('x'), yLabel('y') or the legend ('l').
	 *	Returns null if the given PlotObject does not exist or its label is null */
	public String getLabel(char c) {
		PlotObject plotObject = pp.getPlotObject(c);
		if (plotObject != null)
			return plotObject.label;
		else
			return null;
	}

	/** Gets the flags of the xLabel ('x'), yLabel('y') or the legend ('l').
	 *	Returns -1 if the given PlotObject does not exist */
	public int getObjectFlags(char c) {
		PlotObject plotObject = pp.getPlotObject(c);
		if (plotObject != null)
			return plotObject.flags;
		else
			return -1;
	}

	/** Get the x coordinates of the data set passed with the constructor (if not null)
	 *	or otherwise of the data set of the first 'addPoints'. Returns null if neither exists */
	public float[] getXValues() {
		PlotObject p = getMainCurveObject();
		return p==null ? null : p.xValues;
	}

	/** Get the y coordinates of the data set passed with the constructor (if not null)
	 *	or otherwise of the data set of the first 'addPoints'. Returns null if neither exists */
	public float[] getYValues() {
		PlotObject p = getMainCurveObject();
		return p==null ? null : p.yValues;
	}

	/** Get the data of the n-th Plot Object containing xy data in the sequence they were added
	 *  (Other Plot Objects such as labels, arrows, lines, shapes and hidden PlotObjects are not counted).
	 *	The array returned has elements [0] x data, [1] y data, [2] x error bars, [3] y error bars.
	 *  If no error bars are given, the corresponding arrays are null.
	 *  Returns null if there is no Plot Object with xy data with this index.
	 *  @see #getDataObjectDesignations()
	**/
	public float[][] getDataObjectArrays(int index) {
		int i = 0;
		for (PlotObject plotObject : allPlotObjects) {
			if (plotObject.type != PlotObject.XY_DATA || plotObject.hasFlag(PlotObject.HIDDEN)) continue;
			if (index == i)
				return new float[][] {plotObject.xValues, plotObject.yValues, plotObject.xEValues, plotObject.yEValues};
			i++;
		}
		return null;
	}

	/** Gets an array with human-readable designations of the PlotObjects (curves, labels, ...)
	 *	in the sequence they were added (the object passed with the constructor is first,
	 *	even though it is plotted last). Hidden PlotObjects are included. **/
	public String[] getPlotObjectDesignations() {
		return getPlotObjectDesignations(-1, true);
	}

	/** Gets an array with human-readable designations of the PlotObjects containing xy data
	 *	in the sequence they were added. Other Plot Objects such as labels, arrows, lines,
	 *  shapes and hidden PlotObjects are not counted.
	 *  (the object passed with the constructor is first, even though it is plotted last). */
	public String[] getDataObjectDesignations() {
		return getPlotObjectDesignations(PlotObject.XY_DATA, false);
	}

	/** Returns the number of PlotObjects (curves, labels, ...) passed with the constructor or added by 'add' or 'draw' methods.
	 *  Legend, frame and axes (though internally PlotObjects) are not included */
	public int getNumPlotObjects() {
		return allPlotObjects.size();
	}

	/** Returns the number of PlotObjects fitting the mask.
	 *  Legend, frame and axes (though internally PlotObjects) are not included */
	int getNumPlotObjects(int mask, boolean includeHidden) {
		int nObjects = 0;
		for (PlotObject plotObject : allPlotObjects)
			if ((plotObject.type & mask) != 0 && (includeHidden || !plotObject.hasFlag(PlotObject.HIDDEN)))
				nObjects++;
		return nObjects;
	}

	/** Gets an array with human-readable designations of the PlotObjects with types fitting the mask
	 *  (i.e., 'mask' should be a bitwise or of the types desired) */
	String[] getPlotObjectDesignations(int mask, boolean includeHidden) {
		int nObjects = getNumPlotObjects(mask, includeHidden);
		String[] names = new String[nObjects];
		if (names.length == 0) return names;
		int iData = 1, iArrow = 1, iLine = 1, iText = 1,  iBox = 1, iShape = 1; //Human readable counters of each object type
		int i = 0;
		for (PlotObject plotObject : allPlotObjects) {
			int type = plotObject.type;
			if ((type & mask) == 0 || (!includeHidden && plotObject.hasFlag(PlotObject.HIDDEN))) continue;
			String label = plotObject.label;
			switch (type) {
				case PlotObject.XY_DATA:
					names[i] = "Data Set "+iData+": "+(plotObject.label != null ?
							plotObject.label : "(" + plotObject.yValues.length + " data points)");
					iData++;
					break;
				case PlotObject.ARROWS:
					names[i] = "Arrow Set "+iArrow+" ("+ plotObject.xValues.length + ")";
					iArrow++;
					break;
				case PlotObject.LINE: case PlotObject.NORMALIZED_LINE: case PlotObject.DOTTED_LINE:
					String detail = "";
					if (type == PlotObject.DOTTED_LINE) detail = "dotted ";
					if (plotObject.x ==plotObject.xEnd) detail += "vertical";
					else if (plotObject.y ==plotObject.yEnd) detail += "horizontal";
					if (detail.length()>0) detail = " ("+detail.trim()+")";
					names[i] = "Straight Line "+iLine+detail;
					iLine++;
					break;
				case PlotObject.LABEL: case PlotObject.NORMALIZED_LABEL:
					String text = plotObject.label.replaceAll("\n"," ");
					if (text.length()>45) text = text.substring(0, 40)+"...";
					names[i] = "Text "+iText+": \""+text+'"';
					iText++;
					break;
				case PlotObject.SHAPES:
					String s = plotObject.shapeType;
					String[] words = s.split(" ");
					names[i] = "Shapes (" + words[0] +") " + iShape;
					iShape++;
					break;
			}
			i++;
		}
		return names;
	}

	/** Add the i-th PlotObject (in the sequence how they were added, including hidden ones)
	 *  from another plot to this one. PlotObjects here refers to curves, arrows, labels etc.
	 *  (not legend, axes and frame, though implemented as PlotObjects)
	 *  Use 'update' to update the plot thereafter.
	 *  @return Index of the plotObject added in the sequence they were added */
	public int addObjectFromPlot(Plot plot, int i) {
		PlotObject plotObject = plot.getPlotObjectDeepClone(i);
		plotObject.unsetFlag(PlotObject.CONSTRUCTOR_DATA);
		allPlotObjects.add(plotObject);
		int index = allPlotObjects.size() - 1;
		return index;
	}

	/** Get the style of the i-th PlotObject (curve, label, ...) in the sequence
	 *	they were added (including hidden ones), as String with comma delimiters:
	 *	Main Color, Secondary Color (or "none"), Line Width [, Symbol shape for XY_DATA] [,hidden]
	 *  PlotObjects here refers to curves, arrows, labels etc.
	 *  (not legend, exes and frame, though implemented as PlotObjects) */
	public String getPlotObjectStyle(int i) {
		return getPlotObjectStyle(allPlotObjects.get(i));
	}

	String getPlotObjectStyle(PlotObject plotObject) {
		String styleString = Colors.colorToString(plotObject.color) + "," +
				Colors.colorToString(plotObject.color2) + "," +
				plotObject.lineWidth;
		if (plotObject.type == PlotObject.XY_DATA)
			styleString += ","+SHAPE_NAMES[plotObject.shape];
		if (plotObject.hasFlag(PlotObject.HIDDEN))
			styleString += ",hidden";
		return styleString;
	}

	/** Get the label the i-th PlotObject (in the sequence how they were added, including hidden ones).
	 *  Returns null if no label. PlotObjects here refers to curves, arrows, labels etc.
	 *  (not legend, exes and frame, though implemented as PlotObjects) */
	public String getPlotObjectLabel(int i) {
		return allPlotObjects.get(i).label;
	}

	/** Set the label the i-th PlotObject (in the sequence how they were added, including hidden ones)
	 *  PlotObjects here refers to curves, arrows, labels etc.
	 *  (not legend, exes and frame, though implemented as PlotObjects) */
	public void setPlotObjectLabel(int i, String label) {
		allPlotObjects.get(i).label = label;
	}

	/** Sets the style of the specified PlotObject (curve, label, etc.) from a
	 *	comma-delimited string ("color1,color2,lineWidth[,symbol][,hidden]"),
	 *  where "color2" can be "none" and "symbol" and "hidden" are optional.
	 *  PlotObjects here refers to curves, arrows, labels etc.
	 *  (not legend, exes and frame, though implemented as PlotObjects) */
	public void setStyle(int index, String style) {
		if (index<0 || index>=allPlotObjects.size())
			throw new IllegalArgumentException("Index out of range");
		setPlotObjectStyle(allPlotObjects.get(index), style);
	}

	public void setPlotObjectStyle(int i, String styleString) {
		setStyle(i, styleString);
	}

	void setPlotObjectStyle(PlotObject plotObject, String styleString) {
		String[] items = styleString.split(",");
		int nItems = items.length;
		if (items[nItems-1].indexOf("hidden") >= 0) {
			plotObject.setFlag(PlotObject.HIDDEN);
			nItems = items.length - 1;
		} else
			plotObject.unsetFlag(PlotObject.HIDDEN);
		plotObject.color = Colors.decode(items[0].trim(), plotObject.color);
		plotObject.color2 = Colors.decode(items[1].trim(), null);
		float lineWidth = plotObject.lineWidth;
		if (items.length >= 3) try {
			plotObject.lineWidth = Float.parseFloat(items[2].trim());
		} catch (NumberFormatException e) {};
		if (items.length >= 4 && plotObject.shape!=CUSTOM)
			plotObject.shape = toShape(items[3].trim());
		updateImage();
		return;
	}

	/** Returns the index of the first plot object with x,y data (points, line) or arrows
	 *  with all data equal to those given.  Returns or -1 is no such plot object exists.
	 *  The array 'values' should contain the x, y, x error bar, yerror bar data. The 'values' array may have any size;
	 *  only the data given are compared (e.g. for an array with length 2, there is no check for erro bars).
	 *  Used when adding data from a table not to suggest the same data twice. */
	public int getPlotObjectIndex(float[][] values) {
		return getPlotObjectIndex(PlotObject.XY_DATA|PlotObject.ARROWS, values);
	}

	/** Returns the index of the first plot object fitting the type mask and with all data equal to those given.
	 *  ('mask' should be a bitwise or of the types desired)
	 *  Returns or -1 is no such plot object exists.
	 *  The array 'values' should contain the x, y, x error bar, yerror bar data. The 'values' array may have any size;
	 *  only the data given are compared (e.g. for an array with length 2, there is no check for erro bars).
	 *  Used when adding data from a table not to suggest the same data twice. */
	int getPlotObjectIndex(int typeMask, float[][] values) {
		for (int i=0; i<allPlotObjects.size(); i++) {
			PlotObject plotObject = allPlotObjects.get(i);
			if ((plotObject.type & typeMask) == 0) continue;
			float[][] plotObjectArrays = plotObject.getAllDataValues();
			boolean equal = true;
			for (int j=0; j<Math.min(plotObjectArrays.length, values.length); j++) {
				if (!Arrays.equals(plotObjectArrays[j], values[j])) {
					equal = false;
					break;
				}
			}
			if (equal) return i;
		}
		return -1;
	}

	/** Creates a snapshot of the plot contents (not including axis formats etc),
	 *  for later undo by restorePlotObjects. See also killPlotObjectsSnapshot */
	public void savePlotObjects() {
		allPlotObjectsSnapshot = new Vector<PlotObject>(allPlotObjects.size());
		copyPlotObjectsVector(allPlotObjects, allPlotObjectsSnapshot);
	}

	/** Restores the plot contents (not including axis formats etc) from the snapshot
	 *  previously created by savePlotObjects(). See also killPlotObjectsSnapshot
	 *  Use 'update' to update the plot thereafter. */
	public void restorePlotObjects() {
		if (allPlotObjectsSnapshot != null)
			copyPlotObjectsVector(allPlotObjectsSnapshot, allPlotObjects);
	}

	/** Deletes the snapshot of the plot contents to make space */
	public void killPlotObjectsSnapshot() {
		allPlotObjectsSnapshot = null;
	}

	/** Creates a snapshot of the plot properties (formatting, range etc., not PlotObjects such as data and corresponding curves etc.),
	 *  for later undo by restorePlotProperties. See also killPlotPropertiesSnapshot */
	public void savePlotPlotProperties() {
		pp.rangeMinMax = currentMinMax;
		ppSnapshot = pp.deepClone();
	}

	/** Restores the plot properties (formatting, range etc., not PlotObjects such as data and corresponding curves etc.)
	 *  from a snapshot previously created by savePlotPlotProperties. See also killPlotPropertiesSnapshot.
 	 *  Use 'update' to update the plot thereafter. */
	public void restorePlotProperties() {
		pp = ppSnapshot.deepClone();
		System.arraycopy(pp.rangeMinMax, 0, currentMinMax, 0, Math.min(pp.rangeMinMax.length, currentMinMax.length));
	}

	/** Deletes the snapshot of the plot properties to make space */
	public void killPlotPropertiesSnapshot() {
		ppSnapshot = null;
	}

	private void copyPlotObjectsVector(Vector<PlotObject> src, Vector<PlotObject>dest) {
		if (dest.size() > 0) dest.removeAllElements();
		for (PlotObject plotObject : src)
			dest.add(plotObject.deepClone());
	}

	PlotObject getPlotObjectDeepClone(int i) {
		return allPlotObjects.get(i).deepClone();
	}

	/** Sets the plot range to the initial value determined from minima&maxima or given by setLimits.
	 *	Updates the image if existing and updateImg is true */
	public void setLimitsToDefaults(boolean updateImg) {
		saveMinMax();
		System.arraycopy(defaultMinMax, 0, currentMinMax, 0, defaultMinMax.length);
		if (plotDrawn && updateImg) updateImage();
	}

	/** Sets the plot range to encompass all data. Updates the image if existing and updateImg is true. */
	public void setLimitsToFit(boolean updateImg) {
		saveMinMax();
		currentMinMax = getMinAndMax(true, ALL_AXES_RANGE);
		if (Double.isNaN(defaultMinMax[0]) && Double.isNaN(defaultMinMax[2])) //no range at all so far
			System.arraycopy(currentMinMax, 0, defaultMinMax, 0, Math.min(currentMinMax.length, defaultMinMax.length));

		enlargeRange(currentMinMax);              //avoid points exactly at the border
		//System.arraycopy(currentMinMax, 0, defaultMinMax, 0, currentMinMax.length);
		if (plotDrawn && updateImg) updateImage();
	}

	/** reverts plot range to previous values and updates the image */
	public void setPreviousMinMax() {
		if (Double.isNaN(savedMinMax[0])) return;  //no saved values yet
		double[] swap = new double[currentMinMax.length];
		System.arraycopy(currentMinMax, 0, swap, 0, currentMinMax.length);
		System.arraycopy(savedMinMax, 0, currentMinMax, 0, currentMinMax.length);
		System.arraycopy(swap, 0, savedMinMax, 0, currentMinMax.length);
		updateImage();
	}

	/** Draws the plot (if not done before) in an ImageProcessor and returns the ImageProcessor with the plot. */
	public ImageProcessor getProcessor() {
		draw();
		return ip;
	}

	/** Returns the plot as an ImagePlus.
	 *	If an ImagePlus for this plot already exists, displays the plot in that ImagePlus and returns it. */
	public ImagePlus getImagePlus() {
		if (stack != null) {
			if (imp != null)
				return imp;
			else {
				imp = new ImagePlus(title, stack);
				adjustCalibration(imp.getCalibration());
				return imp;
			}
		}
		if (plotDrawn)
			updateImage();
		else
			draw();
		if (imp != null) {
			if (imp.getProcessor() != ip)
				imp.setProcessor(ip);
			return imp;
		} else {
			ImagePlus imp = new ImagePlus(title, ip);
			setImagePlus(imp);
			return imp;
		}
	}

	/** Sets the ImagePlus where the plot will be displayed. If the ImagePlus is not
	 *	known otherwise (e.g. from getImagePlus), this is needed for changes such as
	 *	zooming in to work correctly. It also sets the calibration of the ImagePlus.
	 *	The ImagePlus is not displayed or updated unless its ImageProcessor is
	 *  no that of the current Plot (then it gets this ImageProcessor).
	 *  Does nothing if imp is unchanged and has the ImageProcessor of this plot.
	 *  'imp' may be null to disconnect the plot from its ImagePlus.
	 *	Does nothing for Plot Stacks. */
	public void setImagePlus(ImagePlus imp) {
		if (imp != null && imp == this.imp && imp.getProcessor() == ip)
			return;
		if (stack != null)
			return;
		if (this.imp != null)
			this.imp.setProperty(PROPERTY_KEY, null);
		this.imp = imp;
		if (imp != null) {
			imp.setIgnoreGlobalCalibration(true);
			adjustCalibration(imp.getCalibration());
			imp.setProperty(PROPERTY_KEY, this);
			if (ip != null && imp.getProcessor() != ip)
				imp.setProcessor(ip);
		}
	}

	/** Adjusts a Calibration object to fit the current axes.
	 *	For log axes, the calibration refers to the base-10 logarithm of the value */
	public void adjustCalibration(Calibration cal) {
		if (xMin == xMax)	//tiff images can't handle infinity in scale, see TiffEncoder.writeScale
			xScale = 1e6;
		if (yMin == yMax)
			yScale = 1e6;
		cal.xOrigin = xBasePxl-xMin*xScale;
		cal.pixelWidth	= 1.0/Math.abs(xScale); //Calibration must not have negative pixel size
		cal.yOrigin = yBasePxl+yMin*yScale;
		cal.pixelHeight = 1.0/Math.abs(yScale);
		cal.setInvertY(yScale >= 0);
		cal.setXUnit(" "); // avoid 'pixels' for scaled units
		if (xMin == xMax)
			xScale = Double.POSITIVE_INFINITY;
		if (yMin == yMax)
			yScale = Double.POSITIVE_INFINITY;
	}

	/** Displays the plot in a PlotWindow.
	 *  Plot stacks are shown in a StackWindow, not in a PlotWindow;
	 *  in this case the return value is null (use getImagePlus().getWindow() instead).
	 *  Also returns null in BatchMode. Note that the PlotWindow might get closed
	 *  immediately if its 'listValues' and 'autoClose' flags are set.
	 *  @see #update()
	 */
	public PlotWindow show() {
		PlotVirtualStack stack = getStack();
		if (stack!=null) {
			getImagePlus().show();
			return null;
		}
		if ((IJ.macroRunning() && IJ.getInstance()==null) || Interpreter.isBatchMode()) {
			imp = getImagePlus();
			imp.setPlot(this);
			WindowManager.setTempCurrentImage(imp);
			if (getMainCurveObject() != null) {
				imp.setProperty("XValues", getXValues()); // Allows values to be retrieved by
				imp.setProperty("YValues", getYValues()); // by Plot.getValues() macro function
			}
			Interpreter.addBatchModeImage(imp);
			return null;
		}
		if (imp != null) {
			Window win = imp.getWindow();
			if (win instanceof PlotWindow && win.isVisible()) {
				updateImage();			// show in existing window
				return (PlotWindow)win;
			} else
				setImagePlus(null);
		}
		PlotWindow pw = new PlotWindow(this);		//note: this may set imp to null if pw has listValues and autoClose are set
		if (IJ.isMacro() && imp!=null) // wait for plot to be displayed
			IJ.selectWindow(imp.getID());
		return pw;
	}

	/**
	 * Appends the current plot to a virtual stack and resets allPlotObjects
	 * for next slice
	 * N. Vischer
	 */
	public void addToStack() {
		if (stack==null)
			stack = new PlotVirtualStack(getSize().width,getSize().height);
		draw();
		stack.addPlot(this);
		IJ.showStatus("addToPlotStack: "+stack.size());
		allPlotObjects.clear();
		textLoc = null;
	}

	public void appendToStack() { addToStack(); }

	/** Returns the virtual stack created by addToStack(). */
	public PlotVirtualStack getStack() {
		IJ.showStatus("");
		return stack;
	}

	/** Draws the plot specified for the first time. Does nothing if the plot has been drawn already.
	 *	Call getProcessor to retrieve the ImageProcessor with it.
	 *	Does no action with respect to the ImagePlus (if any) */
	public void draw() {
		//IJ.log("draw(); plotDrawn="+plotDrawn);
		if (plotDrawn) return;
		getInitialMinAndMax();
		pp.frame.setFont(nonNullFont(pp.frame.getFont(), currentFont)); //make sure we have a number font for calculating the margins
		getBlankProcessor();
		drawContents(ip);
	}

	/** Freezes or unfreezes the plot. In the frozen state, the plot cannot be resized or updated,
	 *	and the Plot class does no modifications to the ImageProcessor.
	 *	Changes are recorded nevertheless and become effective with <code>setFrozen(false)</code>. */
	public void setFrozen(boolean frozen) {
		pp.isFrozen = frozen;
		if (!pp.isFrozen) {	// unfreeze operations ...
			if (imp != null && ip != null) {
				ImageCanvas ic = imp.getCanvas();
				if (ic instanceof PlotCanvas) {
					((PlotCanvas)ic).resetMagnification();
					imp.setTitle(imp.getTitle());   //update magnification in title
				}
				Undo.setup(Undo.TRANSFORM, imp);
			}
			updateImage();
			ImageWindow win = imp == null ? null : imp.getWindow();
			if (win != null) win.updateImage(imp); //show any changes made during the frozen state
		}
	}

	public boolean isFrozen() {
		return pp.isFrozen;
	}

	/** Draws the plot again, ignored if the plot has not been drawn before or the plot is frozen. */
	public void update() {
		updateImage();
	}

	/** Draws the plot again, ignored if the plot has not been drawn before or the plot is frozen.
	 *	If the ImagePlus exist, updates it and its calibration. */
	public void updateImage() {
		if (!plotDrawn || pp.isFrozen) return;
		getBlankProcessor();
		drawContents(ip);
		if (imp == null || stack != null) return;
		adjustCalibration(imp.getCalibration());
		imp.updateAndDraw();
		if (ip != imp.getProcessor())
			imp.setProcessor(ip);
	}

	/** Returns the rectangle where the data are plotted.
	 *	This rectangle includes the black outline frame at the top and left, but not at the bottom
	 *	and right (when the frame is plotted with 1 pxl width).
	 *	The image scale is its width or height in pixels divided by the data range in x or y. */
	public Rectangle getDrawingFrame() {
		if (frame == null)
			getBlankProcessor(); //setup frame if not done yet
		return new Rectangle(frame.x, frame.y, frameWidth, frameHeight);
	}

	/** Creates a new high-resolution plot by scaling it and displays that plot if showIt is true.
	 *	<code>title</code> may be null, then a default title is used. */
	public ImagePlus makeHighResolution(String title, float scale, boolean antialiasedText, boolean showIt) {
		Plot hiresPlot = null;
		try {
			hiresPlot = (Plot)clone();	//shallow clone, thus arrays&objects are not cloned, but they will be used only now
		} catch (Exception e) {return null;}
		hiresPlot.ip = null;
		hiresPlot.imp = null;
		hiresPlot.pp = pp.clone();
		if (!plotDrawn) hiresPlot.getInitialMinAndMax();
		hiresPlot.setScale(scale);
		hiresPlot.setAntialiasedText(antialiasedText);
		hiresPlot.defaultMinMax = currentMinMax.clone();
		ImageProcessor hiresIp = hiresPlot.getProcessor();
		if (title == null || title.length() == 0)
			title = getTitle()+"_HiRes";
		title = WindowManager.makeUniqueName(title);
		ImagePlus hiresImp = new ImagePlus(title, hiresIp);
		Calibration cal = hiresImp.getCalibration();
		hiresPlot.adjustCalibration(cal);
		if (showIt) {
			hiresImp.setIgnoreGlobalCalibration(true);
			hiresImp.show();
		}
		hiresPlot.dispose(); //after drawing, we don't need the plot of the high-resolution image any more
		return hiresImp;
	}

	/** Releases the ImageProcessor and ImagePlus associated with the plot.
	 *	May help garbage collection because some garbage collectors
	 *	are said to be inefficient with circular references. */
	public void dispose() {
		if (imp != null)
			imp.setProperty(PROPERTY_KEY, null);
		imp = null;
		ip = null;
	}

	/** Converts pixels to calibrated coordinates. In contrast to the image calibration, also
	 *	works with log axes and inverted x axes */
	public double descaleX(int x) {
		if (xMin == xMax) return xMin;
		double xv = (x-xBasePxl)/xScale + xMin;
		if (logXAxis) xv = Math.pow(10, xv);
		return xv;
	}

	/** Converts pixels to calibrated coordinates. In contrast to the image calibration, also
	 *	works with log axes */
	public double descaleY(int y) {
		if (yMin == yMax) return yMin;
		double yv = (yBasePxl-y)/yScale +yMin;
		if (logYAxis) yv = Math.pow(10, yv);
		return yv;
	}


	/** Converts calibrated coordinates to pixel coordinates. In contrast to the image calibration, also
	 *	works with log x axis and inverted x axis */
	public double scaleXtoPxl(double x) {
		if (xMin == xMax) {
			if (x==xMin) return xBasePxl;
			else return x>xMin ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY;
		}
		if (logXAxis)
			return xBasePxl+(Math.log10(x)-xMin)*xScale;
		else
			return xBasePxl+(x-xMin)*xScale;
	}

	/** Converts calibrated coordinates to pixel coordinates. In contrast to the image calibration, also
	 *	works with log y axis */
	public double scaleYtoPxl(double y) {
		if (yMin == yMax) {
			if (y==xMin) return yBasePxl;
			else return y>yMin ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY;
		}
		if (logYAxis)
			return yBasePxl-(Math.log10(y)-yMin)*yScale;
		else
			return yBasePxl-(y-yMin)*yScale;
	}

	/** Calibrated coordinates to integer pixel coordinates */
	private int scaleX(double x) {
		if (Double.isNaN(x)) return -1;
		if (xMin == xMax) {
			if (x==xMin) return xBasePxl;
			else return x>xMin ? Integer.MAX_VALUE : Integer.MIN_VALUE;
		}
		if (logXAxis)
			return xBasePxl+(int)Math.round((Math.log10(x)-xMin)*xScale);
		else
			return xBasePxl+(int)Math.round((x-xMin)*xScale);
	}

	/** Converts calibrated coordinates to pixel coordinates. In contrast to the image calibration, also
	 *	works with log axes */
	private int scaleY(double y) {
		if (Double.isNaN(y)) return -1;
		if (yMin == yMax) {
			if (y==yMin) return yBasePxl;
			else return y>yMin ? Integer.MAX_VALUE : Integer.MIN_VALUE;
		}
		if (logYAxis)
			return yBasePxl-(int)Math.round((Math.log10(y)-yMin)*yScale);
		else
			return yBasePxl-(int)Math.round((y-yMin)*yScale);
	}

	/** Converts calibrated coordinates to pixel coordinates. In contrast to the image calibration, also
	 *	works with log axes and inverted x axes. Returns a large number instead NaN for log x axis and zero or negative x */
	private int scaleXWithOverflow(double x) {
		if (!logXAxis || x>0)
			return scaleX(x);
		else
			return xScale > 0 ? -1000000 : 1000000;
	}

	/** Converts calibrated coordinates to pixel coordinates. In contrast to the image calibration, also
	 *	works with log axes and inverted x axes. Returns a large number instead NaN for log y axis and zero or negative y */
	private int scaleYWithOverflow(double y) {
		if (!logYAxis || y>0)
			return scaleY(y);
		else
			return yScale > 0 ? 1000000 : -1000000;
	}

	/** Scales a value of the original plot for a high-resolution plot. Returns an integer number of pixels >=1 */
	int sc(float length) {
		int pixels = (int)(length*scale + 0.5);
		if (pixels < 1) pixels = 1;
		return pixels;
	}

	/** Scales a font of the original plot for a high-resolution plot. */
	Font scFont(Font font) {
		float size = font.getSize2D();
		return scale==1 ? font : font.deriveFont(size*scale);
	}

	/** Returns whether the plot requires color (not grayscale) */
	boolean isColored() {
		for (PlotObject plotObject : allPlotObjects)
			if (isColored(plotObject.color) || isColored(plotObject.color2))
				return true;
		for (PlotObject plotObject : pp.getAllPlotObjects())
			if (plotObject != null && (isColored(plotObject.color) || isColored(plotObject.color2)))
				return true;
		return false;
	}

	/** Whether a color is non-grayscale, which requires color (not grayscale) for the plot */
	boolean isColored(Color c) {
		if (c == null) return false;
		return c.getRed() != c.getGreen() || c.getGreen() != c.getBlue();
	}

	/** Draws the plot contents (all PlotObjects and the frame and legend), without axes etc. */
	void drawContents(ImageProcessor ip) {
		makeRangeGetSteps();
		ip.setColor(Color.black);
		ip.setLineWidth(sc(1));
		float lineWidth = 1;
		Color color = Color.black;
		Font font = defaultFont;

		// draw all the plot objects in the sequence they were added, except for the one of the constructor
		for (PlotObject plotObject : allPlotObjects)
			if (!plotObject.hasFlag(PlotObject.CONSTRUCTOR_DATA)) {
				//properties lineWidth, Font, Color set for one object remain for the next object unless changed
				if (plotObject.lineWidth > 0)
					lineWidth = plotObject.lineWidth;
				else
					plotObject.lineWidth = lineWidth;
				if (plotObject.color != null)
					color = plotObject.color;
				else
					plotObject.color = color;
				if (plotObject.getFont() != null)
					font = plotObject.getFont();
				else
					plotObject.setFont(font);
				//IJ.log("type="+plotObject.type+" color="+plotObject.color);
				drawPlotObject(plotObject, ip);
			}

		// draw the line passed with the constructor last, using the settings present when calling 'draw'
		if (allPlotObjects.size()>0 && allPlotObjects.get(0).hasFlag(PlotObject.CONSTRUCTOR_DATA)) {
			PlotObject mainPlotObject = allPlotObjects.get(0);
			if (mainPlotObject.lineWidth == 0)
				mainPlotObject.lineWidth = currentLineWidth == 0 ? 1 : currentLineWidth;
			lineWidth = mainPlotObject.lineWidth;
			if (mainPlotObject.color == null)
				mainPlotObject.color = currentColor == null ? Color.black : currentColor;
			drawPlotObject(mainPlotObject, ip);
		} else {
			if (currentLineWidth > 0) lineWidth = currentLineWidth; //linewidth when drawing determines frame linewidth
		}

		// finally draw the frame & legend
		if (!plotDrawn && pp.frame.lineWidth==DEFAULT_FRAME_LINE_WIDTH) {  //when modifying PlotObjects styles later, don't change the frame line width any more
			pp.frame.lineWidth = lineWidth;
			if (pp.frame.lineWidth == 0) pp.frame.lineWidth = 1;
			if (pp.frame.lineWidth > 3) pp.frame.lineWidth = 3;
		}
		ip.setLineWidth(sc(pp.frame.lineWidth));
		ip.setColor(pp.frame.color);
		int x2 = frame.x + frame.width - 1;
		int y2 = frame.y + frame.height - 1;
		ip.moveTo(frame.x, frame.y);	// draw the frame. Can't use ip.drawRect because it is inconsistent for different lineWidths
		ip.lineTo(x2, frame.y);
		ip.lineTo(x2, y2);
		ip.lineTo(frame.x, y2);
		ip.lineTo(frame.x, frame.y);
		if (pp.legend != null && (pp.legend.flags & LEGEND_POSITION_MASK) != 0)
			drawPlotObject(pp.legend, ip);

		plotDrawn = true;
	}

	/** Creates the processor if not existing, clears the background and prepares
	 *	it for plotting. Also called by the PlotWindow class to prepare the window. */
	ImageProcessor getBlankProcessor() {
		makeMarginValues();
		//IJ.log("Plot.getBlankPr preferredH="+preferredPlotHeight+" pp.h="+pp.height);
		if (pp.width <= 0 || pp.height <= 0) {
			pp.width = sc(preferredPlotWidth) + leftMargin + rightMargin;
			pp.height = sc(preferredPlotHeight) + topMargin + bottomMargin;
		}
		frameWidth = pp.width - (leftMargin + rightMargin);
		frameHeight = pp.height - (topMargin + bottomMargin);
		boolean isColored = isColored();	//color, not grayscale required?
		if (ip == null || pp.width != ip.getWidth() || pp.height != ip.getHeight() || (isColored != (ip instanceof ColorProcessor))) {
			if (isColored) {
				ip = new ColorProcessor(pp.width, pp.height);
			} else {
				ip = new ByteProcessor(pp.width, pp.height);
				invertedLut = Prefs.useInvertingLut && !Interpreter.isBatchMode() && IJ.getInstance()!=null;
				if (invertedLut) ip.invertLut();
			}
			if (imp != null && stack == null)
				imp.setProcessor(ip);
		}
		if (ip instanceof ColorProcessor)
			Arrays.fill((int[])(ip.getPixels()), 0xffffff);
		else
			Arrays.fill((byte[])(ip.getPixels()), invertedLut ? (byte)0 : (byte)0xff);

		ip.setFont(scFont(defaultFont));
		ip.setLineWidth(sc(1));
		ip.setAntialiasedText(pp.antialiasedText);
		frame = new Rectangle(leftMargin, topMargin, frameWidth+1, frameHeight+1);
		if (pp.frame.color2 != null) {	//background color
			ip.setColor(pp.frame.color2);
			ip.setRoi(frame);
			ip.fill();
			ip.resetRoi();
		}
		ip.setColor(Color.black);
		return ip;
	}

	/** Calculates the margin sizes and sets the class variables accordingly */
	void makeMarginValues() {
		Font font = nonNullFont(pp.frame.getFont(), currentFont);
		float marginScale = 0.1f + 0.9f*font.getSize2D()/12f;
		if (marginScale < 0.7f) marginScale = 0.7f;
		if (marginScale > 2f) marginScale = 2f;
		int addHspace = (int)Tools.getNumberFromList(pp.frame.options, "addhspace="); //user-defined extra space
		int addVspace = (int)Tools.getNumberFromList(pp.frame.options, "addvspace=");
		leftMargin	 = sc(LEFT_MARGIN*marginScale + addHspace);
		rightMargin = sc(RIGHT_MARGIN*marginScale + addHspace);
		topMargin = sc(TOP_MARGIN*marginScale + addVspace);
		bottomMargin = sc(BOTTOM_MARGIN*marginScale + 2 + addVspace);
		if(pp != null && pp.xLabel != null && pp.xLabel.getFont() != null){
			float numberSize = font.getSize2D();
			float labelSize = pp.xLabel.getFont().getSize2D();
			float extraHeight = 1.5f *(labelSize - numberSize);
			if(extraHeight > 0){
				bottomMargin += sc(extraHeight);
				leftMargin += sc(extraHeight);
			}
		}
	}

	/** Calculate the actual range, major step interval and set variables for data <-> pixels scaling */
	double[] makeRangeGetSteps() {
		steps = new double[2];
		logXAxis = hasFlag(X_LOG_NUMBERS);
		logYAxis = hasFlag(Y_LOG_NUMBERS);

		for (int i=0; i<currentMinMax.length; i+=2) {  //for x and y direction
			boolean logAxis = hasFlag(i==0 ? X_LOG_NUMBERS : Y_LOG_NUMBERS);
			//don't zoom in too much (otherwise float conversion to int pixels may be wrong)
			double range = currentMinMax[i+1]-currentMinMax[i];
			double mid = 0.5*(currentMinMax[i+1]+currentMinMax[i]);
			double relativeRange = Math.abs(range/mid);
			if (!logAxis)
				relativeRange = Math.min(relativeRange, Math.abs(range/(defaultMinMax[i+1]-defaultMinMax[i])));
			if (range != 0 && relativeRange<1e-4) {
				currentMinMax[i+1] = mid + 0.5*range*1e-4/relativeRange;
				currentMinMax[i] = mid - 0.5*range*1e-4/relativeRange;
			}
			//no log range if range is too small or not positive values
			if (logAxis) {
				double rangeRatio = currentMinMax[i+1]/currentMinMax[i];
				if (!(rangeRatio > MIN_LOG_RATIO || 1./rangeRatio > MIN_LOG_RATIO) ||
					!(currentMinMax[i] > 10*Float.MIN_VALUE)  || !(currentMinMax[i+1] > 10*Float.MIN_VALUE))
				logAxis = false;
			}
			//for log axes, temporarily work on the logarithm
			if (logAxis) {
				currentMinMax[i] = Math.log10(currentMinMax[i]);
				currentMinMax[i+1] = Math.log10(currentMinMax[i+1]);
			}
			// calculate grid or major tick interval
			if ((i==0 && !simpleXAxis()) || (i==2 && !simpleYAxis())) {
				int minGridspacing = i==0 ? MIN_X_GRIDSPACING : MIN_Y_GRIDSPACING;
				int frameSize = i==0 ? frameWidth : frameHeight;
				double step = Tools.getNumberFromList(pp.frame.options, i==0 ? "xinterval=" : "yinterval="); //user-defined interval
				if (!Double.isNaN(step)) {
					int nSteps = (int)(Math.floor(currentMinMax[i+1]/step+1e-10) - Math.ceil(currentMinMax[i]/step-1e-10));
					if (nSteps < 1) step = Double.NaN;  //user-suppied interval too large, less than two numbers would be shown
					if ((i==0 && nSteps*sc(minGridspacing)*0.5 > frameSize) || i!=0 && nSteps*sc(pp.frame.getFont().getSize()) > frameSize)
						step = Double.NaN;              //user-suppied interval too small, too many numbers would be shown
				}
				if (Double.isNaN(step)) {               //automatic interval
					step = Math.abs((currentMinMax[i+1] - currentMinMax[i]) *
						Math.max(1.0/maxIntervals, (float)sc(minGridspacing)/frameSize+(maxIntervals>12 ? 0.02 : 0.06))); //the smallest allowable step
					step = niceNumber(step);
				}
				if (logAxis && step < 1)
					step = 1;
				steps[i/2] = step;
				//modify limits to grid or minor ticks if desired
				boolean force2grid = hasFlag(i==0 ? X_FORCE2GRID : Y_FORCE2GRID) && !ignoreForce2Grid;
				if (force2grid) {
					int i1 = (int)Math.floor(Math.min(currentMinMax[i],currentMinMax[i+1])/step+1.e-10);
					int i2 = (int)Math.ceil (Math.max(currentMinMax[i],currentMinMax[i+1])/step-1.e-10);
					if (currentMinMax[i+1] > currentMinMax[i]) {	// care about inverted axes with max<min
						currentMinMax[i] = i1 * step;
						currentMinMax[i+1] = i2 * step;
					} else {
						currentMinMax[i] = i2 * step;
						currentMinMax[i+1] = i1 * step;
					}
				//} else if (snapToMinorGrid) {
				//	double stepForSnap = niceNumber(0.15*step);
				//	if (!logXAxis || stepForSnap >= 0.999) {	//don't snap on log axis if minor ticks are not full decades
				//		currentMinMax[i] = stepForSnap * Math.round(currentMinMax[i]/stepForSnap);
				//		currentMinMax[i+1] = stepForSnap * Math.round(currentMinMax[i+1]/stepForSnap);
				//	}
				}
			}
			if (i==0) {
				xMin = currentMinMax[i];
				xMax = currentMinMax[i+1];
				logXAxis = logAxis;
			} else {
				yMin = currentMinMax[i];
				yMax = currentMinMax[i+1];
				logYAxis = logAxis;
			}
			if (logAxis) {
				currentMinMax[i] = Math.pow(10, currentMinMax[i]);
				currentMinMax[i+1] = Math.pow(10, currentMinMax[i+1]);
			}
		}
		//snapToMinorGrid = false;
		ignoreForce2Grid = false;

		// calculate what we need to convert the data to screen pixels
		xBasePxl = leftMargin;
		yBasePxl = topMargin + frameHeight;
		xScale = frameWidth/(xMax-xMin);
		if (!(xMax-xMin!=0.0))	  //if range==0 (all data the same), or NaN shift zero level so one can see the curve
			xBasePxl += sc(10);
		yScale = frameHeight/(yMax-yMin);
		if (!(yMax-yMin!=0.0))
			yBasePxl -= sc(10);
		//IJ.log("x,yScale="+(float)xScale+","+(float)yScale+" xMin,max="+(float)xMin+","+(float)xMax+" yMin.max="+(float)yMin+","+(float)yMax);

		drawAxesTicksGridNumbers(steps);
		return steps;
	}

	public void redrawGrid(){
		if (ip != null) {
			ip.setColor(Color.black);
			drawAxesTicksGridNumbers(steps);
			ip.setColor(Color.black);
		}
	}

	/** Gets the initial plot limits (i.e., x&y ranges). For compatibility with previous versions of ImageJ,
	 *  only the first PlotObject (with numeric data) is used to determine the limits. */
	void getInitialMinAndMax() {
		int axisRangeFlags = 0;
		if (Double.isNaN(defaultMinMax[0])) axisRangeFlags |= X_RANGE;
		if (Double.isNaN(defaultMinMax[2])) axisRangeFlags |= Y_RANGE;
		if (axisRangeFlags != 0) {
			defaultMinMax = getMinAndMax(false, axisRangeFlags);
			enlargeRange(defaultMinMax);
		}
		setLimitsToDefaults(false);			//use the range values to start with, but don't draw yet
	}

	/** Gets the minimum and maximum values from the first XY_DATA or ARROWS plotObject or all such plotObjects;
	 *	axisRangeFlags determine for which axis to calculate the min&max (X_RANGE for x axis, Y_RANGE for y axis);
	 *	for the other axes the limit is taken from defaultMinMax
	 *	Array elements returned are xMin, xMax, yMin, yMax. Also sets enlargeRange to tell which limits should be enlarged
	 *	beyond the minimum or maximum of the data */
	double[] getMinAndMax(boolean allObjects, int axisRangeFlags) {
		boolean invertedXAxis = currentMinMax[1] < currentMinMax[0];
		boolean invertedYAxis = currentMinMax[3] < currentMinMax[2];
		double xSign = invertedXAxis ? -1 : 1;
		double ySign = invertedYAxis ? -1 : 1;
		double[] allMinMax = new double[]{xSign*Double.MAX_VALUE, -xSign*Double.MAX_VALUE, ySign*Double.MAX_VALUE, -ySign*Double.MAX_VALUE};
		for (int i=0; i<allMinMax.length; i++)
			if (((axisRangeFlags>>i/2) & 1)==0)	  //keep default min & max for this axis
				allMinMax[i] = defaultMinMax[i];
		enlargeRange = new int[allMinMax.length];
		for (PlotObject plotObject : allPlotObjects) {
			if ((plotObject.type == PlotObject.XY_DATA || plotObject.type == PlotObject.ARROWS) && !plotObject.hasFlag(PlotObject.HIDDEN)) {
				getMinAndMax(allMinMax, enlargeRange, plotObject, axisRangeFlags);
				if (!allObjects) break;
			}
		}
		if ((axisRangeFlags & X_RANGE) != 0) {
			String[] xCats = labelsInBraces('x'); // if we have categories at the axis, make some space for this text
			if (xCats != null) {
				allMinMax[0] = Math.min(allMinMax[0], -0.5);
				allMinMax[1] = Math.min(allMinMax[1], xCats.length+0.5);
			}
		}
		if ((axisRangeFlags & Y_RANGE) != 0) {
			String[] yCats = labelsInBraces('y');
			if (yCats != null) {
				allMinMax[2] = Math.min(allMinMax[2], -0.5);
				allMinMax[3] = Math.min(allMinMax[3], yCats.length+0.5);
			}
		}
		if (allMinMax[0]==Double.MAX_VALUE && allMinMax[1]==-Double.MAX_VALUE) { // no x values at all? keep previous
			allMinMax[0] = defaultMinMax[0];
			allMinMax[1] = defaultMinMax[1];
		}
		if (allMinMax[2]==Double.MAX_VALUE && allMinMax[3]==-Double.MAX_VALUE) { // no y values at all? keep previous
			allMinMax[2] = defaultMinMax[2];
			allMinMax[3] = defaultMinMax[3];
		}
		return allMinMax;
	}

	/** Enlarges the current minimum and maximum ranges to include the data range of the last plotObject added,
	 *  if it is an XY_DATA or ARROWS plotObject.
	 *  Does not set the new limits as default, does not redraw the plot. */
	void fitRangeToLastPlotObject() {
		if (allPlotObjects.size() < 1) return;
		PlotObject plotObject = allPlotObjects.lastElement();
		if (Double.isNaN(currentMinMax[0]) || Double.isNaN(currentMinMax[2])) {   // no range determined yet?
			setLimitsToFit(false);
		} else {   //we have min&max already, just extend the range if necessary
			enlargeRange = new int[currentMinMax.length];
			getMinAndMax(currentMinMax, enlargeRange, plotObject, ALL_AXES_RANGE);
			enlargeRange(currentMinMax);
		}
	}

	/** Gets the minimum and maximum values from an XY_DATA or ARROWS plotObject;
	 *	axisRangeFlags determine for which axis (X_RANGE for x axis, Y_RANGE for y axis)
	 *	The minimum modifies allMinAndMax[0] (x), allMinAndMax[2] (y); the maximum modifies [1], [3].
	 *	If allMinAndMax values are modified, the corresponding enlargeRange array elements are also set */
	void getMinAndMax(double[] allMinAndMax, int[] enlargeRange, PlotObject plotObject, int axisRangeFlags) {
		boolean invertedXAxis = currentMinMax[1] < currentMinMax[0];
		boolean invertedYAxis = currentMinMax[3] < currentMinMax[2];
		if (plotObject.type == PlotObject.XY_DATA) {
			if ((axisRangeFlags & X_RANGE) != 0) {
				int suggestedEnlarge = 0;
				if (!(plotObject.shape == LINE || plotObject.shape == FILLED) || plotObject.yEValues != null)
					suggestedEnlarge = ALWAYS_ENLARGE;	//enlarge to make space at the obrders (we don't try to keep x=0 at the frame border)
				getMinAndMax(allMinAndMax, enlargeRange, suggestedEnlarge, 0, plotObject.xValues, plotObject.xEValues, invertedXAxis);
				if ((plotObject.shape == BAR || plotObject.shape == SEPARATED_BAR)&& plotObject.xValues.length > 1) {
					int n = plotObject.xValues.length;
					allMinAndMax[0] -= 0.5 * Math.abs(plotObject.xValues[1] - plotObject.xValues[0]);
					allMinAndMax[1] += 0.5 * Math.abs(plotObject.xValues[n - 1] - plotObject.xValues[n - 2]);
				}
			}
			if ((axisRangeFlags & Y_RANGE) != 0) {
				int suggestedEnlarge = 0;
				if (plotObject.shape==DOT || plotObject.xEValues != null) //these can't be seen if merging with the frame
					suggestedEnlarge = ALWAYS_ENLARGE;
				else if (!(plotObject.shape == LINE || plotObject.shape == FILLED))
					suggestedEnlarge = USUALLY_ENLARGE;
				getMinAndMax(allMinAndMax, enlargeRange,  suggestedEnlarge, 2, plotObject.yValues, plotObject.yEValues, invertedYAxis);
				if ((plotObject.shape == BAR || plotObject.shape == SEPARATED_BAR) &&
						(allMinAndMax[2] > 0 && allMinAndMax[3]/allMinAndMax[2] >= 2) && !logYAxis)
					allMinAndMax[2] = 0;           // for bar plots, y min = 0 unless values differ less than a factor of 2
			}
		} else if (plotObject.type == PlotObject.ARROWS) {
			if ((axisRangeFlags & X_RANGE) != 0) {
				getMinAndMax(allMinAndMax, enlargeRange, ALWAYS_ENLARGE, 0, plotObject.xValues, null, invertedXAxis);
				getMinAndMax(allMinAndMax, enlargeRange, ALWAYS_ENLARGE, 0, plotObject.xEValues, null, invertedXAxis);
			}
			if ((axisRangeFlags & Y_RANGE) != 0) {
				getMinAndMax(allMinAndMax, enlargeRange, ALWAYS_ENLARGE, 2, plotObject.yValues, null, invertedYAxis);
				getMinAndMax(allMinAndMax, enlargeRange, ALWAYS_ENLARGE, 2, plotObject.yEValues, null, invertedYAxis);
			}
		}
	}

	/** Gets the minimum and maximum values for a dataset (one direction, x or y),
	 *  taking error bars (if not null) into account.
	 *	The minimum modifies allMinAndMax[axisIndex] the maximum modifies allMinAndMax[axisIndex+1].
	 *	Also cares about whether the range should be enlarged to avoid hiding markers at the borders:
	 *  suggestedEnlarge is 0 for lines or a suggestion for the data type; if the allMinAndMax is
	 *  range is extended, the corresponding enlargeRange item is set accordingly */
	void getMinAndMax(double[] allMinAndMax, int[] enlargeRange, int suggestedEnlarge,
			int axisIndex, float[] data, float[] errorBars, boolean invertedAxis) {
		int nMinEqual = 0, nMaxEqual = 0;
		int minIndex = invertedAxis ? axisIndex+1 : axisIndex;   // index of 'min' value in allMinAndMax, enlargeRange
		int maxIndex = invertedAxis ? axisIndex : axisIndex+1;
		for (int i=0; i<data.length; i++) {
			double v1 = data[i];
			double v2 = data[i];
			if (errorBars != null && i<errorBars.length) {
				v1 -= errorBars[i];
				v2 += errorBars[i];
			}
			if (v1 < allMinAndMax[minIndex]) {
				allMinAndMax[minIndex] = v1;
				nMinEqual = 1;
				enlargeRange[minIndex] = suggestedEnlarge;
				if (suggestedEnlarge == 0 && ((i>0 && i<data.length-1) || v2 != v1)) //for lines except at the end: also enlarge
					enlargeRange[minIndex] = USUALLY_ENLARGE;
			} else if (v1 == allMinAndMax[minIndex])
				nMinEqual++;
			if (v2 > allMinAndMax[maxIndex]) {
				allMinAndMax[maxIndex] = v2;
				nMaxEqual = 1;
				enlargeRange[maxIndex] = suggestedEnlarge;
				if (suggestedEnlarge == 0 && ((i>0 && i<data.length-1) || v2 != v1)) //for lines except at the end: also enlarge
					enlargeRange[maxIndex] = USUALLY_ENLARGE;
			} else if (v2 == allMinAndMax[maxIndex])
				nMaxEqual++;
		}
		//lines with many points (>10%) at min or max? Add extra space at borders ('usually', i.e. unless limit is zero)
		if (enlargeRange[minIndex] == 0 && nMinEqual > 2 && nMinEqual*10 > data.length)
			enlargeRange[minIndex] = USUALLY_ENLARGE;
		if (enlargeRange[maxIndex] == 0 && nMaxEqual > 2 && nMaxEqual*10 > data.length)
			enlargeRange[maxIndex] = USUALLY_ENLARGE;
		//all data at min or max? Always add space to avoid hiding the line behind the frame
		if (nMinEqual == data.length)
			enlargeRange[minIndex] = ALWAYS_ENLARGE;
		if (nMaxEqual == data.length)
			enlargeRange[maxIndex] = ALWAYS_ENLARGE;
		//same min or max as for current data set found already previously, but not asking yet for added space at borders?
		if (nMinEqual>0 && enlargeRange[minIndex]<suggestedEnlarge)
			enlargeRange[minIndex] = suggestedEnlarge;
		if (nMaxEqual>0 && enlargeRange[maxIndex]<suggestedEnlarge)
			enlargeRange[maxIndex] = suggestedEnlarge;
	}

	/** Saves the plot range for later restoring by 'setPreviousMinMax' */
	void saveMinMax() {
		if (!Arrays.equals(currentMinMax, savedMinMax))
			System.arraycopy(currentMinMax, 0, savedMinMax, 0, currentMinMax.length);
	}

	/** Modifies automatic limits to avoid points exactly at the borders.
	 *  This only happens for limits where the corresponding value of the class array 'enlargeRange' is set:
	 *  ALWAYS_ENLARGE: always enlarges the range; USUALLY_ENLARGE means that the limits should not be shifted across zero */
	void enlargeRange(double[] minMax) {
		if (enlargeRange == null) return;
		for (int a=0; a<Math.min(minMax.length, enlargeRange.length); a+=2) { //for all axes (0 for x, 2 for y)
			boolean logAxis = a==0 ? logXAxis : logYAxis;
			if (logAxis) {
				minMax[a] = Math.log10(minMax[a]);
				minMax[a+1] = Math.log10(minMax[a+1]);
			}
			double range = minMax[a+1] - minMax[a];
			double tmpMin = minMax[a] - 0.015*range;
			if (enlargeRange[a] == USUALLY_ENLARGE && !logAxis)  // 'weak' enlarging: dont traverse zero
				minMax[a] = (tmpMin*minMax[a] <= 0) ? 0 : tmpMin;
			else if (enlargeRange[a] == ALWAYS_ENLARGE)
				minMax[a] = tmpMin;
			double tmpMax = minMax[a+1] + 0.015*range;
			if (enlargeRange[a+1] == USUALLY_ENLARGE && !logAxis)
				minMax[a+1] = (tmpMax*minMax[a+1] <= 0) ? 0 : tmpMax;
			else if (enlargeRange[a+1] == ALWAYS_ENLARGE)
				minMax[a+1] = tmpMax;
			if (logAxis) {
				minMax[a] = Math.pow(10, minMax[a]);
				minMax[a+1] = Math.pow(10, minMax[a+1]);
			}
		}
	}

	/** Returns the first font of the list that is not null, or defaultFont if both are null */
	Font nonNullFont(Font font1, Font font2) {
		if (font1 != null)
			return font1;
		else if (font2 != null)
			return font2;
		else return
			defaultFont;
	}

	/** Zooms to a range given in pixels and updates the image */
	void zoomToRect(Rectangle r) {
		saveMinMax();
		currentMinMax[0] = descaleX(r.x);
		currentMinMax[1] = descaleX(r.x + r.width);
		currentMinMax[2] = descaleY(r.y + r.height);
		currentMinMax[3] = descaleY(r.y);
		//snapToMinorGrid = true; //get nice bounds when zooming in
		updateImage();
	}

	/**
	 * Adjusts the plot range when the user clicks one of the overlay symbols at the
	 * axes. Index numbers for arrows start with 0 at the 'down' arrow of the
	 * lower side of the x axis and end with 7 the up arrow at the upper
	 * side of the y axis. Numbers 8 & 9 are for "Reset Range" and "Fit All";
	 * numbers 10-13 for a dialog to set a single limit, and 14-15 for an axis options dialog.
	 * Numbers 10-15 must correspond to the dialogTypes as defined in PlotDialog.
	 */
	void zoomOnRangeArrow(int arrowIndex) {
		if (arrowIndex < 0) return;
		if (arrowIndex < 8) {//0..7 = arrows, 8 = Reset Range, 9 = Fit All, 10..13 = set single limit
			int axisIndex = (arrowIndex / 4) * 2;  //0 for x, 2 for y
			double min = axisIndex == 0 ? xMin : yMin;
			double max = axisIndex == 0 ? xMax : yMax;
			double range = max - min;
			boolean isMin = (arrowIndex % 4) < 2;
			boolean shrinkRange = arrowIndex % 4 == 1 || arrowIndex % 4 == 2;
			double factor = Math.sqrt(2);
			if (shrinkRange)
				factor = 1.0 / factor;
			if (isMin)
				min = max - range * factor;
			else
				max = min + range * factor;
			boolean logAxis = axisIndex == 0 ? logXAxis : logYAxis;
			if (logAxis) {
				min = Math.pow(10, min);
				max = Math.pow(10, max);
			}
			currentMinMax[axisIndex] = min;
			currentMinMax[axisIndex + 1] = max;
		} else if (arrowIndex == 8) {
			setLimitsToDefaults(false);
		} else if (arrowIndex == 9) {
			setLimitsToFit(false);
		} else if (arrowIndex <= 15) {
			int dialogType = arrowIndex;
			new PlotDialog(this, dialogType).showDialog(imp.getWindow());
		}
		if (arrowIndex <= 9) // the PlotDialog cares about updating the plot
			updateImage();
	}

	/**
	 * Zooms in or out  active plots while keeping focus on cursor position
	 * Above or below frame: zoom x only
	 * Left or right of frame: zoom y only
	 * Corners: focus is in center
	 *  N. Vischer
	*/
	void zoom(int x, int y, double zoomFactor) {
		boolean wasLogX = logXAxis;
		boolean wasLogY = logYAxis;
		double plotX = descaleX(x);
		double plotY = descaleY(y);
		IJ.showStatus ("" + plotX);
		boolean insideX = x > frame.x && x < frame.x + frame.width;
		boolean insideY = y > frame.y && y < frame.y + frame.height;
		if (!insideX && !insideY) {
			insideX = true;
			insideY = true;
			x = frame.x + frame.width / 2;
			y = frame.y + frame.height / 2;
		}
		int leftPart = x - frame.x;
		int rightPart = frame.x + frame.width - x;
		int highPart = y - frame.y;
		int lowPart = frame.y + frame.height - y;

		if (insideX) {
			currentMinMax[0] = descaleX((int) (x - leftPart / zoomFactor));
			currentMinMax[1] = descaleX((int) (x + rightPart / zoomFactor));
		}
		if (insideY) {
			currentMinMax[2] = descaleY((int) (y + lowPart / zoomFactor));
			currentMinMax[3] = descaleY((int) (y - highPart / zoomFactor));
		}
		updateImage();
		if (wasLogX != logXAxis ){//log-lin was automatically changed
			int changedX = (int) scaleXtoPxl(plotX);
			int left = changedX - leftPart;
			int right = changedX + rightPart;
			currentMinMax[0] = descaleX(left);
			currentMinMax[1] = descaleX(right);
			updateImage();
		}
		if (wasLogY != logYAxis){//log-lin was automatically changed
			int changedY = (int) scaleYtoPxl(plotY);
			int bottom = changedY + lowPart;
			int top = changedY + highPart;
			currentMinMax[2] = descaleY(bottom);
			currentMinMax[3] = descaleY(top);
			updateImage();
		}
	}

	/** Moves the plot range by a given number of pixels and updates the image */
	void scroll(int dx, int dy) {
		if (logXAxis) {
			currentMinMax[0] /= Math.pow(10, dx/xScale);
			currentMinMax[1] /= Math.pow(10, dx/xScale);
		} else {
			currentMinMax[0] -= dx/xScale;
			currentMinMax[1] -= dx/xScale;
		}
		if (logYAxis) {
			currentMinMax[2] *= Math.pow(10, dy/yScale);
			currentMinMax[3] *= Math.pow(10, dy/yScale);
		} else {
			currentMinMax[2] += dy/yScale;
			currentMinMax[3] += dy/yScale;
		}
		updateImage();
	}

	/** Whether to draw simple axes without ticks, grid and numbers only for min, max*/
	private boolean simpleXAxis() {
		return !hasFlag(X_TICKS | X_MINOR_TICKS | X_LOG_TICKS | X_GRID | X_NUMBERS);
	}

	private boolean simpleYAxis() {
		return !hasFlag(Y_TICKS | Y_MINOR_TICKS | Y_LOG_TICKS | Y_GRID | Y_NUMBERS);
	}

	/** Draws ticks, grid and axis label for each tick/grid line.
	 *	The grid or major tick spacing in each direction is given by steps */
	void drawAxesTicksGridNumbers(double[] steps) {

		if (ip==null)
			return;
		String[] xCats = labelsInBraces('x');   // create categories for the axes (if any)
		String[] yCats = labelsInBraces('y');
		String multiplySymbol = getMultiplySymbol(); // for scientific notation
		Font scFont = scFont(pp.frame.getFont());
		Font scFontMedium = scFont.deriveFont(scFont.getSize2D()*10f/12f); //for axis numbers if full size does not fit
		Font scFontSmall = scFont.deriveFont(scFont.getSize2D()*9f/12f);   //for subscripts
		ip.setFont(scFont);
		FontMetrics fm = ip.getFontMetrics();
		int fontAscent = fm.getAscent();
		ip.setJustification(LEFT);
		// ---	A l o n g	X	A x i s
		int yOfXAxisNumbers = topMargin + frameHeight + fm.getHeight()*5/4 + sc(2);
		if (hasFlag(X_NUMBERS | (logXAxis ? (X_TICKS | X_MINOR_TICKS) : X_LOG_TICKS) + X_GRID)) {
			Font baseFont = scFont;
			boolean majorTicks = logXAxis ? hasFlag(X_LOG_TICKS) : hasFlag(X_TICKS);
			boolean minorTicks = hasFlag(X_MINOR_TICKS);
			minorTicks = minorTicks && (xCats == null);
			double step = steps[0];
			int i1 = (int)Math.ceil (Math.min(xMin, xMax)/step-1.e-10);
			int i2 = (int)Math.floor(Math.max(xMin, xMax)/step+1.e-10);
			int suggestedDigits = (int)Tools.getNumberFromList(pp.frame.options, "xdecimals="); //is not given, NaN cast to 0
			int digits = getDigits(xMin, xMax, step, 7, suggestedDigits);
			int y1 = topMargin;
			int y2 = topMargin + frameHeight;
			if (xMin==xMax) {
				if (hasFlag(X_NUMBERS)) {
					String s = IJ.d2s(xMin,getDigits(xMin, 0.001*xMin, 5, suggestedDigits));
					int y = yBasePxl;
					ip.drawString(s, xBasePxl-ip.getStringWidth(s)/2, yOfXAxisNumbers);
				}
			} else {
				if (hasFlag(X_NUMBERS)) {
					int w1 = ip.getStringWidth(IJ.d2s(currentMinMax[0], logXAxis ? -1 : digits));
					int w2 = ip.getStringWidth(IJ.d2s(currentMinMax[1], logXAxis ? -1 : digits));
					int wMax = Math.max(w1,w2);
					if (wMax > Math.abs(step*xScale)-sc(8)) {
						baseFont = scFontMedium;   //small font if there is not enough space for the numbers
						ip.setFont(baseFont);
					}
				}

				for (int i=0; i<=(i2-i1); i++) {
					double v = (i+i1)*step;
					int x = (int)Math.round((v - xMin)*xScale) + leftMargin;

					if (xCats!= null) {
						int index = (int) v;
						double remainder =  Math.abs(v - Math.round(v));
						if(index >= 0 && index < xCats.length  && remainder < 1e-9){
							String s = xCats[index];
							String[] parts = s.split("\n");
							int w = 0;
							for(int jj = 0; jj < parts.length; jj++)
								w = Math.max(w, ip.getStringWidth(parts[jj]));

							ip.drawString(s, x-w/2, yOfXAxisNumbers);
							//ip.drawString(s, x-ip.getStringWidth(s)/2, yOfXAxisNumbers);
						}
						continue;
					}

					if (hasFlag(X_GRID)) {
						ip.setColor(gridColor);
						ip.drawLine(x, y1, x, y2);
						ip.setColor(Color.black);
					}
					if (majorTicks) {
						ip.drawLine(x, y1, x, y1+sc(tickLength));
						ip.drawLine(x, y2, x, y2-sc(tickLength));
					}
					if (hasFlag(X_NUMBERS)) {
						if (logXAxis || digits<0) {
							drawExpString(logXAxis ? Math.pow(10,v) : v, logXAxis ? -1 : -digits,
									x, yOfXAxisNumbers-fontAscent/2, CENTER, fontAscent, baseFont, scFontSmall, multiplySymbol);
						} else {
							String s = IJ.d2s(v,digits);
							ip.drawString(s, x-ip.getStringWidth(s)/2, yOfXAxisNumbers);
						}
					}
				}
				boolean haveMinorLogNumbers = i2-i1 < 2;		//nunbers on log minor ticks only if < 2 decades
				if (minorTicks && (!logXAxis || step > 1.1)) {  //'standard' log minor ticks only for full decades
					double mstep = niceNumber(step*0.19);       //non-log: 4 or 5 minor ticks per major tick
					double minorPerMajor = step/mstep;
					if (Math.abs(minorPerMajor-Math.round(minorPerMajor)) > 1e-10) //major steps are not an integer multiple of minor steps? (e.g. user step 90 deg)
						mstep = step/4;
					if (logXAxis && mstep < 1) mstep = 1;
					i1 = (int)Math.ceil (Math.min(xMin,xMax)/mstep-1.e-10);
					i2 = (int)Math.floor(Math.max(xMin,xMax)/mstep+1.e-10);
					for (int i=i1; i<=i2; i++) {
						double v = i*mstep;
						int x = (int)Math.round((v - xMin)*xScale) + leftMargin;
						ip.drawLine(x, y1, x, y1+sc(minorTickLength));
						ip.drawLine(x, y2, x, y2-sc(minorTickLength));
					}
				} else if (logXAxis && majorTicks && Math.abs(xScale)>sc(MIN_X_GRIDSPACING)) {		//minor ticks for log
					int minorNumberLimit = haveMinorLogNumbers ? (int)(0.12*Math.abs(xScale)/(fm.charWidth('0')+sc(2))) : 0;   //more numbers on minor ticks when zoomed in
					i1 = (int)Math.floor(Math.min(xMin,xMax)-1.e-10);
					i2 = (int)Math.ceil (Math.max(xMin,xMax)+1.e-10);
					for (int i=i1; i<=i2; i++) {
						for (int m=2; m<10; m++) {
							double v = i+Math.log10(m);
							if (v > Math.min(xMin,xMax) && v < Math.max(xMin,xMax)) {
								int x = (int)Math.round((v - xMin)*xScale) + leftMargin;
								ip.drawLine(x, y1, x, y1+sc(minorTickLength));
								ip.drawLine(x, y2, x, y2-sc(minorTickLength));
								if (m<=minorNumberLimit)
									drawExpString(Math.pow(10,v), 0, x, yOfXAxisNumbers-fontAscent/2, CENTER,
											fontAscent, baseFont, scFontSmall, multiplySymbol);
							}
						}
					}
				}
			}
		}
		// ---	A l o n g	Y	A x i s
		ip.setFont(scFont);
		int maxNumWidth = 0;
		int xNumberRight = leftMargin-sc(2)-ip.getStringWidth("0")/2;
		Rectangle rect = ip.getStringBounds("0169");
		int yNumberOffset = -rect.y-rect.height/2;
		if (hasFlag(Y_NUMBERS | (logYAxis ? (Y_TICKS | Y_MINOR_TICKS) : Y_LOG_TICKS) + Y_GRID)) {
			ip.setJustification(RIGHT);
			Font baseFont = scFont;
			boolean majorTicks = logYAxis ? hasFlag(Y_LOG_TICKS) : hasFlag(Y_TICKS);
			boolean minorTicks = logYAxis ? hasFlag(Y_LOG_TICKS) : hasFlag(Y_MINOR_TICKS);
			minorTicks = minorTicks && (yCats == null);
			double step = steps[1];
			int i1 = (int)Math.ceil (Math.min(yMin, yMax)/step-1.e-10);
			int i2 = (int)Math.floor(Math.max(yMin, yMax)/step+1.e-10);
			int suggestedDigits = (int)Tools.getNumberFromList(pp.frame.options, "ydecimals="); //is not given, NaN cast to 0
			int digits = getDigits(yMin, yMax, step, 5, suggestedDigits);
			int x1 = leftMargin;
			int x2 = leftMargin + frameWidth;
			if (yMin==yMax) {
				if (hasFlag(Y_NUMBERS)) {
					String s = IJ.d2s(yMin,getDigits(yMin, 0.001*yMin, 5, suggestedDigits));
					maxNumWidth = ip.getStringWidth(s);
					int y = yBasePxl;
					ip.drawString(s, xNumberRight, y+fontAscent/2+sc(1));
				}
			} else {
				int digitsForWidth = logYAxis ? -1 : digits;
				if (digitsForWidth < 0) {
					digitsForWidth--; //"1.0*10^5" etc. needs more space than 1.0*5, simulate by adding one decimal
					xNumberRight += sc(1)+ip.getStringWidth("0")/4;
				}
				String str1 = IJ.d2s(currentMinMax[2], digitsForWidth);
				String str2 = IJ.d2s(currentMinMax[3], digitsForWidth);
				if (digitsForWidth < 0) {
					str1 = str1.replaceFirst("E",multiplySymbol);
					str2 = str2.replaceFirst("E",multiplySymbol);
				}
				int w1 = ip.getStringWidth(str1);
				int w2 = ip.getStringWidth(str2);
				int wMax = Math.max(w1,w2);
				if (hasFlag(Y_NUMBERS)) {
					if (wMax > xNumberRight - sc(4) - (pp.yLabel.label.length()>0 ? fm.getHeight() : 0)) {
						baseFont = scFontMedium;   //small font if there is not enough space for the numbers
						ip.setFont(baseFont);
					}
				}
				//IJ.log(IJ.d2s(currentMinMax[2],digits)+": w="+w1+"; "+IJ.d2s(currentMinMax[3],digits)+": w="+w2+baseFont+" Space="+(leftMargin-sc(4+5)-fm.getHeight()));
				for (int i=i1; i<=i2; i++) {
					double v = step==0 ? yMin : i*step;
					int y = topMargin + frameHeight - (int)Math.round((v - yMin)*yScale);

					if (yCats != null){
						int index = (int) v;
						double remainder =  Math.abs(v - Math.round(v));
						if(index >= 0 && index < yCats.length  && remainder < 1e-9){
							String s = yCats[index];
							int multiLineOffset = 0; // multi-line cat labels
							for(int jj = 0; jj < s.length(); jj++)
								if(s.charAt(jj) == '\n')
									multiLineOffset -= rect.height/2;

							ip.drawString(s, xNumberRight, y+yNumberOffset+ multiLineOffset);
						}
						continue;
					}

					if (hasFlag(Y_GRID)) {
						ip.setColor(gridColor);
						ip.drawLine(x1, y, x2, y);
						ip.setColor(Color.black);
					}
					if (majorTicks) {
						ip.drawLine(x1, y, x1+sc(tickLength), y);
						ip.drawLine(x2, y, x2-sc(tickLength), y);
					}
					if (hasFlag(Y_NUMBERS)) {
						int w = 0;
						if (logYAxis || digits<0) {
							w = drawExpString(logYAxis ? Math.pow(10,v) : v, logYAxis ? -1 : -digits,
									xNumberRight, y, RIGHT, fontAscent, baseFont, scFontSmall, multiplySymbol);
						} else {
							String s = IJ.d2s(v,digits);
							w = ip.getStringWidth(s);
							ip.drawString(s, xNumberRight, y+yNumberOffset);
						}
						if (w > maxNumWidth) maxNumWidth = w;
					}
				}
				boolean haveMinorLogNumbers = i2-i1 < 2;        //numbers on log minor ticks only if < 2 decades
				if (minorTicks && (!logYAxis || step > 1.1)) {  //'standard' log minor ticks only for full decades
					double mstep = niceNumber(step*0.19);       //non-log: 4 or 5 minor ticks per major tick
					double minorPerMajor = step/mstep;
					if (Math.abs(minorPerMajor-Math.round(minorPerMajor)) > 1e-10) //major steps are not an integer multiple of minor steps? (e.g. user step 90 deg)
						mstep = step/4;
					if (logYAxis && step < 1) mstep = 1;
					i1 = (int)Math.ceil (Math.min(yMin,yMax)/mstep-1.e-10);
					i2 = (int)Math.floor(Math.max(yMin,yMax)/mstep+1.e-10);
					for (int i=i1; i<=i2; i++) {
						double v = i*mstep;
						int y = topMargin + frameHeight - (int)Math.round((v - yMin)*yScale);
						ip.drawLine(x1, y, x1+sc(minorTickLength), y);
						ip.drawLine(x2, y, x2-sc(minorTickLength), y);
					}
				}
				if (logYAxis && majorTicks && Math.abs(yScale)>sc(MIN_X_GRIDSPACING)) {		 //minor ticks for log within the decade
					int minorNumberLimit = haveMinorLogNumbers ? (int)(0.4*Math.abs(yScale)/fm.getHeight()) : 0;	//more numbers on minor ticks when zoomed in
					i1 = (int)Math.floor(Math.min(yMin,yMax)-1.e-10);
					i2 = (int)Math.ceil(Math.max(yMin,yMax)+1.e-10);
					for (int i=i1; i<=i2; i++) {
						for (int m=2; m<10; m++) {
							double v = i+Math.log10(m);
							if (v > Math.min(yMin,yMax) && v < Math.max(yMin,yMax)) {
								int y = topMargin + frameHeight - (int)Math.round((v - yMin)*yScale);
								ip.drawLine(x1, y, x1+sc(minorTickLength), y);
								ip.drawLine(x2, y, x2-sc(minorTickLength), y);
								if (m<=minorNumberLimit) {
									int w = drawExpString(Math.pow(10,v), 0, xNumberRight, y, RIGHT,
											fontAscent, baseFont, scFontSmall, multiplySymbol);
									if (w > maxNumWidth) maxNumWidth = w;
								}
							}
						}
					}
				}
			}
		}
		// --- Write min&max of range if simple style without any axis format flags
		ip.setFont(scFont);
		ip.setJustification(LEFT);
		String xLabelToDraw = pp.xLabel.label;
		String yLabelToDraw = pp.yLabel.label;
		if (simpleYAxis()) { // y-axis min&max
			int digits = getDigits(yMin, yMax, 0.001*(yMax-yMin), 6, 0);
			String s = IJ.d2s(yMax, digits);
			int sw = ip.getStringWidth(s);
			if ((sw+sc(4)) > leftMargin)
				ip.drawString(s, sc(4), topMargin-sc(4));
			else
				ip.drawString(s, leftMargin-ip.getStringWidth(s)-sc(4), topMargin+10);
			s = IJ.d2s(yMin, digits);
			sw = ip.getStringWidth(s);
			if ((sw+4)>leftMargin)
				ip.drawString(s, sc(4), topMargin+frame.height);
			else
				ip.drawString(s, leftMargin-ip.getStringWidth(s)-sc(4), topMargin+frame.height);
			if (logYAxis) yLabelToDraw += " (LOG)";
		}
		int y = yOfXAxisNumbers;
		if (simpleXAxis()) { // x-axis min&max
			int digits = getDigits(xMin, xMax, 0.001*(xMax-xMin), 7, 0);
			ip.drawString(IJ.d2s(xMin,digits), leftMargin, y);
			String s = IJ.d2s(xMax,digits);
			ip.drawString(s, leftMargin + frame.width-ip.getStringWidth(s)+6, y);
			y -= fm.getHeight();
			if (logXAxis) xLabelToDraw += " (LOG)";
		} else
			y += sc(1);
		// --- Write x and y axis text labels
		if (xCats == null) {
			ip.setFont(pp.xLabel.getFont() == null ? scFont : scFont(pp.xLabel.getFont()));
			ImageProcessor xLabel = stringToPixels(xLabelToDraw);
			if(xLabel != null){
				int xpos = leftMargin+(frame.width-xLabel.getWidth())/2;
				int ypos = y + scFont.getSize()/3;//topMargin + frame.height + bottomMargin-xLabel.getHeight();
				ip.insert(xLabel, xpos, ypos);
			}
		}
		if (yCats == null) {
			ip.setFont(pp.yLabel.getFont() == null ? scFont : scFont(pp.yLabel.getFont()));
			ImageProcessor yLabel = stringToPixels(yLabelToDraw);
			if(yLabel != null){
				yLabel = yLabel.rotateLeft();
				int xRightOfYLabel = xNumberRight - maxNumWidth - sc(2);
				int xpos = xRightOfYLabel - yLabel.getWidth() - sc(2);
				int ypos = topMargin + (frame.height -yLabel.getHeight())/2;
				ip.insert(yLabel, xpos, ypos);
			}
		}
	}

	/** Returns the array of categories from an axis label in the form {cat1,cat2,cat3}, or null if not this form
	 *  @param labelCode  can be 'x' or 'y', for the x or y axis label*/
	String[] labelsInBraces(char labelCode) {
		String s = getLabel(labelCode);
		if (s.startsWith("{") && s.endsWith("}")) {
			String inBraces = s.substring(1, s.length() - 1);
			String[] catLabels = inBraces.split(",");
			return catLabels;
		} else {
			return null;
		}
	}

	/** Returns the smallest "nice" number >= v. "Nice" numbers are .. 0.5, 1, 2, 5, 10, 20 ... */
	double niceNumber(double v) {
		double base = Math.pow(10,Math.floor(Math.log10(v)-1.e-6));
		if (v > 5.0000001*base) return 10*base;
		else if (v > 2.0000001*base) return 5*base;
		else return 2*base;
	}

	/** draw something like 1.2 10^-9; returns the width of the string drawn.
	 *	'Digits' should be >=0 for drawing the mantissa (=1.38 in this example), negative to draw only 10^exponent
	 *	Currently only supports center justification and right justification (y of center line)
	 *	Fonts baseFont, smallFont should be scaled already
	 *  Returns the width of the String */
	int drawExpString(double value, int digits, int x, int y, int justification,
			int fontAscent, Font baseFont, Font smallFont, String multiplySymbol) {
		String base = "10";
		String exponent = null;
		String s = IJ.d2s(value, digits<=0 ? -1 : -digits);
		if (Tools.parseDouble(s) == 0) s = "0"; //don't write 0 as 0*10^0
		int ePos = s.indexOf('E');
		if (ePos < 0)
			base = s;	//can't have exponential format, e.g. NaN
		else {
			if (digits>=0) {
				base = s.substring(0,ePos);
				if (digits == 0)
					base = Integer.toString((int)Math.round(Tools.parseDouble(base)));
				base += multiplySymbol+"10";
			}
			exponent = s.substring(ePos+1);
		}
		//IJ.log(s+" -> "+base+"^"+exponent+"  maxAsc="+fontAscent+" font="+baseFont);
		ip.setJustification(RIGHT);
		int width = ip.getStringWidth(base);
		if (exponent != null) {
			ip.setFont(smallFont);
			int wExponent = ip.getStringWidth(exponent);
			width += wExponent;
			if (justification == CENTER) x += width/2;
			ip.drawString(exponent, x, y+fontAscent*3/10);
			x -= wExponent;
			ip.setFont(baseFont);
		}
		ip.drawString(base, x, y+fontAscent*7/10);
		return width;
	}

	/** Returns the user-supplied (via setOptions) or default multiplication symbol (middot) */
	String getMultiplySymbol() {
		String multiplySymbol = Tools.getStringFromList(pp.frame.options, "msymbol=");
		if (multiplySymbol==null)
			multiplySymbol = Tools.getStringFromList(pp.frame.options, "multiplysymbol=");
		return multiplySymbol != null ? multiplySymbol : MULTIPLY_SYMBOL;
	}

	//Returns a pixelMap containting labelStr.
	//Uses font of current ImageProcessor.
	//Returns null for empty or blank-only strings
	//Supports !!subscript!! and ^^superscript^^
	ByteProcessor stringToPixels(String labelStr) {
		Font bigFont = ip.getFont();
		Rectangle rect = ip.getStringBounds(labelStr);
		int ww = rect.width * 2;
		int hh = rect.height * 3;//enough space, will be cropped later
		int y0 = rect.height * 2;//base line
		if (ww <= 0 || hh <= 0) {
			return null;
		}
		ByteProcessor box = new ByteProcessor(ww, hh);
		box.setColor(Color.WHITE);
		//box.setColor(Color.LIGHT_GRAY); //make box visible for test
		box.fill();
		box.setColor(Color.black);
		box.setAntialiasedText(pp.antialiasedText);
		if (invertedLut) {
			box.invertLut();
		}
		box.setFont(bigFont);

		FontMetrics fm = box.getFontMetrics();
		int ascent = fm.getAscent();
		int offSub = ascent / 6;
		int offSuper = -ascent / 2;
		Font smallFont = bigFont.deriveFont((float) (bigFont.getSize() * 0.7));

		Rectangle bigBounds = box.getStringBounds(labelStr);
		boolean doParse = (labelStr.indexOf("^^") >= 0 || labelStr.indexOf("!!") >= 0);
		doParse = doParse && (labelStr.indexOf("^^^") < 0 && labelStr.indexOf("!!!") < 0);
		if (!doParse) {
			box.drawString(labelStr, 0, y0);
			Rectangle cropRect = new Rectangle(bigBounds);
			cropRect.y += y0;
			box.setRoi(cropRect);
			ImageProcessor boxI = box.crop();
			box = boxI.convertToByteProcessor();
			return box;
		}

		if (labelStr.endsWith("^^") || labelStr.endsWith("!!")) {
			labelStr = labelStr.substring(0, labelStr.length() - 2);
		}
		if (labelStr.startsWith("^^") || labelStr.startsWith("!!")) {
			labelStr = " " + labelStr;
		}

		box.setFont(smallFont);
		Rectangle smallBounds = box.getStringBounds(labelStr);
		box.setFont(bigFont);
		int upperBound = y0 + smallBounds.y + offSuper;
		int lowerBound = y0 + smallBounds.y + smallBounds.height + offSub;

		int h = fm.getHeight();
		int len = labelStr.length();
		int[] tags = new int[len];
		int nTags = 0;

		for (int jj = 0; jj < len - 2; jj++) {//get positions where font size changes
			if (labelStr.substring(jj, jj + 2).equals("^^")) {
				tags[nTags++] = jj;
			}
			if (labelStr.substring(jj, jj + 2).equals("!!")) {
				tags[nTags++] = -jj;
			}
		}
		tags[nTags++] = len;
		tags = Arrays.copyOf(tags, nTags);

		int leftIndex = 0;
		int xRight = 0;
		int y2 = y0;

		boolean subscript = labelStr.startsWith("!!");
		for (int pp = 0; pp < tags.length; pp++) {//draw all text fragments
			int rightIndex = tags[pp];
			rightIndex = Math.abs(rightIndex);
			String part = labelStr.substring(leftIndex, rightIndex);
			boolean small = pp % 2 == 1;//toggle odd/even
			if (small) {
				box.setFont(smallFont);
				if (subscript) {
					y2 = y0 + offSub;
				} else {//superscript:
					y2 = y0 + offSuper;
				}
			} else {
				box.setFont(bigFont);
				y2 = y0;
			}
			xRight++;
			int partWidth = box.getStringWidth(part);
			box.drawString(part, xRight, y2);
			leftIndex = rightIndex + 2;
			subscript = tags[pp] < 0;//negative positions = subscript
			xRight += partWidth;
		}
		xRight += h / 4;
		Rectangle cropRect = new Rectangle(0, upperBound, xRight, lowerBound - upperBound);
		box.setRoi(cropRect);
		ImageProcessor boxI = box.crop();
		box = boxI.convertToByteProcessor();
		return box;
	}

	/** Returns the number of digits to display the number n with resolution 'resolution';
	 *  (if n is integer and small enough to display without scientific notation,
	 *  no decimals are needed, irrespective of 'resolution')
	 *  Scientific notation is used for more than 'maxDigits' (must be >=3), and indicated
	 *  by a negative return value, or if suggestedDigits is negative
	 *  Returns 'suggestedDigits' if not 0 and compatible with the resolution; negative values of
	 *  'suggestedDigits' switch to scientific notation. */
	static int getDigits(double n, double resolution, int maxDigits, int suggestedDigits) {
		if (n==Math.round(n) && Math.abs(n) < Math.pow(10,maxDigits-1)-1) //integers and not too big
			return suggestedDigits;
		else
			return getDigits2(n, resolution, maxDigits, suggestedDigits);
	}

	/** Number of digits to display the range between n1 and n2 with resolution 'resolution';
	 *  Scientific notation is used for more than 'maxDigits' (must be >=3), and indicated
	 *  by a negative return value
	 *  Returns 'suggestedDigits' if not 0 and compatible with the resolution; negative values of
	 *  'suggestedDigits' switch to sceintific notation. */
	static int getDigits(double n1, double n2, double resolution, int maxDigits, int suggestedDigits) {
		if (n1==0 && n2==0) return suggestedDigits;
		return getDigits2(Math.max(Math.abs(n1),Math.abs(n2)), resolution, maxDigits, suggestedDigits);
	}

	static int getDigits2(double n, double resolution, int maxDigits, int suggestedDigits) {
		if (Double.isNaN(n) || Double.isInfinite(n))
			return 0; //no scientific notation
		int log10ofN = (int)Math.floor(Math.log10(Math.abs(n))+1e-7);
		int digits = resolution != 0 ?
				-(int)Math.floor(Math.log10(Math.abs(resolution))+1e-7) :
				Math.max(0, -log10ofN+maxDigits-2);
		int sciDigits = -Math.max((log10ofN+digits),1);
		//IJ.log("n="+(float)n+"digitsRaw="+digits+" log10ofN="+log10ofN+" sciDigits="+sciDigits);
		if ((digits < -2 && log10ofN >= maxDigits) || suggestedDigits < 0)
			digits = sciDigits; //scientific notation for large numbers or if desired via suggestedDigits (plot.setOptions)
		else if (digits < 0)
			digits = 0;
		else if (digits > maxDigits-1 && log10ofN < -2)
			digits = sciDigits; // scientific notation for small numbers
		return digits < 0 ? Math.min(sciDigits, suggestedDigits) : Math.max(digits, suggestedDigits);
	}

	static boolean isInteger(double n) {
		return n==Math.round(n);
	}

	private void drawPlotObject(PlotObject plotObject, ImageProcessor ip) {
		//IJ.log("DRAWING type="+plotObject.type+" lineWidth="+plotObject.lineWidth+" shape="+plotObject.shape);
		if (plotObject.hasFlag(PlotObject.HIDDEN)) return;
		ip.setColor(plotObject.color);
		ip.setLineWidth(sc(plotObject.lineWidth));
		int type = plotObject.type;
		switch (type) {
			case PlotObject.XY_DATA:
				ip.setClipRect(frame);
				int nPoints = Math.min(plotObject.xValues.length, plotObject.yValues.length);

				if (plotObject.shape==BAR || plotObject.shape==SEPARATED_BAR)
					drawBarChart(plotObject);       // (separated) bars

				if (plotObject.shape == FILLED) {   // filling below line
					ip.setColor(plotObject.color2 != null ? plotObject.color2 : plotObject.color);
					drawFloatPolyLineFilled(ip, plotObject.xValues, plotObject.yValues, nPoints);
				}
				ip.setColor(plotObject.color);
				ip.setLineWidth(sc(plotObject.lineWidth));

				if (plotObject.yEValues != null)    // error bars in front of bars and fill area below the line, but behind lines and marker symbols
					drawVerticalErrorBars(plotObject.xValues, plotObject.yValues, plotObject.yEValues);
				if (plotObject.xEValues != null)
					drawHorizontalErrorBars(plotObject.xValues, plotObject.yValues, plotObject.xEValues);

				if (plotObject.hasFilledMarker()) { // fill markers with secondary color
					int markSize = plotObject.getMarkerSize();
					ip.setColor(plotObject.color2);
					ip.setLineWidth(1);
					for (int i=0; i<nPoints; i++)
						if ((!logXAxis || plotObject.xValues[i]>0) && (!logYAxis || plotObject.yValues[i]>0)
								&& !Double.isNaN(plotObject.xValues[i]) && !Double.isNaN(plotObject.yValues[i]))
							fillShape(plotObject.shape, scaleX(plotObject.xValues[i]), scaleY(plotObject.yValues[i]), markSize);
					ip.setColor(plotObject.color);
					ip.setLineWidth(sc(plotObject.lineWidth));
				}
				if (plotObject.hasCurve()) {        // draw the lines between the points
					if (plotObject.shape == CONNECTED_CIRCLES)
						ip.setColor(plotObject.color2 == null ? Color.black : plotObject.color2);
					drawFloatPolyline(ip, plotObject.xValues, plotObject.yValues, nPoints);
					ip.setColor(plotObject.color);
				}
				if (plotObject.hasMarker()) {       // draw the marker symbols
					int markSize = plotObject.getMarkerSize();
					ip.setColor(plotObject.color);
					Font saveFont = ip.getFont();
					for (int i=0; i<Math.min(plotObject.xValues.length, plotObject.yValues.length); i++) {
						if ((!logXAxis || plotObject.xValues[i]>0) && (!logYAxis || plotObject.yValues[i]>0)
						&& !Double.isNaN(plotObject.xValues[i]) && !Double.isNaN(plotObject.yValues[i]))
							drawShape(plotObject, scaleX(plotObject.xValues[i]), scaleY(plotObject.yValues[i]), plotObject.shape, markSize, i);
					}
					if (plotObject.shape==CUSTOM)
						ip.setFont(saveFont);
				}
				ip.setClipRect(null);
				break;
			case PlotObject.ARROWS:
				ip.setClipRect(frame);
				for (int i=0; i<plotObject.xValues.length; i++) {
					int xt1 = scaleX(plotObject.xValues[i]);
					int yt1 = scaleY(plotObject.yValues[i]);
					int xt2 = scaleX(plotObject.xEValues[i]);
					int yt2 = scaleY(plotObject.yEValues[i]);
					double dist = calculateDistance(xt1, yt1, xt2, yt2);
					if (xt1==xt2 && yt1==yt2)
						ip.drawDot(xt1, yt1);
					else if (dist < sc(1.5f*MIN_ARROWHEAD_LENGTH))
						ip.drawLine(xt1, yt1, xt2, yt2);
					else {
						int arrowHeadLength = (int)(dist*RELATIVE_ARROWHEAD_SIZE+0.5);
						if (arrowHeadLength > sc(MAX_ARROWHEAD_LENGTH)) arrowHeadLength = sc(MAX_ARROWHEAD_LENGTH);
						if (arrowHeadLength < sc(MIN_ARROWHEAD_LENGTH)) arrowHeadLength = sc(MIN_ARROWHEAD_LENGTH);
						drawArrow(xt1, yt1, xt2, yt2, arrowHeadLength);
					}
				}
				ip.setClipRect(null);
				break;

			case PlotObject.SHAPES:
				int iBoxWidth = 20;
				ip.setClipRect(frame);
				String shType = plotObject.shapeType.toLowerCase();
				if (shType.contains("rectangles")) {
					int nShapes = plotObject.shapeData.size();

					for (int i = 0; i < nShapes; i++) {
						float[] corners = (float[])(plotObject.shapeData.get(i));
						int x1 = scaleX(corners[0]);
						int y1 = scaleY(corners[1]);
						int x2 = scaleX(corners[2]);
						int y2 = scaleY(corners[3]);

					ip.setLineWidth(sc(plotObject.lineWidth));
						int left = Math.min(x1, x2);
						int right = Math.max(x1, x2);
						int top = Math.min(y1, y2);
						int bottom = Math.max(y1, y2);

						Rectangle r1 = new Rectangle(left, top, right-left, bottom - top);
						Rectangle cBox = frame.intersection(r1);
						if (plotObject.color2 != null) {
							ip.setColor(plotObject.color2);
							ip.fillRect(cBox.x, cBox.y, cBox.width, cBox.height);
						}
						ip.setColor(plotObject.color);
						ip.drawRect(cBox.x, cBox.y, cBox.width, cBox.height);
					}
					ip.setClipRect(null);
					break;
				}
				if (shType.equals("redraw_grid")) {
				ip.setLineWidth(sc(1));
					redrawGrid();
					ip.setClipRect(null);
					break;
				}
				if (shType.contains("boxes")) {

					String[] parts = Tools.split(shType);
					for (int jj = 0; jj < parts.length; jj++) {
						String[] pairs = parts[jj].split("=");
						if ((pairs.length == 2) && pairs[0].equals("width")) {
							iBoxWidth = Integer.parseInt(pairs[1]);
						}
					}
					boolean horizontal = shType.contains("boxesx");
					int nShapes = plotObject.shapeData.size();
					int halfWidth = Math.round(sc(iBoxWidth / 2));
					for (int i = 0; i < nShapes; i++) {

						float[] coords = (float[])(plotObject.shapeData.get(i));

						if (!horizontal) {

							int x = scaleX(coords[0]);
							int y1 = scaleY(coords[1]);
							int y2 = scaleY(coords[2]);
							int y3 = scaleY(coords[3]);
							int y4 = scaleY(coords[4]);
							int y5 = scaleY(coords[5]);
							ip.setLineWidth(sc(plotObject.lineWidth));

							Rectangle r1 = new Rectangle(x - halfWidth, y4, halfWidth * 2, y2 - y4);
							Rectangle cBox = frame.intersection(r1);
							if (y1 != y2 || y4 != y5)//otherwise omit whiskers
							{
								ip.drawLine(x, y1, x, y5);//whiskers
							}
							if (plotObject.color2 != null) {
								ip.setColor(plotObject.color2);
								ip.fillRect(cBox.x, cBox.y, cBox.width, cBox.height);
							}
							ip.setColor(plotObject.color);
							ip.drawRect(cBox.x, cBox.y, cBox.width, cBox.height);
							ip.setClipRect(frame);
							ip.drawLine(x - halfWidth, y3, x + halfWidth - 1, y3);
						}

					if (horizontal) {

							int y = scaleY(coords[0]);
							int x1 = scaleX(coords[1]);
							int x2 = scaleX(coords[2]);
							int x3 = scaleX(coords[3]);
							int x4 = scaleX(coords[4]);
							int x5 = scaleX(coords[5]);
							ip.setLineWidth(sc(plotObject.lineWidth));
							if(x1 !=x2 || x4 != x5)//otherwise omit whiskers
								ip.drawLine(x1, y, x5, y);//whiskers
							Rectangle r1 = new Rectangle(x2, y - halfWidth, x4 - x2, halfWidth * 2);
							Rectangle cBox = frame.intersection(r1);
							if (plotObject.color2 != null) {
								ip.setColor(plotObject.color2);
								ip.fillRect(cBox.x, cBox.y, cBox.width, cBox.height);
							}
							ip.setColor(plotObject.color);
							ip.drawRect(cBox.x, cBox.y, cBox.width, cBox.height);
							ip.setClipRect(frame);
							ip.drawLine(x3, y - halfWidth, x3, y + halfWidth - 1);
						}
					}
					ip.setClipRect(null);
					break;
				}
			case PlotObject.LINE:
				if (Double.isNaN(plotObject.x) || Double.isNaN(plotObject.y)) break;
				ip.setClipRect(frame);
				ip.drawLine(scaleX(plotObject.x), scaleY(plotObject.y), scaleX(plotObject.xEnd), scaleY(plotObject.yEnd));
				ip.setClipRect(null);
				break;
			case PlotObject.NORMALIZED_LINE:
				ip.setClipRect(frame);
				int ix1 = leftMargin + (int)(plotObject.x*frameWidth);
				int iy1 = topMargin	 + (int)(plotObject.y*frameHeight);
				int ix2 = leftMargin + (int)(plotObject.xEnd*frameWidth);
				int iy2 = topMargin	 + (int)(plotObject.yEnd*frameHeight);
				ip.drawLine(ix1, iy1, ix2, iy2);
				ip.setClipRect(null);
				break;
			case PlotObject.DOTTED_LINE:
				ip.setClipRect(frame);
				ix1 = scaleX(plotObject.x);
				iy1 = scaleY(plotObject.y);
				ix2 = scaleX(plotObject.xEnd);
				iy2 = scaleY(plotObject.yEnd);
				double length = calculateDistance(ix1, ix2, iy1, iy2) + 0.1;
				int n = (int)(length/plotObject.step);
				for (int i = 0; i<=n; i++)
					ip.drawDot(ix1 + (int)Math.round((ix2-ix1)*(double)i/n), iy1 + (int)Math.round((iy2-iy1)*(double)i/n));
				ip.setClipRect(null);
				break;
			case PlotObject.LABEL:
			case PlotObject.NORMALIZED_LABEL:
				ip.setJustification(plotObject.justification);
				if (plotObject.getFont() != null)
					ip.setFont(scFont(plotObject.getFont()));
				int xt = type==PlotObject.LABEL ? scaleX(plotObject.x) : leftMargin + (int)(plotObject.x*frameWidth);
				int yt = type==PlotObject.LABEL ? scaleY(plotObject.y) : topMargin + (int)(plotObject.y*frameHeight);
				ip.drawString(plotObject.label, xt, yt);
				break;
			case PlotObject.LEGEND:
				drawLegend(plotObject, ip);
				break;
		}
	}

	/** Draw a bar at each point */
	void drawBarChart(PlotObject plotObject) {
		int n = Math.min(plotObject.xValues.length, plotObject.yValues.length);
		String[] xCats = labelsInBraces('x'); // do we have categories at the x axis instead of numbers?
		boolean separatedBars = plotObject.shape == SEPARATED_BAR || xCats != null;
		int halfBarWidthInPixels = n <= 1 ? Math.max(1, frameWidth/2-2) : 0;
		if (separatedBars && n > 1)
			halfBarWidthInPixels = Math.max(1, (int)Math.round(Math.abs
				(0.5*(plotObject.xValues[n-1] - plotObject.xValues[0])/(n-1) * xScale * SEPARATED_BAR_WIDTH)));
		int y0 = scaleYWithOverflow(0);
		boolean yZeroInFrame = !logYAxis && yBasePxl>frame.y && yBasePxl<frame.y+frame.height;
		int prevY = y0;
		for (int i = 0; i < n; i++) {
			int left=0, right=0;
			if (halfBarWidthInPixels == 0) {         //bar boundaries in the middle between successive x values
				left = scaleX(i > 0 ? 0.5f*(plotObject.xValues[i-1]+plotObject.xValues[i]) :
						1.5f*plotObject.xValues[i] - 0.5f*plotObject.xValues[i+1]);
				right = scaleX(i < n-1 ? 0.5f*(plotObject.xValues[i]+plotObject.xValues[i+1]) :
						1.5f*plotObject.xValues[i] - 0.5f*plotObject.xValues[i-1]);
			} else {
				int x = scaleX(plotObject.xValues[i]);
				left = x - halfBarWidthInPixels;     //separated bars or n<=1 : fixed bar width
				right = x + halfBarWidthInPixels;
			}
			if (left < frame.x) left = frame.x;
			if (left > frame.x+frame.width) left = frame.x+frame.width;
			if (right < frame.x) right = frame.x;
			if (right > frame.x+frame.width) right = frame.x+frame.width;
			int y = scaleYWithOverflow(plotObject.yValues[i]);
			if (plotObject.color2 != null) {
				ip.setColor(plotObject.color2);
				for (int x2 = Math.min(left,right); x2 <= Math.max(left,right); x2++)
					ip.drawLine(x2, y0, x2, y);      //cant use ip.fillRect (ignores the clipRect), so we it fill line by line
			}
			ip.setColor(plotObject.color);
			ip.setLineWidth(sc(plotObject.lineWidth));
			if (separatedBars) {
				ip.drawLine(left, y0, left, y);      //up
				ip.drawLine(left, y, right, y);      //right
				ip.drawLine(right, y, right, y0);    //down
				if (yZeroInFrame)
					ip.drawLine(left, y0, right, y0);//baseline
			} else {
				ip.drawLine(left, prevY, left, y);   //up or down
				ip.drawLine(left, y, right, y);      //right
				if (i == n - 1)
					ip.drawLine(right, y, right, y0);//last down
				prevY = y;
			}
		}
	}

	/** Draw the symbol for the data point number 'pointIndex' (pointIndex < 0 when drawing the legend) */
	void drawShape(PlotObject plotObject, int x, int y, int shape, int size, int pointIndex) {
		if (ip==null)
			return;
		int lineWidth = ip.getLineWidth();
		if (shape == DIAMOND)
			size = (int)(size*1.21);
		int xbase = x-sc(size/2);
		int ybase = y-sc(size/2);
		int xend = x+sc(size/2);
		int yend = y+sc(size/2);
		if (lineWidth>3) {
			int newLineWidth = 3;
			ip.setLineWidth(newLineWidth);
		}
		//IJ.log("drawShape: "+size+" "+size);
		switch(shape) {
			case X:
				ip.drawLine(xbase,ybase,xend,yend);
				ip.drawLine(xend,ybase,xbase,yend);
				break;
			case BOX:
				ip.drawLine(xbase,ybase,xend,ybase);
				ip.drawLine(xend,ybase,xend,yend);
				ip.drawLine(xend,yend,xbase,yend);
				ip.drawLine(xbase,yend,xbase,ybase);
				break;
			case TRIANGLE:
				ip.drawLine(x,ybase-sc(1),xend+sc(1),yend); //height must be odd, otherwise rounding leads to asymmetric shape
				ip.drawLine(x,ybase-sc(1),xbase-sc(1),yend);
				ip.drawLine(xend+sc(1),yend,xbase-sc(1),yend);
				break;
			case CROSS:
				ip.drawLine(xbase,y,xend,y);
				ip.drawLine(x,ybase,x,yend);
				break;
			case DIAMOND:
				ip.drawLine(xbase,y,x,ybase);
				ip.drawLine(x,ybase,xend,y);
				ip.drawLine(xend,y,x,yend);
				ip.drawLine(x,yend,xbase,y);
				break;
			case DOT:
				ip.drawDot(x, y); //uses current line width
				break;
			case CUSTOM:
				if (plotObject.macroCode==null || frame==null)
					break;
				if (x<frame.x || y<frame.y || x>=frame.x+frame.width || y>=frame.y+frame.height)
					break;
				ImagePlus imp = new ImagePlus("", ip);
				WindowManager.setTempCurrentImage(imp);
				StringBuilder sb = new StringBuilder(140+plotObject.macroCode.length());
				sb.append("x="); sb.append(x);
				sb.append(";y="); sb.append(y);
				sb.append(";setColor('");
				sb.append(Tools.c2hex(plotObject.color));
				sb.append("');s="); sb.append(sc(1));
				boolean drawingLegend = pointIndex < 0;
				double xVal = 0;
				double yVal = 0;
				if (!drawingLegend) {
					xVal = plotObject.xValues[pointIndex];
					yVal = plotObject.yValues[pointIndex];
				}
				sb.append(";i="); sb.append(drawingLegend ? 0 : pointIndex);
				sb.append(";xval=" + xVal);
				sb.append(";yval=" + yVal);
				sb.append(";");
				sb.append(plotObject.macroCode);
				if (!drawingLegend ||!sb.toString().contains("d2s") ) {// a graphical symbol won't contain "d2s" ..
					String rtn = IJ.runMacro(sb.toString());//.. so it can go to the legend
					if ("[aborted]".equals(rtn))
					plotObject.macroCode = null;
				}
				WindowManager.setTempCurrentImage(null);
				break;
			default: // CIRCLE, CONNECTED_CIRCLES: 5x5 oval approximated by 5x5 square without corners
				if (sc(size) < 5.01) {
					ip.drawLine(x-1, y-2, x+1, y-2);
					ip.drawLine(x-1, y+2, x+1, y+2);
					ip.drawLine(x+2, y+1, x+2, y-1);
					ip.drawLine(x-2, y+1, x-2, y-1);
				} else {
					int r = sc(0.5f*size-0.5f);
					ip.drawOval(x-r, y-r, 2*r, 2*r);
				}
				break;
		}
		ip.setLineWidth(lineWidth);
	}

	/** Fill the area of the symbols for data points (except for shape=DOT)
	 *	Note that ip.fill, ip.fillOval etc. can't be used here: they do not care about the clip rectangle */
	void fillShape(int shape, int x0, int y0, int size) {
		if (shape == DIAMOND) size = (int)(size*1.21);
		int r = sc(size/2)-1;
		switch(shape) {
			case BOX:
				for (int dy=-r; dy<=r; dy++)
					for (int dx=-r; dx<=r; dx++)
						ip.drawDot(x0+dx, y0+dy);
				break;
			case TRIANGLE:
				int ybase = y0 - r - sc(1);
				int yend = y0 + r;
				double halfWidth = sc(size/2)+sc(1)-1;
				double hwStep = halfWidth/(yend-ybase+1);
				for (int y=yend; y>=ybase; y--, halfWidth -= hwStep) {
					int dx = (int)(Math.round(halfWidth));
					for (int x=x0-dx; x<=x0+dx; x++)
						ip.drawDot(x,y);
				}
				break;
			case DIAMOND:
				ybase = y0 - r - sc(1);
				yend = y0 + r;
				halfWidth = sc(size/2)+sc(1)-1;
				hwStep = halfWidth/(yend-ybase+1);
				for (int y=yend; y>=ybase; y--) {
					int dx = (int)(Math.round(halfWidth-(hwStep+1)*Math.abs(y-y0)));
					for (int x=x0-dx; x<=x0+dx; x++)
						ip.drawDot(x,y);
				}
				break;
			case CIRCLE: case CONNECTED_CIRCLES:
				int rsquare = (r+1)*(r+1);
				for (int dy=-r; dy<=r; dy++)
					for (int dx=-r; dx<=r; dx++)
						if (dx*dx + dy*dy <= rsquare)
							ip.drawDot(x0+dx, y0+dy);
				break;
		}
	}

	/** Adds an arrow from position 1 to 2 given in pixels; 'size' is the length of the arrowhead
	 *	@deprecated Use as a public method is not supported any more because it is incompatible with rescaling */
	@Deprecated
	public void drawArrow(int x1, int y1, int x2, int y2, double size) {
		double dx = x2 - x1;
		double dy = y2 - y1;
		double ra = Math.sqrt(dx * dx + dy * dy);
		dx /= ra;
		dy /= ra;
		int x3 = (int) Math.round(x2 - dx * size);	//arrow base
		int y3 = (int) Math.round(y2 - dy * size);
		double r = 0.3 * size;
		int x4 = (int) Math.round(x3 + dy * r);
		int y4 = (int) Math.round(y3 - dx * r);
		int x5 = (int) Math.round(x3 - dy * r);
		int y5 = (int) Math.round(y3 + dx * r);
		ip.moveTo(x1, y1); ip.lineTo(x2, y2);
		ip.moveTo(x4, y4); ip.lineTo(x2, y2); ip.lineTo(x5, y5);
	}

	private void drawVerticalErrorBars(float[] x, float[] y, float[] e) {
		int nPoints = Math.min(Math.min(x.length, y.length), e.length);
		for (int i=0; i<nPoints; i++) {
			if (Float.isNaN(x[i]) || Float.isNaN(y[i]) || (logXAxis && !(x[i] >0))) continue;
			int x0 = scaleX(x[i]);
			int yPlus = scaleYWithOverflow(y[i] + e[i]);
			int yMinus = scaleYWithOverflow(y[i] - e[i]);
			ip.moveTo(x0,yMinus);
			ip.lineTo(x0, yPlus);
		}
	}

	private void drawHorizontalErrorBars(float[] x, float[] y, float[] e) {
		int nPoints = Math.min(Math.min(x.length, y.length), e.length);
		float[] xpoints = new float[2];
		float[] ypoints = new float[2];
		for (int i=0; i<nPoints; i++) {
			if (Float.isNaN(x[i]) || Float.isNaN(y[i]) || (logXAxis && !(y[i] >0))) continue;
			int y0 = scaleY(y[i]);
			int xPlus = scaleXWithOverflow(x[i] + e[i]);
			int xMinus = scaleXWithOverflow(x[i] - e[i]);
			ip.moveTo(xMinus,y0);
			ip.lineTo(xPlus, y0);
		}
	}

	/** Draw a polygon line; NaN values interrupt it. */
	void drawFloatPolyline(ImageProcessor ip, float[] x, float[] y, int n) {
		if (x==null || x.length==0) return;
		int x1, y1;
		boolean isNaN0;
		boolean isNaN1 = true; //no previous point
		int x2 = scaleX(x[0]);
		int y2 = scaleY(y[0]);
		boolean isNaN2 = Float.isNaN(x[0]) || Float.isNaN(y[0]) || (logXAxis && x[0]<=0) || (logYAxis && y[0]<=0);
		for (int i=1; i<n; i++) {
			x1 = x2;
			y1 = y2;
			isNaN0 = isNaN1;
			isNaN1 = isNaN2;
			x2 = scaleX(x[i]);
			y2 = scaleY(y[i]);
			isNaN2 = Float.isNaN(x[i]) || Float.isNaN(y[i]) || (logXAxis && x[i]<=0) || (logYAxis && y[i]<=0);
			if (!isNaN1 && !isNaN2)
				ip.drawLine(x1, y1, x2, y2);
			else if (isNaN0 && !isNaN1 && isNaN2) // an isolated point
				ip.drawLine(x1, y1, x1, y1);
		}
		if (isNaN1 && !isNaN2)
			ip.drawLine(x2, y2, x2, y2);          // the last (isolated) point
	}

	/**
	 * Fills space between polyline and y=0 with the current color (the secondary color of the plotObject)
	 */
	void drawFloatPolyLineFilled(ImageProcessor ip, float[] xF, float[] yF, int len) {
		if (xF == null || len <=1)
			return;
		ip.setLineWidth(1);
		int y0 = scaleYWithOverflow(0);
		int x1, y1;
		int x2 = scaleX(xF[0]);
		int y2 = scaleY(yF[0]);
		boolean isNaN1;
		boolean isNaN2 = Float.isNaN(xF[0]) || Float.isNaN(yF[0]) || (logXAxis && xF[0]<=0) || (logYAxis && yF[0]<=0);
		for (int i = 1; i < len; i++) {
			isNaN1 = isNaN2;
			isNaN2 = Float.isNaN(xF[i]) || Float.isNaN(yF[i]) || (logXAxis && xF[i]<=0) || (logYAxis && yF[i]<=0);
			x1 = x2;
			y1 = y2;
			x2 = scaleX(xF[i]);
			y2 = scaleY(yF[i]);
			int left = x1;
			int right = x2;
			if (isNaN1 || isNaN2) continue;
			if (left < frame.x && right < frame.x) continue; // ignore if all outside the plot area
			if (left >= frame.x+frame.width && right >= frame.x+frame.width) continue;
			if (left < frame.x) left = frame.x;
			if (left >= frame.x+frame.width) left = frame.x+frame.width-1;
			if (right < frame.x) right = frame.x;
			if (right >= frame.x+frame.width) right = frame.x+frame.width-1;
			if (left != right) {
				for (int xi = Math.min(left,right); xi <= Math.max(left,right); xi++) {
					int yi = (int)Math.round(y1 + (double)(y2 - y1)*(double)(xi - x1)/(double)(x2 - x1));
					/* double yMin = Math.min(yF[i-1], yF[i]);
					double yMax = Math.max(yF[i-1], yF[i]);
					if (y < yMin) y = yMin; // dont extrapolate (in case rounding to pixels falls outside [xi, xi+1] interval)
					if (y > yMax) y = yMax;*/
					ip.drawLine(xi, y0, xi, yi);
				}
			} else {
				ip.drawLine(left, y0, left, y2);
			}
		}
	}
	
	/** Returns only indexed and sorted plot objects, if at least one label is indexed like "1__MyLabel" */
	Vector<PlotObject> getIndexedPlotObjects(){
		boolean withIndex = false;
		int len = allPlotObjects.size();
		String[] labels = new String[len];
		Vector<PlotObject> indexedObjects = new Vector<PlotObject>();
		for(int jj = 0; jj < len; jj++){
			PlotObject plotObject = allPlotObjects.get(jj);
			labels[jj] = "";
			if (plotObject.type == PlotObject.XY_DATA && !plotObject.hasFlag(PlotObject.HIDDEN) && plotObject.label != null) {
				String label = plotObject.label;
				if(label.indexOf("__") >=0  && label.indexOf("__") <= 2){
					labels[jj]= plotObject.label;
					withIndex = true;
				}
			}
		}
		int[] ranks = Tools.rank(labels);
		for(int jj = 0; jj < len; jj++){
			if(labels[ranks[jj]] != ""){
				int index = ranks[jj];
				indexedObjects.add(allPlotObjects.get(index));
			}
		}
		if(!withIndex)
			return null;	
		return indexedObjects;
	}	

	/** Draw the legend */
	void drawLegend(PlotObject legendObject, ImageProcessor ip) {
		ip.setFont(scFont(legendObject.getFont()));
		int nLabels = 0;
		int maxStringWidth = 0;
		float maxLineThickness = 0;
		Vector<PlotObject> usedPlotObjects = allPlotObjects;
		Vector<PlotObject> indexedObjects = getIndexedPlotObjects();
		if(indexedObjects != null)
			usedPlotObjects= indexedObjects;
		
		for (PlotObject plotObject : usedPlotObjects)
			if (plotObject.type == PlotObject.XY_DATA && !plotObject.hasFlag(PlotObject.HIDDEN) && plotObject.label != null) {		//label exists: was set now or previously
				nLabels++;
				String label = plotObject.label;
				if (indexedObjects != null)
					label = label.substring(label.indexOf("__") + 2);
				int w = ip.getStringWidth(label);
				if (w > maxStringWidth) maxStringWidth = w;
				if (plotObject.lineWidth > maxLineThickness) maxLineThickness = plotObject.lineWidth;
			}
		if (nLabels == 0) return;
		if (pp.antialiasedText && scale > 1)		//fix incorrect width of large fonts
			maxStringWidth = (int)((1 + 0.004*scale) * maxStringWidth);
		int frameThickness = sc(legendObject.lineWidth > 0 ? legendObject.lineWidth : 1);
		FontMetrics fm = ip.getFontMetrics();
		ip.setJustification(LEFT);
		int lineHeight = fm.getHeight();
		int height = nLabels*lineHeight + 2*sc(LEGEND_PADDING);
		int width = maxStringWidth + sc(3*LEGEND_PADDING + LEGEND_LINELENGTH + maxLineThickness);
		int positionCode = legendObject.flags & LEGEND_POSITION_MASK;
		if (positionCode == AUTO_POSITION)
			positionCode = autoLegendPosition(width, height, frameThickness);
		Rectangle rect = legendRect(positionCode, width, height, frameThickness);
		int x0 = rect.x;
		int y0 = rect.y;

		ip.setColor(Color.white);
		ip.setLineWidth(1);
		if (!legendObject.hasFlag(LEGEND_TRANSPARENT)) {
			ip.setRoi(x0, y0, width, height);
			ip.fill();
		} else if (hasFlag(X_GRID | Y_GRID)) {	//erase grid
			int grid = ip instanceof ColorProcessor ? (gridColor.getRGB() & 0xffffff) : ip.getBestIndex(gridColor);
			for (int y=y0; y<y0+height; y++)
				for (int x=x0; x<x0+width; x++)
					if ((ip.getPixel(x, y) & 0xffffff) == grid)
						ip.drawPixel(x, y);
		}
		ip.setLineWidth(frameThickness);
		ip.setColor(legendObject.color);
		ip.drawRect(x0-frameThickness/2, y0-frameThickness/2, width+frameThickness, height);
		boolean bottomUp = legendObject.hasFlag(LEGEND_BOTTOM_UP);
		int y = y0 + frameThickness/2 + sc(LEGEND_PADDING) + lineHeight/2;
		if (bottomUp) y += (nLabels-1) * lineHeight;
		int xText = x0 + frameThickness/2 + sc(2f*LEGEND_PADDING + LEGEND_LINELENGTH + maxLineThickness);
		int xMarker = x0 + frameThickness/2 + sc(LEGEND_PADDING + 0.5f*(LEGEND_LINELENGTH + maxLineThickness));
		int xLine0 = x0 + frameThickness/2 + sc(LEGEND_PADDING) + 1;
		for (PlotObject plotObject : usedPlotObjects)
			if (plotObject.type == PlotObject.XY_DATA && !plotObject.hasFlag(PlotObject.HIDDEN) && plotObject.label != null) {		//label exists: was set now or previously
				int shape = plotObject.shape;
				if (shape == SEPARATED_BAR) shape = BOX; //for bar plots, draw a square in the legend
				int yShiftLine = 0;
				if (shape == FILLED || shape == BAR && plotObject.color2 != null)  //shift line up to make space for fill pattern
					yShiftLine = sc(0.1f*legendObject.getFontSize() + 0.3f*plotObject.lineWidth);
				int markerSize = plotObject.getMarkerSize();
				if (plotObject.shape == SEPARATED_BAR && markerSize < 0.6*legendObject.getFontSize())
					markerSize = 2*(int)(0.3*legendObject.getFontSize()) + 1; // for 'separated bar', a larger box (an odd number, to have it centered)
				if (plotObject.hasFilledMarker() || (plotObject.shape == SEPARATED_BAR && plotObject.color2 != null)) {
					ip.setColor(plotObject.color2);
					fillShape(shape, xMarker, y, markerSize);
				} else if (yShiftLine != 0) {  //fill area below line (shape=FILLED or BAR)
					ip.setColor(plotObject.color2 == null ? plotObject.color : plotObject.color2);
					ip.fillRect(xLine0, y-yShiftLine, 2*(xMarker - xLine0)+1, yShiftLine+(int)(0.3*legendObject.getFontSize()));
				}
				int lineWidth = sc(plotObject.lineWidth);
				if (lineWidth < 1) lineWidth = 1;
				ip.setLineWidth(lineWidth);
				if (plotObject.hasCurve() || plotObject.shape==BAR) {
					Color c = plotObject.shape == CONNECTED_CIRCLES ?
							(plotObject.color2 == null ? Color.black : plotObject.color2) :
							plotObject.color;
					ip.setColor(c);
					ip.fillRect(xLine0, y-lineWidth/2-yShiftLine, 2*(xMarker - xLine0)+1, lineWidth); //draw line as a rectangle
				}
				if (plotObject.hasMarker() || plotObject.shape == SEPARATED_BAR) {
					Font saveFont = ip.getFont();
					ip.setColor(plotObject.color);
					drawShape(plotObject, xMarker, y, shape, markerSize, -1);
					if (plotObject.shape==CUSTOM) ip.setFont(saveFont);
				}
				ip.setColor(plotObject.color);
				ip.setLineWidth(frameThickness);
				String label = plotObject.label;
				if (indexedObjects != null){
					int start = label.indexOf("__");
					if(start >=0)
						label = label.substring(start+2);
				}
				ip.drawString(label, xText, y+ lineHeight/2);
				y += bottomUp ? -lineHeight : lineHeight;
			}
	}

	/** The legend area; positionCode should be TOP_LEFT, TOP_RIGHT, etc. */
	Rectangle legendRect(int positionCode, int width, int height, int frameThickness)  {
		boolean leftPosition = positionCode == TOP_LEFT || positionCode == BOTTOM_LEFT;
		boolean topPosition	 = positionCode == TOP_LEFT || positionCode == TOP_RIGHT;
		int x0 = (leftPosition) ?
				leftMargin + sc(2*LEGEND_PADDING) + frameThickness/2 :
				leftMargin + frameWidth - width - sc(2*LEGEND_PADDING) - frameThickness/2;
		int y0 = (topPosition) ?
				topMargin + sc(LEGEND_PADDING) + frameThickness/2 :
				topMargin + frameHeight - height - sc(LEGEND_PADDING) + frameThickness/2;
		if (hasFlag(Y_TICKS))
			x0 += (leftPosition ? 1 : -1) * sc(tickLength - LEGEND_PADDING);
		if (hasFlag(X_TICKS))
			y0 += (topPosition ? 1 : -1) * sc(tickLength - LEGEND_PADDING/2);
		return new Rectangle(x0, y0, width, height);
	}

	/** The position code of the legend position where the smallest amount of foreground pixels is covered */
	int autoLegendPosition(int width, int height, int frameThickness) {
		int background = ip instanceof ColorProcessor ? (0xffffff) : (ip.isInvertedLut() ? 0 : 0xff);
		int grid = ip instanceof ColorProcessor ? (gridColor.getRGB() & 0xffffff) : ip.getBestIndex(gridColor);
		int bestPosition = 0;
		int minCoveredPixels = Integer.MAX_VALUE;
		for (int positionCode : new int[]{TOP_LEFT, TOP_RIGHT, BOTTOM_RIGHT, BOTTOM_LEFT}) {
			Rectangle rect = legendRect(positionCode, width, height, frameThickness);
			int coveredPixels = 0;
			for (int y = rect.y - frameThickness/2; y <= rect.y + rect.height + frameThickness/2; y++)
				for (int x = rect.x - frameThickness/2; x <= rect.x + rect.width + frameThickness/2; x++) {
					int pixel = ip.getPixel(x, y) & 0xffffff;
					if (pixel != background && pixel != grid)
						coveredPixels ++;
				}
			if (coveredPixels < minCoveredPixels) {
				minCoveredPixels = coveredPixels;
				bestPosition = positionCode;
			}
		}
		return bestPosition;
	}

	/** Returns the x, y coordinates at the cursor position or the nearest point as a String */
	String getCoordinates(int x, int y) {
		if (frame==null) return "";
		String text = "";
		if (!frame.contains(x, y))
			return text;
		double xv = descaleX(x); // cursor location
		double yv = descaleY(y);
		boolean yIsValue = false;
		if (!hasMultiplePlots()) {
			PlotObject p = getMainCurveObject(); // display x and f(x) instead of cursor y
			if (p != null) {
				double bestDx = Double.MAX_VALUE;
				double xBest = 0, yBest = 0;
				for (int i=0; i<Math.min(p.xValues.length, p.yValues.length); i++) {
					double xp = p.xValues[i];
					if (Math.abs(xp-xv) < bestDx) {
						bestDx = Math.abs(xp-xv);
						xBest = xp;
						yBest = p.yValues[i];
					}
				}
				if (Math.abs(scaleXtoPxl(xBest)-x) < 50) {	//ignore points more than 50 pixels away in x
					xv = xBest;
					yv = yBest;
					yIsValue = true;
				}
			}
		}
		if (!Double.isNaN(xv)) {
			int significantDigits = logXAxis ? -2 : getDigits(xv, 0.001*(xMax-xMin), 6, 0);
			text =	"X=" + IJ.d2s(xv, significantDigits)+", Y";
			if (yIsValue) text += "(X)";
			significantDigits = logYAxis ? -2 : getDigits(yv, 0.001*(yMax-yMin), 6, 0);
			text +="="+ IJ.d2s(yv, significantDigits);
		}
		return text;
		//}catch(Exception e){IJ.handleException(e);return "ERR";}
	}


	/** Returns a reference to the PlotObject having the data passed with the constructor or (if that was null)
	 *	the first x & y data added later. Otherwise returns null. */
	private PlotObject getMainCurveObject() {
		for (PlotObject plotObject : allPlotObjects) {
			if (plotObject.type == PlotObject.XY_DATA)
				return plotObject;
		}
		return null;
	}

	/** Returns a reference to the PlotObject with x & y data (points, curve) added last, or null if none. */
	private PlotObject getLastCurveObject() {
		for (int i=allPlotObjects.size()-1; i>=0; i--) {
			if (allPlotObjects.get(i).type == PlotObject.XY_DATA)
				return allPlotObjects.get(i);
		}
		return null;
	}

	/** returns whether there are several plots so that one cannot give a single y value for a given x value */
	private boolean hasMultiplePlots() {
		int nPlots = 0;
		for (PlotObject plotObject : allPlotObjects) {
			if (plotObject.type == PlotObject.ARROWS)
				return true;
			else if (plotObject.type == PlotObject.XY_DATA) {
				nPlots ++;
				if (nPlots > 1) return true;
			}
		}
		return nPlots > 1;
	}

	public void setPlotMaker(PlotMaker plotMaker) {
		this.plotMaker = plotMaker;
	}

	PlotMaker getPlotMaker() {
		return plotMaker;
	}

	/** Returns the labels of the (non-hidden) datasets as linefeed-delimited String.
	 *	If the label is not set, a blank line is added. */
	String getDataLabels() {
		String labels = "";
		boolean first = true;
		for (PlotObject plotObject : allPlotObjects)
			if (plotObject.type == PlotObject.XY_DATA && !plotObject.hasFlag(PlotObject.HIDDEN)) {
				if (first)
					first = false;
				else
					labels += '\n';
				if (plotObject.label != null) labels += plotObject.label;
			}
		return labels;
	}

	/** Creates a ResultsTable with the plot data. Returns an empty table if no data. */
	public ResultsTable getResultsTable() {
		return getResultsTable(true);
	}

	/** Creates a ResultsTable with the data of the plot. Returns null if no data.
	 * Does not write the first x column if writeFirstXColumn is false.
	 * When all columns are the same length, x columns equal to the first x column are
	 * not written, independent of writeFirstXColumn.
	 * Column headings are "X", "Y", "X1", "Y1", etc, irrespective of any labels of the data sets
	 */
	public ResultsTable getResultsTable(boolean writeFirstXColumn) {
		return getResultsTable(writeFirstXColumn, false);
	}

	/** Creates a ResultsTable with the data of the plot. Returns null if no data.
	 * When all columns are the same length, x columns equal to the first x column are
	 * not written, independent of writeFirstXColumn.
	 * When the data sets have labels, they are used for column headings
	 */
	public ResultsTable getResultsTableWithLabels() {
		return getResultsTable(true, true);
	}

	/** Creates a ResultsTable with the data of the plot. Returns null if no data.
	 * Does not write the first x column if writeFirstXColumn is false.
	 * When all columns are the same length, x columns equal to the first x column are
	 * not written, independent of writeFirstXColumn.
	 * When the data sets have labels and useLabels is true, they are used for column headings,
	 * otherwise columns are named X, Y, X1, Y1, ... */
	ResultsTable getResultsTable(boolean writeFirstXColumn, boolean useLabels) {
		ResultsTable rt = new ResultsTable();
		// find the longest x-value data set and count the data sets
		int nDataSets =	 0;
		int tableLength = 0;
		for (PlotObject plotObject : allPlotObjects)
			if (plotObject.xValues != null) {
				nDataSets++;
				tableLength = Math.max(tableLength, plotObject.xValues.length);
			}
		if (nDataSets == 0)
			return null;
		// enter columns one by one to lists of data and headings
		ArrayList<String> headings = new ArrayList<String>(2*nDataSets);
		ArrayList<float[]> data = new ArrayList<float[]>(2*nDataSets);
		int dataSetNumber = 0;
		int arrowsNumber = 0;
		PlotObject firstXYobject = null;
		boolean allSameLength = true;
		for (PlotObject plotObject : allPlotObjects) {
			if (plotObject.type==PlotObject.XY_DATA) {
				if (firstXYobject != null && firstXYobject.xValues.length!=plotObject.xValues.length) {
					allSameLength = false;
					break;
				}
				if (firstXYobject==null)
					firstXYobject = plotObject;
			}
		}
		firstXYobject = null;
		for (PlotObject plotObject : allPlotObjects) {
			if (plotObject.type==PlotObject.XY_DATA) {
				boolean sameX = firstXYobject!=null && Arrays.equals(firstXYobject.xValues, plotObject.xValues) && allSameLength;
				boolean sameXY = sameX && Arrays.equals(firstXYobject.yValues, plotObject.yValues); //ignore duplicates (e.g. Markers plus Curve)
				boolean writeX = firstXYobject==null ? writeFirstXColumn : !sameX;
				addToLists(headings, data, plotObject, dataSetNumber, writeX, /*writeY=*/!sameXY, /*multipleSets=*/nDataSets>1, useLabels);
				if (firstXYobject == null)
					firstXYobject = plotObject;
				dataSetNumber++;
			} else if (plotObject.type==PlotObject.ARROWS) {
				addToLists(headings, data, plotObject, arrowsNumber, /*writeX=*/true, /*writeY=*/true, /*multipleSets=*/nDataSets>1, /*useLabels=*/false);
				arrowsNumber++;
			}
		}
		// populate the ResultsTable
		int nColumns = headings.size();
		for (int line=0; line<tableLength; line++) {
			for (int col=0; col<nColumns; col++) {
				String heading = headings.get(col);
				float[] values = data.get(col);
				if (line<values.length)
					rt.setValue(heading, line, values[line]);
				else
					rt.setValue(heading, line, "");
			}
		}
		// set the decimals (precision) of the table columns
		nColumns = rt.getLastColumn() + 1;
		for (int i=0; i<nColumns; i++)
			rt.setDecimalPlaces(i, getPrecision(rt.getColumn(i)));
		return rt;
	}

	// when writing data in scientific mode, use at least 4 decimals behind the decimal point
	static final int MIN_SCIENTIFIC_DIGITS = 4;
	// when writing float data, precision should be at least 1e-5*data range
	static final double MIN_FLOAT_PRECISION = 1e-5;

	void addToLists(ArrayList<String> headings, ArrayList<float[]>data, PlotObject plotObject,
			int dataSetNumber, boolean writeX, boolean writeY, boolean multipleSets, boolean useLabels) {
		String plotObjectLabel = useLabels ? replaceSpacesEtc(plotObject.label) : null;
		if (writeX) {
			String label = null;                                                     // column header for x column
			if (plotObject.type!=PlotObject.ARROWS) {
				String plotXLabel = getLabel('x');
				if (dataSetNumber==0 && plotXLabel!=null) {                          // use x axis label for 1st dataset if permitted
					if (useLabels)
						label = replaceSpacesEtc(plotXLabel);
					else if (plotXLabel.startsWith(" ") && plotXLabel.endsWith(" ")) // legacy: always use axis label for 1st data if spaces at start&end
						label = plotXLabel.substring(1,plotXLabel.length()-1);
				} else if (plotObjectLabel != null && dataSetNumber>0)
					label = "X_"+plotObjectLabel;                                    // use "X_" + dataset label
				if (label != null && headings.contains(label))
					label = null; // avoid duplicate labels (not possible in ResultsTable)
			}
			if (label == null) {                                                     // create default label if no specific label yet
				label = plotObject.type == PlotObject.ARROWS ? "XStart" : "X";
				if (multipleSets) label += dataSetNumber;
			}
			headings.add(label);
			data.add(plotObject.xValues);
		}
		if (writeY) {
			String label = null;;                                                     // column header for y column
			if (plotObject.type!=PlotObject.ARROWS) {
				String plotYLabel = getLabel('y');
				if (dataSetNumber==0 && plotYLabel!=null) {
					if (useLabels && plotObjectLabel == null)                         // use y axis label for 1st dataset if no data set label
						label = replaceSpacesEtc(plotYLabel);
					else if (plotYLabel.startsWith(" ") && plotYLabel.endsWith(" "))  // legacy: always use axis label for 1st data if spaces at start&end
						label = plotYLabel.substring(1,plotYLabel.length()-1);
				}
				if (plotObjectLabel != null)
					label = plotObjectLabel;
				if (label != null && headings.contains(label))
					label = null; // avoid duplicate labels (not possible in ResultsTable)
			}
			if (label == null) {                                                     // create default label if no specific label yet
				label = plotObject.type == PlotObject.ARROWS ? "YStart" : "Y";
				if (multipleSets) label += dataSetNumber;
			}
			headings.add(label);
			data.add(plotObject.yValues);
		}
		if (plotObject.xEValues != null) {
			String label = plotObject.type == PlotObject.ARROWS ? "XEnd" : "XERR";
			if (multipleSets) label += dataSetNumber;
			headings.add(label);
			data.add(plotObject.xEValues);
		}
		if (plotObject.yEValues != null) {
			String label = plotObject.type == PlotObject.ARROWS ? "YEnd" : "ERR";
			if (multipleSets) label += dataSetNumber;
			headings.add(label);
			data.add(plotObject.yEValues);
		}
	}

	/** Convert a string to a label suitable for a ResultsTable without whitespace, quotes or commas,
	 *  to avoid problems when saving and reading the table. Returns null if an empty string or null. */
	static String replaceSpacesEtc(String s) {
		if (s == null) return null;
		s = s.trim().replaceAll("[\\s,]", "_").replace("\"","''");
		if (s.length() == 0) return null;
		return s;
	}

	/** get the number of digits for writing a column to the results table or the clipboard */
	static int getPrecision(float[] values) {
		int setDigits = Analyzer.getPrecision();
		int measurements = Analyzer.getMeasurements();
		boolean scientificNotation = (measurements&Measurements.SCIENTIFIC_NOTATION)!=0;
		if (scientificNotation) {
			if (setDigits<MIN_SCIENTIFIC_DIGITS)
				setDigits = MIN_SCIENTIFIC_DIGITS;
			return -setDigits;
		}
		boolean allInteger = true;
		float min = Float.MAX_VALUE, max = -Float.MAX_VALUE;
		for (int i=0; i<values.length; i++) {
			if ((int)values[i]!=values[i] && !Float.isNaN(values[i])) {
				allInteger = false;
			if (values[i] < min) min = values[i];
			if (values[i] > max) max = values[i];
			}
		}
		if (allInteger)
			return 0;
		int digits = (max - min) > 0 ? getDigits(min, max, MIN_FLOAT_PRECISION*(max-min), 15, 0) :
				getDigits(max, MIN_FLOAT_PRECISION*Math.abs(max), 15, 0);
		if (setDigits>Math.abs(digits))
			digits = setDigits * (digits < 0 ? -1 : 1);		//use scientific notation if needed
		return digits;
	}

	/** Whether a given flag 'what' is set */
	boolean hasFlag(int what) {
		return (pp.axisFlags&what) != 0;
	}

	/* Obsolete, replaced by add(shape,x,y). */
	public void addPoints(String dummy, float[] x, float[] y, int shape) {
		addPoints(x, y, shape);
	}

	/** Plots a histogram from an array using auto-binning.
	 *  @param values	array containing the population
	 *  N.Vischer
	 */
	public void addHistogram(double[] values) {
		addHistogram(values, 0, 0);
	}

	/** Plots a histogram from an array using the specified bin width.
	 *  @param values	array containing the population
	 *  @param binWidth	set zero for auto-binning
	 *  N.Vischer
	 */
	public void addHistogram(double[] values, double binWidth) {
		addHistogram(values, binWidth, 0);
	}

	/** Plots a histogram of the value distribution (bin counts) from an array
	 *  @param values	array containing the values for the population
	 *  @param binWidth	set zero for auto-binning
	 *  @param binCenter any x value can be the center of a bin
	 *  N.Vischer
	 */
	public void addHistogram(double[] values, double binWidth, double binCenter) {
		int len = values.length;
		double min = Double.POSITIVE_INFINITY;
		double max = Double.NEGATIVE_INFINITY;
		double[] cleanVals = new double[len];
		int count = 0;
		double sum = 0, sum2 = 0;
		for (int i = 0; i < len; i++) {
			double val = values[i];
			if (!Double.isNaN(val)) {
				cleanVals[count++] = val;
				sum += val;
				sum2 += val * val;
				if (val < min)
					min = val;
				if (val > max)
					max = val;
			}
		}
		if (binWidth <= 0) {//autobinning
			double stdDev = Math.sqrt(((count * sum2 - sum * sum) / count) / count);//not count - 1
			// use Scott's method (1979 Biometrika, 66:605-610) for optimal binning: 3.49*sd*N^-1/3
			binWidth = 3.49 * stdDev * (Math.pow(count, -1.0 / 3));

		}
		double modCenter = binCenter % binWidth;
		double modMin = min % binWidth;
		double diff = modMin - modCenter;
		double firstBin = min-diff;
		while(firstBin  - binWidth * 0.499 > min)
			firstBin -= binWidth;
		int nBins =  (int) ((max - firstBin)/binWidth);
		double lastBin = firstBin + nBins * binWidth;
		while(lastBin  + binWidth * 0.499 < max)
			lastBin += binWidth;
		nBins = (int) Math.round((lastBin - firstBin)/binWidth) + 1;
		if (nBins == 1)
			nBins = 2;
		if (nBins > 9999) {
			IJ.error("max bins > 9999");
			return;
		}
		double[] histo = new double[nBins];
		double[] xValues = new double[nBins];
		for (int i = 0; i < nBins; i++)
			xValues[i] = firstBin + i * binWidth;
		for (int i = 0; i < count; i++) {
			double val = cleanVals[i];
			double indexD = (val - firstBin) / binWidth;
			int index = (int) Math.round(indexD);
			if (index < 0 || index >= nBins) {
				IJ.error("index out of range");
				return;
			} else
				histo[index]++;
		}
		add("bar", xValues, histo);
	}

	/* Obsolete, replaced by add("error bars",errorBars). */
	public void addErrorBars(String dummy, float[] errorBars) {
		addErrorBars(errorBars);
	}

	/* Obsolete; replaced by setFont(). */
	public void changeFont(Font font) {
		setFont(font);
	}
	
}

/** This class contains the properties of the plot, such as size, format, range, etc, except for the data+format (plot contents).
 *  To enable reading serialized PlotObjects of plots created with previous versions of ImageJ,
 *  the variable names MUST NEVER be changed! Also any additions should be made after careful thought,
 *  since they have to be kept for all future versions. */
class PlotProperties implements Cloneable, Serializable {
	/** The serialVersionUID should not be modified, otherwise saved plots won't be readable any more */
	static final long serialVersionUID = 1L;
	//
	PlotObject frame = new PlotObject(Plot.DEFAULT_FRAME_LINE_WIDTH);	 //the frame, including background color and axis numbering
	PlotObject xLabel = new PlotObject(PlotObject.AXIS_LABEL);		//the x axis label (string & font)
	PlotObject yLabel = new PlotObject(PlotObject.AXIS_LABEL);		//the x axis label (string & font)
	PlotObject legend;												//the legend (if any)
	int width = 0;													//canvas width (note: when stored, this must fit the image)
	int height = 0;
	int axisFlags;													//these define axis layout
	double[] rangeMinMax;											//currentMinMax when writing, sets defaultMinMax when reading
	boolean antialiasedText = true;
	boolean isFrozen;							                    //modifications (size, range, contents) don't update the ImageProcessor

	/** Returns an array of all PlotObjects defined as PlotProperties. Note that some may be null */
	PlotObject[] getAllPlotObjects() {
		return new PlotObject[]{frame, xLabel, xLabel, legend};
	}

	/** Returns the PlotObject for xLabel ('x'), yLabel('y'), frame ('f'; includes number font) or the legend ('l'). */
	PlotObject getPlotObject(char c) {
		switch(c) {
			case 'x':  return xLabel;
			case 'y':  return yLabel;
			case 'f':  return frame;
			case 'l':  return legend;
			default:   return null;
		}
	}

	/** A shallow clone that does not duplicate arrays or objects */
	public PlotProperties clone() {
		try {
			return (PlotProperties)(super.clone());
		} catch (CloneNotSupportedException e) {
			return null;
		}
	}

	/** A deep clone; it also duplicates arrays and pPlotObjects */
	public PlotProperties deepClone() {
		PlotProperties pp2 = clone(); //shallow clone
		if (frame != null)  pp2.frame  = frame.deepClone();
		if (xLabel != null) pp2.xLabel = xLabel.deepClone();
		if (yLabel != null) pp2.yLabel = yLabel.deepClone();
		if (legend != null) pp2.legend = legend.deepClone();
		if (rangeMinMax != null) pp2.rangeMinMax = rangeMinMax.clone();
		return pp2;
	}

} // class PlotProperties

/** This class contains the data and properties for displaying a curve, a set of arrows, a line or a label in a plot,
 *	as well as the legend, axis labels, and frame (including background and fonts of axis numbering).
 *	Note that all properties such as lineWidths and Fonts have to be scaled up for high-resolution plots.
 *	This class allows serialization for writing into tiff files.
 *  To enable reading serialized PlotObjects of plots created with previous versions of ImageJ,
 *  the variable names MUST NEVER be changed! Also any additions should be made after careful thought,
 *  since they have to be kept for all future versions. */
class PlotObject implements Cloneable, Serializable {
	/** The serialVersionUID should not be modified, otherwise saved plots won't be readable any more */
	static final long serialVersionUID = 1L;
	/** Constants for the type of objects. These are powers of two so one can use them as masks */
	public final static int XY_DATA = 1, ARROWS = 2, LINE = 4, NORMALIZED_LINE = 8, DOTTED_LINE = 16,
			LABEL = 32, NORMALIZED_LABEL = 64, LEGEND = 128, AXIS_LABEL = 256, FRAME = 512, SHAPES = 1024;
	/** mask for recovering font style from the flags */
	final static int FONT_STYLE_MASK = 0x0f;
	/** flag for the data set passed with the constructor. Note that 0 to 0x0f are reserved for fonts modifiers, 0x010-0x800 are reserved for legend modifiers */
	public final static int CONSTRUCTOR_DATA = 0x1000;
	/** flag for hiding a PlotObject */
	public final static int HIDDEN = 0x2000;
	/** Type of the object; XY_DATA stands for curve or markers, can be also ARROWS ... SHAPES */
	public int type = XY_DATA;
	/** bitwise combination of flags, or the position of a legend */
	public int flags;
	/**  Options, currently only for FRAME, see Plot.setOptions */
	public String options;
	/** The x and y data arrays and the error bars (if non-null). These arrays also serve as x0, y0, x1, y1
	 *	arrays for plotting arrays of arrows */
	public float[] xValues, yValues, xEValues, yEValues;
	/** For SHAPES: For boxplots with whiskers ('boxes'), elements of the ArrayList are float[6] with x and all 5 y values
	 *  (for 'boxesx', y and all 5 x values), for 'rectangles', float[4] with x1, y1, x2, y2. */
	public ArrayList shapeData;
	/** For SHAPES only, shape type & options. Currently implemented: 'boxes', 'boxesx' (box plots with whiskers), 'rectangles', 'redraw_grid' */
	public String shapeType; //e.g. "boxes width=20"
	/** Type of the points, such as Plot.LINE, Plot.CROSS etc. (for type = XY_DATA) */
	public int shape;
	/** The line width in pixels for 'normal' plots (for high-resolution plots, to be multiplied by a scale factor) */
	public float lineWidth;
	/** The color of the object, must not be null */
	public Color color;
	/** The secondary color (for filling closed symbols and for the line of CIRCLES_AND_LINE, may be null for unfilled/default */
	public Color color2;
	/** Labels and lines: Position (NORMALIZED objects: relative units 0...1). */
	public double x, y;
	/** Lines only: End position */
	public double xEnd, yEnd;
	/** Dotted lines only: step */
	public int step;
	/** A label for the y data of the curve, a text to draw, or the text of a legend (tab-delimited lines) */
	public String label;
	/** Labels only: Justification can be Plot.LEFT, Plot.CENTER or Plot.RIGHT */
	public int justification;
	/** Macro code for drawing symbols */
	public String macroCode;
	/** Text objects (labels, legend, axis labels) only: the font; maybe null for default. This is not serialized (transient) */
	private transient Font font;
	/** String for representation of the font family (for Serialization); may be null for default. Font style is in flags, font size in fontSize. */
	private String fontFamily;
	/** Font size (for Serialization), for 'normal' plots (for high-resolution plots, to be multiplied by a scale factor) */
	private float fontSize;


	/** Generic constructor */
	PlotObject(int type) {
		this.type = type;
	}

	/** Constructor for XY_DATA, i.e., a curve or set of points */
	PlotObject(float[] xValues, float[] yValues, float[] yErrorBars, int shape, float lineWidth, Color color, Color color2, String yLabel) {
		this.type = XY_DATA;
		this.xValues = xValues;
		this.yValues = yValues;
		this.yEValues = yErrorBars;
		this.shape = shape;
		this.lineWidth = lineWidth;
		this.color = color;
		this.color2 = color2;
		this.label = yLabel;
		if (shape==Plot.CUSTOM)
			this.macroCode = yLabel;
	}

	/** Constructor for a set of arrows */
	PlotObject(float[] x1, float[] y1, float[] x2, float[] y2, float lineWidth, Color color) {
		this.type = ARROWS;
		this.xValues = x1;
		this.yValues = y1;
		this.xEValues = x2;
		this.yEValues = y2;
		this.lineWidth = lineWidth;
		this.color = color;
	}

	/** Constructor for a set of shapes */
	PlotObject(String shapeType, ArrayList shapeData, float lineWidth,  Color color, Color color2) {
		this.type = SHAPES;
		this.shapeData = shapeData;
		this.shapeType = shapeType;
		this.lineWidth = lineWidth;
		this.color = color;
		this.color2 = color2;
	}

	/** Constructor for a line */
	PlotObject(double x, double y, double xEnd, double yEnd, float lineWidth, int step, Color color, int type) {
		this.type = type;
		this.x = x;
		this.y = y;
		this.xEnd = xEnd;
		this.yEnd = yEnd;
		this.lineWidth = lineWidth;
		this.step = step;
		this.color = color;
	}

	/** Constructor for a label or NORMALIZED_LABEL */
	PlotObject(String label, double x, double y, int justification, Font font, Color color, int type) {
		this.type = type;
		this.label = label;
		this.x = x;
		this.y = y;
		this.justification = justification;
		setFont(font);
		this.color = color;
	}

	/** Constructor for the legend. <code>flags</code> is bitwise or of TOP_LEFT etc. and LEGEND_TRANSPARENT if desired.
	 *  Note that the labels in the legend are those of the data plotObjects */
	PlotObject(float lineWidth, Font font, Color color, int flags) {
		this.type = LEGEND;
		this.lineWidth = lineWidth;
		setFont(font);
		this.color = color;
		this.flags = flags;
	}

	/** Constructor for the frame, including axis numbers. In the current version, the primary color (line color) is always black */
	PlotObject(float lineWidth) {
		this.type = FRAME;
		this.color = Color.black;
		this.lineWidth = lineWidth;
	}

	/** Whether a given flag 'what' is set */
	boolean hasFlag(int what) {
		return (flags&what) != 0;
	}

	/** Sets a given flag  */
	void setFlag(int what) {
		flags |= what;
	}

	/** Unsets a given flag  */
	void unsetFlag(int what) {
		flags = flags & (~what);
	}

	/** Whether an XY_DATA object has a curve to draw */
	boolean hasCurve() {
		return type == XY_DATA && (shape == Plot.LINE || shape == Plot.CONNECTED_CIRCLES || shape == Plot.FILLED);
	}

	/** Whether an XY_DATA object has markers to draw */
	boolean hasMarker() {
		return type == XY_DATA && (shape == Plot.CIRCLE || shape == Plot.X || shape == Plot.BOX || shape == Plot.TRIANGLE
				|| shape == Plot.CROSS || shape == Plot.DIAMOND || shape == Plot.DOT || shape == Plot.CONNECTED_CIRCLES
				|| shape == Plot.CUSTOM);
	}

	/** Whether an XY_DATA object has markers that can be filled */
	boolean hasFilledMarker() {
		return type == XY_DATA && color2 != null && (shape == Plot.CIRCLE || shape == Plot.BOX || shape == Plot.TRIANGLE ||
				shape == Plot.DIAMOND || shape == Plot.CONNECTED_CIRCLES);
	}

	/** Size of the markers for an XY_DATA object with markers */
	int getMarkerSize() {
		if (lineWidth<=1)
			return 5;
		else if (lineWidth<=3)
			return 7;
		else
			return (int)(lineWidth+4);
	}

	/** Sets the font. Also writes font properties for serialization. */
	void setFont(Font font) {
		if (font == this.font) return;
		this.font = font;
		if (font == null) {
			fontFamily = null;
		} else {
			fontFamily = font.getFamily();
			flags = (flags & ~FONT_STYLE_MASK) | font.getStyle();
			fontSize = font.getSize2D();
		}
	}

	/** Returns the font, or null if none specified */
	Font getFont() {
		if (font == null && fontFamily != null)     //after recovery from serialization, create the font from its description
			font = FontUtil.getFont(fontFamily, flags&FONT_STYLE_MASK, fontSize);
		return font;
	}

	/** Returns the font size */
	float getFontSize() {
		return fontSize;
	}

	/** Returns all data xValues, yValues, xEValues, yEValues as a float[][] array. Note that future versions may have more data. */
	float[][] getAllDataValues() {
		return new float[][] {xValues, yValues, xEValues, yEValues};
	}

	/** A shallow clone that does not duplicate arrays or objects */
	public PlotObject clone() {
		try {
			return (PlotObject)(super.clone());
		} catch (CloneNotSupportedException e) {
			return null;
		}
	}

	/** A deep clone, which duplicates arrays etc.
	 *  Note that colors & font are not cloned; it is assumed that these wil not be modified but replaced,
	 *  so the clone remains unaffected */
	public PlotObject deepClone() {
		PlotObject po2 = clone();
		if (xValues != null) po2.xValues = xValues.clone();
		if (yValues != null) po2.yValues = yValues.clone();
		if (xEValues != null) po2.xEValues = xEValues.clone();
		if (yEValues != null) po2.yEValues = yEValues.clone();
		if (shapeData != null) po2.shapeData = cloneArrayList(shapeData);
		return po2;
	}

	/** A clone of an array list one level deeper than a shallow clone.
	 *  The clone() method of the objects in the list must be accessible */
	private ArrayList cloneArrayList(ArrayList src) {
		ArrayList dest = (ArrayList)(src.clone());     //shallow clone
		Class[] noClasses = new Class[0];
		Object[] noObjects = new Object[0];
		for (int i=0; i<dest.size(); i++) {
			Object o = dest.get(i);
			if (o != null) try {
				Method cloneMethod = o.getClass().getMethod("clone", noClasses);
				dest.set(i, cloneMethod.invoke(o, noObjects));
			} catch (Exception e) {}
		}
		return dest;
	}

	/** Converts old (pre-1.52i) type codes for the PlotObjects to the new ones, which can be used as masks */
	void updateType() {
		type = 1<<type;
	}

	public String toString() {  //for debug messages
		String s = "PlotObject type="+type+" flags="+flags+" xV:"+(xValues==null ? "-":yValues.length)+" yV:"+(yValues==null ? "-":yValues.length)+" label="+label+" col="+color+" fSize="+fontSize+" ff="+fontFamily;
		return s;
	}
} // class PlotObject