introductionToProgramming/common/Draw.java

/******************************************************************************
 *  Compilation:  javac Draw.java
 *  Execution:    java Draw
 *  Dependencies: none
 *
 *  Drawing library. This class provides a basic capability for creating
 *  drawings with your programs. It uses a simple graphics model that
 *  allows you to create drawings consisting of points, lines, and curves
 *  in a window on your computer and to save the drawings to a file.
 *  This is the object-oriented version of standard draw; it supports
 *  multiple independent drawing windows.
 *
 *  Todo
 *  ----
 *    -  Add support for gradient fill, etc.
 *
 *  Remarks
 *  -------
 *    -  don't use AffineTransform for rescaling since it inverts
 *       images and strings
 *    -  careful using setFont in inner loop within an animation -
 *       it can cause flicker
 *
 ******************************************************************************/
package common;

import java.awt.BasicStroke;
import java.awt.Color;
import java.awt.Component;
import java.awt.FileDialog;
import java.awt.Font;
import java.awt.FontMetrics;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.Image;
import java.awt.MediaTracker;
import java.awt.RenderingHints;
import java.awt.Toolkit;

import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import java.awt.event.MouseEvent;
import java.awt.event.MouseListener;
import java.awt.event.MouseMotionListener;
import java.awt.event.KeyEvent;
import java.awt.event.KeyListener;

import java.util.Timer;
import java.util.TimerTask;

import java.awt.geom.Arc2D;
import java.awt.geom.Ellipse2D;
import java.awt.geom.GeneralPath;
import java.awt.geom.Line2D;
import java.awt.geom.Rectangle2D;

import java.awt.image.BufferedImage;

import java.io.File;
import java.io.IOException;

import java.net.MalformedURLException;
import java.net.URL;
import java.net.URI;
import java.net.URISyntaxException;

import java.util.ArrayList;
import java.util.LinkedList;
import java.util.TreeSet;

import javax.imageio.ImageIO;

import javax.swing.ImageIcon;
import javax.swing.JFrame;
import javax.swing.JLabel;
import javax.swing.JMenu;
import javax.swing.JMenuBar;
import javax.swing.JMenuItem;
import javax.swing.KeyStroke;

/**
 *  The <code>Draw</code> data type provides a basic capability for
 *  creating drawings with your programs. It uses a simple graphics model that
 *  allows you to create drawings consisting of points, lines, and curves
 *  in a window on your computer and to save the drawings to a file.
 *  This is the object-oriented version of standard draw; it supports
 *  multiple independent drawing windows.
 *  <p>
 *  For additional documentation, see
 *  <a href="https://introcs.cs.princeton.edu/31datatype">Section 3.1</a> of
 *  <i>Computer Science: An Interdisciplinary Approach</i> by Robert Sedgewick and Kevin Wayne.
 *
 *  @author Robert Sedgewick
 *  @author Kevin Wayne
 */
public final class Draw implements ActionListener, MouseListener, MouseMotionListener, KeyListener {

    /**
     *  The color aqua (0, 255, 255).
     */
    public static final Color AQUA = new Color(0, 255, 255);

    /**
     *  The color black (0, 0, 0).
     */
    public static final Color BLACK = Color.BLACK;

    /**
     *  The color blue (0, 0, 255).
     */
    public static final Color BLUE = Color.BLUE;

    /**
     *  The color cyan (0, 255, 255).
     */
    public static final Color CYAN = Color.CYAN;

    /**
     *  The color fuscia (255, 0, 255).
     */
    public static final Color FUSCIA = new Color(255, 0, 255);

    /**
     *  The color dark gray (64, 64, 64).
     */
    public static final Color DARK_GRAY = Color.DARK_GRAY;

    /**
     *  The color gray (128, 128, 128).
     */
    public static final Color GRAY = Color.GRAY;

    /**
     *  The color green (0, 128, 0).
     */
    public static final Color GREEN = new Color(0, 128, 0);

    /**
     *  The color light gray (192, 192, 192).
     */
    public static final Color LIGHT_GRAY = Color.LIGHT_GRAY;

    /**
     *  The color lime (0, 255, 0).
     */
    public static final Color LIME = new Color(0, 255, 0);

    /**
     *  The color magenta (255, 0, 255).
     */
    public static final Color MAGENTA = Color.MAGENTA;

    /**
     *  The color maroon (128, 0, 0).
     */
    public static final Color MAROON = new Color(128, 0, 0);

    /**
     *  The color navy (0, 0, 128).
     */
    public static final Color NAVY = new Color(0, 0, 128);

    /**
     *  The color olive (128, 128, 0).
     */
    public static final Color OLIVE = new Color(128, 128, 0);

    /**
     *  The color orange (255, 200, 0).
     */
    public static final Color ORANGE = Color.ORANGE;

    /**
     *  The color pink (255, 175, 175).
     */
    public static final Color PINK = Color.PINK;

    /**
     *  The color purple (128, 0, 128).
     */
    public static final Color PURPLE = new Color(128, 0, 128);

    /**
     *  The color red (255, 0, 0).
     */
    public static final Color RED = Color.RED;

    /**
     *  The color silver (192, 192, 192).
     */
    public static final Color SILVER = new Color(192, 192, 192);

    /**
     *  The color teal (0, 128, 128).
     */
    public static final Color TEAL = new Color(0, 128, 128);

    /**
     *  The color white (255, 255, 255).
     */
    public static final Color WHITE = Color.WHITE;

    /**
     *  The color yellow (255, 255, 0).
     */
    public static final Color YELLOW = Color.YELLOW;

    /**
     *  A 100% transparent color, for a transparent background.
     */
    public static final Color TRANSPARENT = new Color(0, 0, 0, 0);

    /**
     * The shade of blue used in <em>Introduction to Programming in Java</em>.
     * It is Pantone 300U. The RGB values are approximately (9, 90, 166).
     */
    public static final Color BOOK_BLUE = new Color(9, 90, 166);

    /**
     * The shade of light blue used in <em>Introduction to Programming in Java</em>.
     * The RGB values are approximately (103, 198, 243).
     */
    public static final Color BOOK_LIGHT_BLUE = new Color(103, 198, 243);

    /**
     * The shade of red used in <em>Algorithms, 4th edition</em>.
     * It is Pantone 1805U. The RGB values are approximately (150, 35, 31).
     */
    public static final Color BOOK_RED = new Color(150, 35, 31);

    /**
     * The shade of orange used in Princeton University's identity.
     * It is PMS 158. The RGB values are approximately (245, 128, 37).
     */
    public static final Color PRINCETON_ORANGE = new Color(245, 128, 37);

    // default colors
    private static final Color DEFAULT_PEN_COLOR = BLACK;
    private static final Color DEFAULT_BACKGROUND_COLOR = WHITE;


    // boundary of drawing canvas, 0% border
    private static final double BORDER = 0.0;
    private static final double DEFAULT_XMIN = 0.0;
    private static final double DEFAULT_XMAX = 1.0;
    private static final double DEFAULT_YMIN = 0.0;
    private static final double DEFAULT_YMAX = 1.0;

    // default canvas size is SIZE-by-SIZE
    private static final int DEFAULT_SIZE = 512;

    // default pen radius
    private static final double DEFAULT_PEN_RADIUS = 0.002;

    // default font
    private static final Font DEFAULT_FONT = new Font("SansSerif", Font.PLAIN, 16);

    // default title of drawing window
    private static final String DEFAULT_WINDOW_TITLE = "Draw";

    // current pen color
    private Color penColor = DEFAULT_PEN_COLOR;

    // background color
    private Color backgroundColor = DEFAULT_BACKGROUND_COLOR;

    // current title of drawing window
    private String windowTitle = DEFAULT_WINDOW_TITLE;

    // canvas size
    private int width  = DEFAULT_SIZE;
    private int height = DEFAULT_SIZE;

    // current pen radius
    private double penRadius = DEFAULT_PEN_RADIUS;

    // show we draw immediately or wait until next show?
    private boolean defer = false;

    private double xmin = DEFAULT_XMIN;
    private double xmax = DEFAULT_XMAX;
    private double ymin = DEFAULT_YMIN;
    private double ymax = DEFAULT_YMAX;

    // for synchronization
    private final Object mouseLock = new Object();
    private final Object keyLock = new Object();

    // current font
    private Font font = DEFAULT_FONT;

    // the JLabel for drawing
    private JLabel draw;

    // double buffered graphics
    private BufferedImage offscreenImage, onscreenImage;
    private Graphics2D offscreen, onscreen;

    // the frame for drawing to the screen
    private JFrame frame;

    // is the JFrame visible (upon calling draw())?
    private static boolean isJFrameVisible = true;

    // mouse state
    private boolean isMousePressed = false;
    private double mouseX = 0;
    private double mouseY = 0;

    // keyboard state
    private final LinkedList<Character> keysTyped = new LinkedList<Character>();
    private final TreeSet<Integer> keysDown = new TreeSet<Integer>();

    // event-based listeners
    private final ArrayList<DrawListener> listeners = new ArrayList<DrawListener>();

    // timer
    private Timer timer;

    /**
     * Initializes an empty drawing object.
     */
    public Draw() {
        initCanvas();
        initGUI();
    }

    // initialize the drawing canvas
    private void initCanvas() {

        // BufferedImage stuff
        offscreenImage = new BufferedImage(2*width, 2*height, BufferedImage.TYPE_INT_ARGB);
        onscreenImage  = new BufferedImage(2*width, 2*height, BufferedImage.TYPE_INT_ARGB);
        offscreen = offscreenImage.createGraphics();
        onscreen  = onscreenImage.createGraphics();
        offscreen.scale(2.0, 2.0);  // since we made it 2x as big

        // initialize drawing window
        offscreen.setBackground(DEFAULT_BACKGROUND_COLOR);
        offscreen.clearRect(0, 0, width, height);
        onscreen.setBackground(DEFAULT_BACKGROUND_COLOR);
        onscreen.clearRect(0, 0, 2*width, 2*height);

        // set the pen color
        offscreen.setColor(penColor);

        // add antialiasing
        RenderingHints hints = new RenderingHints(null);
        hints.put(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON);
        hints.put(RenderingHints.KEY_RENDERING, RenderingHints.VALUE_RENDER_QUALITY);
        offscreen.addRenderingHints(hints);
    }

    // initialize the GUI
    private void initGUI() {

        // create the JFrame (if necessary)
        if (frame == null) {
            frame = new JFrame();
            frame.addKeyListener(this);    // JLabel cannot get keyboard focus
            frame.setFocusTraversalKeysEnabled(false);  // allow VK_TAB with isKeyPressed()
            frame.setResizable(false);
            // frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);            // closes all windows
            frame.setDefaultCloseOperation(JFrame.DISPOSE_ON_CLOSE);      // closes only current window
            frame.setTitle(windowTitle);
            frame.setJMenuBar(createMenuBar());
        }

        // create the ImageIcon
        RetinaImageIcon icon = new RetinaImageIcon(onscreenImage);
        draw = new JLabel(icon);
        draw.addMouseListener(this);
        draw.addMouseMotionListener(this);

        // finish up the JFrame
        frame.setContentPane(draw);
        frame.pack();
        frame.requestFocusInWindow();
        frame.setVisible(false);
    }


    /**
     * Makes the drawing window visible or invisible.
     *
     * @param  isVisible if {@code true}, makes the drawing window visible,
     *         otherwise hides the drawing window.
     */
    public void setVisible(boolean isVisible) {
        isJFrameVisible = isVisible;
        frame.setVisible(isVisible);
    }

    /**
     * Sets the upper-left hand corner of the drawing window to be (x, y),
     * where (0, 0) is upper left.
     *
     * @param  x the number of pixels from the left
     * @param  y the number of pixels from the top
     * @throws IllegalArgumentException if the width or height is 0 or negative
     */
    public void setLocationOnScreen(int x, int y) {
        if (x <= 0 || y <= 0) throw new IllegalArgumentException();
        frame.setLocation(x, y);
    }

    /**
     * Sets the default close operation.
     *
     * @param  value the value, typically {@code JFrame.EXIT_ON_CLOSE}
     *         (close all windows) or {@code JFrame.DISPOSE_ON_CLOSE}
     *         (close current window)
     */
    public void setDefaultCloseOperation(int value) {
        frame.setDefaultCloseOperation(value);
    }

    /**
     * Sets the canvas (drawing area) to be 512-by-512 pixels.
     * This also clears the current drawing using the default background color (white).
     * Ordinarily, this method is called once, at the very beginning of a program.
     */
    public void setCanvasSize() {
        setCanvasSize(DEFAULT_SIZE, DEFAULT_SIZE);
    }

    /**
     * Sets the canvas (drawing area) to be <em>width</em>-by-<em>height</em> pixels.
     * This also clears the current drawing using the default background color (white).
     * Ordinarily, this method is called once, at the very beginning of a program.
     *
     * @param  canvasWidth the width as a number of pixels
     * @param  canvasHeight the height as a number of pixels
     * @throws IllegalArgumentException unless both {@code canvasWidth}
     *         and {@code canvasHeight} are positive
     */
    public void setCanvasSize(int canvasWidth, int canvasHeight) {
        if (canvasWidth < 1 || canvasHeight < 1) {
            throw new IllegalArgumentException("width and height must be positive");
        }
        width = canvasWidth;
        height = canvasHeight;
        initCanvas();
        initGUI();
    }


    // create the menu bar
    private JMenuBar createMenuBar() {
        JMenuBar menuBar = new JMenuBar();
        JMenu menu = new JMenu("File");
        menuBar.add(menu);
        JMenuItem menuItem1 = new JMenuItem(" Save...   ");
        menuItem1.addActionListener(this);
        // Java 11: use getMenuShortcutKeyMaskEx()
        // Java 8:  use getMenuShortcutKeyMask()
        menuItem1.setAccelerator(KeyStroke.getKeyStroke(KeyEvent.VK_S,
                                Toolkit.getDefaultToolkit().getMenuShortcutKeyMaskEx()));
        menu.add(menuItem1);
        return menuBar;
    }

    /**
     * Closes the drawing window.
     * This allows the client program to terminate instead of requiring
     * the user to close the drawing window manually.
     * Drawing after calling this method will restore the previous window state.
     */
    public void close() {
        frame.dispose();
    }

   /***************************************************************************
    *  Input validation helper methods.
    ***************************************************************************/

    // throw an IllegalArgumentException if x is NaN or infinite
    private static void validate(double x, String name) {
        if (Double.isNaN(x)) throw new IllegalArgumentException(name + " is NaN");
        if (Double.isInfinite(x)) throw new IllegalArgumentException(name + " is infinite");
    }

    // throw an IllegalArgumentException if s is null
    private static void validateNonnegative(double x, String name) {
        if (x < 0) throw new IllegalArgumentException(name + " negative");
    }

    // throw an IllegalArgumentException if s is null
    private static void validateNotNull(Object x, String name) {
        if (x == null) throw new IllegalArgumentException(name + " is null");
    }


   /***************************************************************************
    *  Set the title of the drawing window.
    ***************************************************************************/

    /**
     * Sets the title of the drawing window to the specified string.
     *
     * @param  windowTitle the title of the window
     * @throws IllegalArgumentException if {@code title} is {@code null}
     */
    public void setTitle(String windowTitle) {
        validateNotNull(windowTitle, "title");
        this.windowTitle = windowTitle;
        frame.setTitle(windowTitle);
    }

   /***************************************************************************
    *  User and screen coordinate systems.
    ***************************************************************************/

    /**
     * Sets the x-scale to the default range (between 0.0 and 1.0).
     */
    public void setXscale() {
        setXscale(DEFAULT_XMIN, DEFAULT_XMAX);
    }

    /**
     * Sets the y-scale to the default range (between 0.0 and 1.0).
     */
    public void setYscale() {
        setYscale(DEFAULT_YMIN, DEFAULT_YMAX);
    }

    /**
     * Sets the x-scale to the specified range.
     *
     * @param min the minimum value of the x-scale
     * @param max the maximum value of the x-scale
     * @throws IllegalArgumentException if {@code (max == min)}
     * @throws IllegalArgumentException if either {@code min} or {@code max} is either NaN or infinite
     */
    public void setXscale(double min, double max) {
        validate(min, "min");
        validate(max, "max");
        double size = max - min;
        if (size == 0.0) throw new IllegalArgumentException("the min and max are the same");
        xmin = min - BORDER * size;
        xmax = max + BORDER * size;
    }

    /**
     * Sets the y-scale to the specified range.
     *
     * @param min the minimum value of the y-scale
     * @param max the maximum value of the y-scale
     * @throws IllegalArgumentException if {@code (max == min)}
     * @throws IllegalArgumentException if either {@code min} or {@code max} is either NaN or infinite
     */
    public void setYscale(double min, double max) {
        validate(min, "min");
        validate(max, "max");
        double size = max - min;
        if (size == 0.0) throw new IllegalArgumentException("the min and max are the same");
        ymin = min - BORDER * size;
        ymax = max + BORDER * size;
    }

    /**
     * Sets both the x-scale and y-scale to the default range (between 0.0 and 1.0).
     */
    public void setScale() {
        setXscale();
        setYscale();
    }

    /**
     * Sets both the x-scale and y-scale to the (same) specified range.
     * @param min the minimum value of the y-scale
     * @param max the maximum value of the y-scale
     * @throws IllegalArgumentException if {@code (max == min)}
     * @throws IllegalArgumentException if either {@code min} or {@code max} is either NaN or infinite
     */
    public void setScale(double min, double max) {
        setXscale(min, max);
        setYscale(min, max);
    }


    // helper functions that scale from user coordinates to screen coordinates and back
    private double  scaleX(double x) { return width  * (x - xmin) / (xmax - xmin); }
    private double  scaleY(double y) { return height * (ymax - y) / (ymax - ymin); }
    private double factorX(double w) { return w * width  / Math.abs(xmax - xmin);  }
    private double factorY(double h) { return h * height / Math.abs(ymax - ymin);  }
    private double   userX(double x) { return xmin + x * (xmax - xmin) / width;    }
    private double   userY(double y) { return ymax - y * (ymax - ymin) / height;   }


    /**
     * Clears the screen using the default background color (white).
     */
    public void clear() {
        clear(DEFAULT_BACKGROUND_COLOR);
    }

    /**
     * Clears the screen using the specified background color.
     * To make the background transparent, use {@code Draw.TRANSPARENT}.
     *
     * @param color the color to make the background
     * @throws IllegalArgumentException if {@code color} is {@code null}
     */
    public void clear(Color color) {
        validateNotNull(color, "color");

        backgroundColor = color;
        offscreen.setBackground(backgroundColor);
        offscreen.clearRect(0, 0, width, height);

        draw();
    }

    /**
     * Returns the current pen radius.
     *
     * @return the current pen radius
     */
    public double getPenRadius() {
        return penRadius;
    }

    /**
     * Sets the pen radius to the default (0.002).
     */
    public void setPenRadius() {
        setPenRadius(DEFAULT_PEN_RADIUS);
    }

    /**
     * Sets the radius of the pen to the given size.
     *
     * @param  radius the radius of the pen
     * @throws IllegalArgumentException if {@code radius} is negative, NaN, or infinite
     */
    public void setPenRadius(double radius) {
        validate(radius, "pen radius");
        validateNonnegative(radius, "pen radius");

        penRadius = radius * DEFAULT_SIZE;
        BasicStroke stroke = new BasicStroke((float) penRadius, BasicStroke.CAP_ROUND, BasicStroke.JOIN_ROUND);
        // BasicStroke stroke = new BasicStroke((float) penRadius);
        offscreen.setStroke(stroke);
    }

    /**
     * Returns the current pen color.
     *
     * @return the current pen color
     */
    public Color getPenColor() {
        return penColor;
    }

    /**
     * Returns the current background color.
     *
     * @return the current background color
     */
    public Color getBackgroundColor() {
        return backgroundColor;
    }

    /**
     * Sets the pen color to the default color (black).
     */
    public void setPenColor() {
        setPenColor(DEFAULT_PEN_COLOR);
    }

    /**
     * Sets the pen color to the given color.
     *
     * @param color the color to make the pen
     * @throws IllegalArgumentException if {@code color} is {@code null}
     */
    public void setPenColor(Color color) {
        validateNotNull(color, "color");
        penColor = color;
        offscreen.setColor(penColor);
    }

    /**
     * Sets the pen color to the given RGB color.
     *
     * @param  red the amount of red (between 0 and 255)
     * @param  green the amount of green (between 0 and 255)
     * @param  blue the amount of blue (between 0 and 255)
     * @throws IllegalArgumentException if {@code red}, {@code green},
     *         or {@code blue} is outside its prescribed range
     */
    public void setPenColor(int red, int green, int blue) {
        if (red   < 0 || red   >= 256) throw new IllegalArgumentException("red must be between 0 and 255");
        if (green < 0 || green >= 256) throw new IllegalArgumentException("green must be between 0 and 255");
        if (blue  < 0 || blue  >= 256) throw new IllegalArgumentException("blue must be between 0 and 255");
        setPenColor(new Color(red, green, blue));
    }


    /**
     * Turns on xor mode.
     */
    public void xorOn() {
        offscreen.setXORMode(backgroundColor);
    }

    /**
     * Turns off xor mode.
     */
    public void xorOff() {
        offscreen.setPaintMode();
    }

    /**
     * Returns the current {@code JLabel} for use in some other GUI.
     *
     * @return the current {@code JLabel}
     */
    public JLabel getJLabel() {
        return draw;
    }

    /**
     * Returns the current font.
     *
     * @return the current font
     */
    public Font getFont() {
        return font;
    }

    /**
     * Sets the font to the default font (sans serif, 16 point).
     */
    public void setFont() {
        setFont(DEFAULT_FONT);
    }

    /**
     * Sets the font to the given value.
     *
     * @param font the font
     * @throws IllegalArgumentException if {@code font} is {@code null}
     */
    public void setFont(Font font) {
        validateNotNull(font, "font");
        this.font = font;
    }


   /***************************************************************************
    *  Drawing geometric shapes.
    ***************************************************************************/

    /**
     * Draws a line from (x0, y0) to (x1, y1).
     *
     * @param x0 the x-coordinate of the starting point
     * @param y0 the y-coordinate of the starting point
     * @param x1 the x-coordinate of the destination point
     * @param y1 the y-coordinate of the destination point
     * @throws IllegalArgumentException if any coordinate is either NaN or infinite
     */
    public void line(double x0, double y0, double x1, double y1) {
        validate(x0, "x0");
        validate(y0, "y0");
        validate(x1, "x1");
        validate(y1, "y1");
        offscreen.draw(new Line2D.Double(scaleX(x0), scaleY(y0), scaleX(x1), scaleY(y1)));
        draw();
    }

    /**
     * Draws one pixel at (x, y).
     *
     * @param x the x-coordinate of the pixel
     * @param y the y-coordinate of the pixel
     * @throws IllegalArgumentException if {@code x} or {@code y} is either NaN or infinite
     */
    private void pixel(double x, double y) {
        validate(x, "x");
        validate(y, "y");
        offscreen.fillRect((int) Math.round(scaleX(x)), (int) Math.round(scaleY(y)), 1, 1);
    }

    /**
     * Draws a point at (x, y).
     *
     * @param x the x-coordinate of the point
     * @param y the y-coordinate of the point
     * @throws IllegalArgumentException if either {@code x} or {@code y} is either NaN or infinite
     */
    public void point(double x, double y) {
        validate(x, "x");
        validate(y, "y");

        double xs = scaleX(x);
        double ys = scaleY(y);
        double r = penRadius;
        // double ws = factorX(2*r);
        // double hs = factorY(2*r);
        // if (ws <= 1 && hs <= 1) pixel(x, y);
        if (r <= 1) pixel(x, y);
        else offscreen.fill(new Ellipse2D.Double(xs - r/2, ys - r/2, r, r));
        draw();
    }

    /**
     * Draws a circle of the specified radius, centered at (<em>x</em>, <em>y</em>).
     *
     * @param  x the x-coordinate of the center of the circle
     * @param  y the y-coordinate of the center of the circle
     * @param  radius the radius of the circle
     * @throws IllegalArgumentException if {@code radius} is negative
     * @throws IllegalArgumentException if any argument is either NaN or infinite
     */
    public void circle(double x, double y, double radius) {
        validate(x, "x");
        validate(y, "y");
        validate(radius, "radius");
        validateNonnegative(radius, "radius");

        double xs = scaleX(x);
        double ys = scaleY(y);
        double ws = factorX(2*radius);
        double hs = factorY(2*radius);
        if (ws <= 1 && hs <= 1) pixel(x, y);
        else offscreen.draw(new Ellipse2D.Double(xs - ws/2, ys - hs/2, ws, hs));
        draw();
    }

    /**
     * Draws a filled circle of the specified radius, centered at (<em>x</em>, <em>y</em>).
     *
     * @param  x the x-coordinate of the center of the circle
     * @param  y the y-coordinate of the center of the circle
     * @param  radius the radius of the circle
     * @throws IllegalArgumentException if {@code radius} is negative
     * @throws IllegalArgumentException if any argument is either NaN or infinite
     */
    public void filledCircle(double x, double y, double radius) {
        validate(x, "x");
        validate(y, "y");
        validate(radius, "radius");
        validateNonnegative(radius, "radius");

        double xs = scaleX(x);
        double ys = scaleY(y);
        double ws = factorX(2*radius);
        double hs = factorY(2*radius);
        if (ws <= 1 && hs <= 1) pixel(x, y);
        else offscreen.fill(new Ellipse2D.Double(xs - ws/2, ys - hs/2, ws, hs));
        draw();
    }


    /**
     * Draws an ellipse with the specified semimajor and semiminor axes,
     * centered at (<em>x</em>, <em>y</em>).
     *
     * @param  x the <em>x</em>-coordinate of the center of the ellipse
     * @param  y the <em>y</em>-coordinate of the center of the ellipse
     * @param  semiMajorAxis is the semimajor axis of the ellipse
     * @param  semiMinorAxis is the semiminor axis of the ellipse
     * @throws IllegalArgumentException if either {@code semiMajorAxis}
     *         or {@code semiMinorAxis} is negative
     * @throws IllegalArgumentException if any argument is either NaN or infinite
     */
    public void ellipse(double x, double y, double semiMajorAxis, double semiMinorAxis) {
        validate(x, "x");
        validate(y, "y");
        validate(semiMajorAxis, "semimajor axis");
        validate(semiMinorAxis, "semiminor axis");
        validateNonnegative(semiMajorAxis, "semimajor axis");
        validateNonnegative(semiMinorAxis, "semiminor axis");

        double xs = scaleX(x);
        double ys = scaleY(y);
        double ws = factorX(2*semiMajorAxis);
        double hs = factorY(2*semiMinorAxis);
        if (ws <= 1 && hs <= 1) pixel(x, y);
        else offscreen.draw(new Ellipse2D.Double(xs - ws/2, ys - hs/2, ws, hs));
        draw();
    }

    /**
     * Draws a filled ellipse with the specified semimajor and semiminor axes,
     * centered at (<em>x</em>, <em>y</em>).
     *
     * @param  x the <em>x</em>-coordinate of the center of the ellipse
     * @param  y the <em>y</em>-coordinate of the center of the ellipse
     * @param  semiMajorAxis is the semimajor axis of the ellipse
     * @param  semiMinorAxis is the semiminor axis of the ellipse
     * @throws IllegalArgumentException if either {@code semiMajorAxis}
     *         or {@code semiMinorAxis} is negative
     * @throws IllegalArgumentException if any argument is either NaN or infinite
     */
    public void filledEllipse(double x, double y, double semiMajorAxis, double semiMinorAxis) {
        validate(x, "x");
        validate(y, "y");
        validate(semiMajorAxis, "semimajor axis");
        validate(semiMinorAxis, "semiminor axis");
        validateNonnegative(semiMajorAxis, "semimajor axis");
        validateNonnegative(semiMinorAxis, "semiminor axis");

        double xs = scaleX(x);
        double ys = scaleY(y);
        double ws = factorX(2*semiMajorAxis);
        double hs = factorY(2*semiMinorAxis);
        if (ws <= 1 && hs <= 1) pixel(x, y);
        else offscreen.fill(new Ellipse2D.Double(xs - ws/2, ys - hs/2, ws, hs));
        draw();
    }

    /**
     * Draws a circular arc of the specified radius,
     * centered at (<em>x</em>, <em>y</em>), from angle1 to angle2 (in degrees).
     *
     * @param  x the <em>x</em>-coordinate of the center of the circle
     * @param  y the <em>y</em>-coordinate of the center of the circle
     * @param  radius the radius of the circle
     * @param  angle1 the starting angle. 0 would mean an arc beginning at 3 o'clock.
     * @param  angle2 the angle at the end of the arc. For example, if
     *         you want a 90 degree arc, then angle2 should be angle1 + 90.
     * @throws IllegalArgumentException if {@code radius} is negative
     * @throws IllegalArgumentException if any argument is either NaN or infinite
     */
    public void arc(double x, double y, double radius, double angle1, double angle2) {
        validate(x, "x");
        validate(y, "y");
        validate(radius, "arc radius");
        validate(angle1, "angle1");
        validate(angle2, "angle2");
        validateNonnegative(radius, "arc radius");

        while (angle2 < angle1) angle2 += 360;
        double xs = scaleX(x);
        double ys = scaleY(y);
        double ws = factorX(2*radius);
        double hs = factorY(2*radius);
        if (ws <= 1 && hs <= 1) pixel(x, y);
        else offscreen.draw(new Arc2D.Double(xs - ws/2, ys - hs/2, ws, hs, angle1, angle2 - angle1, Arc2D.OPEN));
        draw();
    }

    /**
     * Draws a square of the specified size, centered at (<em>x</em>, <em>y</em>).
     *
     * @param  x the <em>x</em>-coordinate of the center of the square
     * @param  y the <em>y</em>-coordinate of the center of the square
     * @param  halfLength one half the length of any side of the square
     * @throws IllegalArgumentException if {@code halfLength} is negative
     * @throws IllegalArgumentException if any argument is either NaN or infinite
     */
    public void square(double x, double y, double halfLength) {
        validate(x, "x");
        validate(y, "y");
        validate(halfLength, "halfLength");
        validateNonnegative(halfLength, "half length");

        double xs = scaleX(x);
        double ys = scaleY(y);
        double ws = factorX(2*halfLength);
        double hs = factorY(2*halfLength);
        if (ws <= 1 && hs <= 1) pixel(x, y);
        else offscreen.draw(new Rectangle2D.Double(xs - ws/2, ys - hs/2, ws, hs));
        draw();
    }

    /**
     * Draws a square of the specified size, centered at (<em>x</em>, <em>y</em>).
     *
     * @param  x the <em>x</em>-coordinate of the center of the square
     * @param  y the <em>y</em>-coordinate of the center of the square
     * @param  halfLength one half the length of any side of the square
     * @throws IllegalArgumentException if {@code halfLength} is negative
     * @throws IllegalArgumentException if any argument is either NaN or infinite
     */
    public void filledSquare(double x, double y, double halfLength) {
        validate(x, "x");
        validate(y, "y");
        validate(halfLength, "halfLength");
        validateNonnegative(halfLength, "half length");

        double xs = scaleX(x);
        double ys = scaleY(y);
        double ws = factorX(2*halfLength);
        double hs = factorY(2*halfLength);
        if (ws <= 1 && hs <= 1) pixel(x, y);
        else offscreen.fill(new Rectangle2D.Double(xs - ws/2, ys - hs/2, ws, hs));
        draw();
    }


    /**
     * Draws a rectangle of the specified size, centered at (<em>x</em>, <em>y</em>).
     *
     * @param  x the <em>x</em>-coordinate of the center of the rectangle
     * @param  y the <em>y</em>-coordinate of the center of the rectangle
     * @param  halfWidth one half the width of the rectangle
     * @param  halfHeight one half the height of the rectangle
     * @throws IllegalArgumentException if either {@code halfWidth} or {@code halfHeight} is negative
     * @throws IllegalArgumentException if any argument is either NaN or infinite
     */
    public void rectangle(double x, double y, double halfWidth, double halfHeight) {
        validate(x, "x");
        validate(y, "y");
        validate(halfWidth, "halfWidth");
        validate(halfHeight, "halfHeight");
        validateNonnegative(halfWidth, "half width");
        validateNonnegative(halfHeight, "half height");

        double xs = scaleX(x);
        double ys = scaleY(y);
        double ws = factorX(2*halfWidth);
        double hs = factorY(2*halfHeight);
        if (ws <= 1 && hs <= 1) pixel(x, y);
        else offscreen.draw(new Rectangle2D.Double(xs - ws/2, ys - hs/2, ws, hs));
        draw();
    }

    /**
     * Draws a filled rectangle of the specified size, centered at (<em>x</em>, <em>y</em>).
     *
     * @param  x the <em>x</em>-coordinate of the center of the rectangle
     * @param  y the <em>y</em>-coordinate of the center of the rectangle
     * @param  halfWidth one half the width of the rectangle
     * @param  halfHeight one half the height of the rectangle
     * @throws IllegalArgumentException if either {@code halfWidth} or {@code halfHeight} is negative
     * @throws IllegalArgumentException if any argument is either NaN or infinite
     */
    public void filledRectangle(double x, double y, double halfWidth, double halfHeight) {
        validate(x, "x");
        validate(y, "y");
        validate(halfWidth, "halfWidth");
        validate(halfHeight, "halfHeight");
        validateNonnegative(halfWidth, "half width");
        validateNonnegative(halfHeight, "half height");

        double xs = scaleX(x);
        double ys = scaleY(y);
        double ws = factorX(2*halfWidth);
        double hs = factorY(2*halfHeight);
        if (ws <= 1 && hs <= 1) pixel(x, y);
        else offscreen.fill(new Rectangle2D.Double(xs - ws/2, ys - hs/2, ws, hs));
        draw();
    }

    /**
     * Draws a polygon with the vertices
     * (<em>x</em><sub>0</sub>, <em>y</em><sub>0</sub>),
     * (<em>x</em><sub>1</sub>, <em>y</em><sub>1</sub>), ...,
     * (<em>x</em><sub><em>n</em>–1</sub>, <em>y</em><sub><em>n</em>–1</sub>).
     *
     * @param  x an array of all the <em>x</em>-coordinates of the polygon
     * @param  y an array of all the <em>y</em>-coordinates of the polygon
     * @throws IllegalArgumentException unless {@code x[]} and {@code y[]}
     *         are of the same length
     * @throws IllegalArgumentException if any coordinate is either NaN or infinite
     * @throws IllegalArgumentException if either {@code x[]} or {@code y[]} is {@code null}
     */
    public void polygon(double[] x, double[] y) {
        validateNotNull(x, "x-coordinate array");
        validateNotNull(y, "y-coordinate array");
        for (int i = 0; i < x.length; i++) validate(x[i], "x[" + i + "]");
        for (int i = 0; i < y.length; i++) validate(y[i], "y[" + i + "]");

        int n1 = x.length;
        int n2 = y.length;
        if (n1 != n2) throw new IllegalArgumentException("arrays must be of the same length");
        int n = n1;
        if (n == 0) return;

        GeneralPath path = new GeneralPath();
        path.moveTo((float) scaleX(x[0]), (float) scaleY(y[0]));
        for (int i = 0; i < n; i++)
            path.lineTo((float) scaleX(x[i]), (float) scaleY(y[i]));
        path.closePath();
        offscreen.draw(path);
        draw();
    }

    /**
     * Draws a filled polygon with the vertices
     * (<em>x</em><sub>0</sub>, <em>y</em><sub>0</sub>),
     * (<em>x</em><sub>1</sub>, <em>y</em><sub>1</sub>), ...,
     * (<em>x</em><sub><em>n</em>–1</sub>, <em>y</em><sub><em>n</em>–1</sub>).
     *
     * @param  x an array of all the <em>x</em>-coordinates of the polygon
     * @param  y an array of all the <em>y</em>-coordinates of the polygon
     * @throws IllegalArgumentException unless {@code x[]} and {@code y[]}
     *         are of the same length
     * @throws IllegalArgumentException if any coordinate is either NaN or infinite
     * @throws IllegalArgumentException if either {@code x[]} or {@code y[]} is {@code null}
     */
    public void filledPolygon(double[] x, double[] y) {
        validateNotNull(x, "x-coordinate array");
        validateNotNull(y, "y-coordinate array");
        for (int i = 0; i < x.length; i++) validate(x[i], "x[" + i + "]");
        for (int i = 0; i < y.length; i++) validate(y[i], "y[" + i + "]");

        int n1 = x.length;
        int n2 = y.length;
        if (n1 != n2) throw new IllegalArgumentException("arrays must be of the same length");
        int n = n1;
        if (n == 0) return;

        GeneralPath path = new GeneralPath();
        path.moveTo((float) scaleX(x[0]), (float) scaleY(y[0]));
        for (int i = 0; i < n; i++)
            path.lineTo((float) scaleX(x[i]), (float) scaleY(y[i]));
        path.closePath();
        offscreen.fill(path);
        draw();
    }



   /***************************************************************************
    *  Drawing images.
    ***************************************************************************/

    // get an image from the given filename
    private static Image getImage(String filename) {
        if (filename == null) throw new IllegalArgumentException();

        // to read from file
        ImageIcon icon = new ImageIcon(filename);

        // try to read from URL
        if (icon.getImageLoadStatus() != MediaTracker.COMPLETE) {
            try {
                URI uri = new URI(filename);
                if (uri.isAbsolute()) {
                    URL url = uri.toURL();
                    icon = new ImageIcon(url);
                }
            }
            catch (MalformedURLException | URISyntaxException e) {
                /* not a url */
            }
        }

        // in case file is inside a .jar (classpath relative to Draw)
        if (icon.getImageLoadStatus() != MediaTracker.COMPLETE) {
            URL url = Draw.class.getResource(filename);
            if (url != null)
                icon = new ImageIcon(url);
        }

        // in case file is inside a .jar (classpath relative to root of jar)
        if (icon.getImageLoadStatus() != MediaTracker.COMPLETE) {
            URL url = Draw.class.getResource("/" + filename);
            if (url == null) throw new IllegalArgumentException("could not read image: '" + filename + "'");
            icon = new ImageIcon(url);
        }

        return icon.getImage();
    }

    /**
     * Draws the specified image centered at (<em>x</em>, <em>y</em>).
     * The supported image formats are typically JPEG, PNG, GIF, TIFF, and BMP.
     * As an optimization, the picture is cached, so there is no performance
     * penalty for redrawing the same image multiple times (e.g., in an animation).
     * However, if you change the picture file after drawing it, subsequent
     * calls will draw the original picture.
     *
     * @param  x the center <em>x</em>-coordinate of the image
     * @param  y the center <em>y</em>-coordinate of the image
     * @param  filename the name of the image/picture, e.g., "ball.gif"
     * @throws IllegalArgumentException if the image filename is invalid
     * @throws IllegalArgumentException if either {@code x} or {@code y} is either NaN or infinite
     */
    public void picture(double x, double y, String filename) {
        validate(x, "x");
        validate(y, "y");
        validateNotNull(filename, "filename");

        Image image = getImage(filename);
        double xs = scaleX(x);
        double ys = scaleY(y);
        int ws = image.getWidth(null);
        int hs = image.getHeight(null);
        if (ws < 0 || hs < 0) throw new IllegalArgumentException("image " + filename + " is corrupt");

        offscreen.drawImage(image, (int) Math.round(xs - ws/2.0), (int) Math.round(ys - hs/2.0), null);
        draw();
    }

    /**
     * Draws the specified image centered at (<em>x</em>, <em>y</em>),
     * rotated given number of degrees.
     * The supported image formats are typically JPEG, PNG, GIF, TIFF, and BMP.
     *
     * @param  x the center <em>x</em>-coordinate of the image
     * @param  y the center <em>y</em>-coordinate of the image
     * @param  filename the name of the image/picture, e.g., "ball.gif"
     * @param  degrees is the number of degrees to rotate counterclockwise
     * @throws IllegalArgumentException if the image filename is invalid
     * @throws IllegalArgumentException if {@code x}, {@code y}, {@code degrees} is NaN or infinite
     * @throws IllegalArgumentException if {@code filename} is {@code null}
     */
    public void picture(double x, double y, String filename, double degrees) {
        validate(x, "x");
        validate(y, "y");
        validate(degrees, "degrees");
        validateNotNull(filename, "filename");

        Image image = getImage(filename);
        double xs = scaleX(x);
        double ys = scaleY(y);
        int ws = image.getWidth(null);
        int hs = image.getHeight(null);
        if (ws < 0 || hs < 0) throw new IllegalArgumentException("image " + filename + " is corrupt");

        offscreen.rotate(Math.toRadians(-degrees), xs, ys);
        offscreen.drawImage(image, (int) Math.round(xs - ws/2.0), (int) Math.round(ys - hs/2.0), null);
        offscreen.rotate(Math.toRadians(+degrees), xs, ys);

        draw();
    }

    /**
     * Draws the specified image centered at (<em>x</em>, <em>y</em>),
     * rescaled to the specified bounding box.
     * The supported image formats are typically JPEG, PNG, GIF, TIFF, and BMP.
     *
     * @param  x the center <em>x</em>-coordinate of the image
     * @param  y the center <em>y</em>-coordinate of the image
     * @param  filename the name of the image/picture, e.g., "ball.gif"
     * @param  scaledWidth the width of the scaled image (in screen coordinates)
     * @param  scaledHeight the height of the scaled image (in screen coordinates)
     * @throws IllegalArgumentException if either {@code scaledWidth}
     *         or {@code scaledHeight} is negative
     * @throws IllegalArgumentException if the image filename is invalid
     * @throws IllegalArgumentException if {@code x} or {@code y} is either NaN or infinite
     * @throws IllegalArgumentException if {@code filename} is {@code null}
     */
    public void picture(double x, double y, String filename, double scaledWidth, double scaledHeight) {
        validate(x, "x");
        validate(y, "y");
        validate(scaledWidth, "scaled width");
        validate(scaledHeight, "scaled height");
        validateNotNull(filename, "filename");
        validateNonnegative(scaledWidth, "scaled width");
        validateNonnegative(scaledHeight, "scaled height");

        Image image = getImage(filename);
        double xs = scaleX(x);
        double ys = scaleY(y);
        double ws = factorX(scaledWidth);
        double hs = factorY(scaledHeight);
        if (ws < 0 || hs < 0) throw new IllegalArgumentException("image " + filename + " is corrupt");
        if (ws <= 1 && hs <= 1) pixel(x, y);
        else {
            offscreen.drawImage(image, (int) Math.round(xs - ws/2.0),
                                       (int) Math.round(ys - hs/2.0),
                                       (int) Math.round(ws),
                                       (int) Math.round(hs), null);
        }
        draw();
    }


    /**
     * Draws the specified image centered at (<em>x</em>, <em>y</em>), rotated
     * given number of degrees, and rescaled to the specified bounding box.
     * The supported image formats are typically JPEG, PNG, GIF, TIFF, and BMP.
     *
     * @param  x the center <em>x</em>-coordinate of the image
     * @param  y the center <em>y</em>-coordinate of the image
     * @param  filename the name of the image/picture, e.g., "ball.gif"
     * @param  scaledWidth the width of the scaled image (in screen coordinates)
     * @param  scaledHeight the height of the scaled image (in screen coordinates)
     * @param  degrees is the number of degrees to rotate counterclockwise
     * @throws IllegalArgumentException if either {@code scaledWidth}
     *         or {@code scaledHeight} is negative
     * @throws IllegalArgumentException if the image filename is invalid
     */
    public void picture(double x, double y, String filename, double scaledWidth, double scaledHeight, double degrees) {
        validate(x, "x");
        validate(y, "y");
        validate(scaledWidth, "scaled width");
        validate(scaledHeight, "scaled height");
        validate(degrees, "degrees");
        validateNotNull(filename, "filename");
        validateNonnegative(scaledWidth, "scaled width");
        validateNonnegative(scaledHeight, "scaled height");

        Image image = getImage(filename);
        double xs = scaleX(x);
        double ys = scaleY(y);
        double ws = factorX(scaledWidth);
        double hs = factorY(scaledHeight);
        if (ws < 0 || hs < 0) throw new IllegalArgumentException("image " + filename + " is corrupt");
        if (ws <= 1 && hs <= 1) pixel(x, y);

        offscreen.rotate(Math.toRadians(-degrees), xs, ys);
        offscreen.drawImage(image, (int) Math.round(xs - ws/2.0),
                                   (int) Math.round(ys - hs/2.0),
                                   (int) Math.round(ws),
                                   (int) Math.round(hs), null);
        offscreen.rotate(Math.toRadians(+degrees), xs, ys);

        draw();
    }


   /***************************************************************************
    *  Drawing text.
    ***************************************************************************/

    /**
     * Writes the given text string in the current font, centered at (<em>x</em>, <em>y</em>).
     *
     * @param  x the center <em>x</em>-coordinate of the text
     * @param  y the center <em>y</em>-coordinate of the text
     * @param  text the text to write
     * @throws IllegalArgumentException if {@code text} is {@code null}
     * @throws IllegalArgumentException if {@code x} or {@code y} is either NaN or infinite
     */
    public void text(double x, double y, String text) {
        validate(x, "x");
        validate(y, "y");
        validateNotNull(text, "text");

        offscreen.setFont(font);
        FontMetrics metrics = offscreen.getFontMetrics();
        double xs = scaleX(x);
        double ys = scaleY(y);
        int ws = metrics.stringWidth(text);
        int hs = metrics.getDescent();
        offscreen.drawString(text, (float) (xs - ws/2.0), (float) (ys + hs));
        draw();
    }

    /**
     * Writes the given text string in the current font, centered at (<em>x</em>, <em>y</em>) and
     * rotated by the specified number of degrees.
     * @param  x the center <em>x</em>-coordinate of the text
     * @param  y the center <em>y</em>-coordinate of the text
     * @param  text the text to write
     * @param  degrees is the number of degrees to rotate counterclockwise
     * @throws IllegalArgumentException if {@code text} is {@code null}
     * @throws IllegalArgumentException if {@code x}, {@code y}, or {@code degrees} is either NaN or infinite
     */
    public void text(double x, double y, String text, double degrees) {
        validate(x, "x");
        validate(y, "y");
        validate(degrees, "degrees");
        validateNotNull(text, "text");

        double xs = scaleX(x);
        double ys = scaleY(y);
        offscreen.rotate(Math.toRadians(-degrees), xs, ys);
        text(x, y, text);
        offscreen.rotate(Math.toRadians(+degrees), xs, ys);
    }

    /**
     * Writes the given text string in the current font, left-aligned at (<em>x</em>, <em>y</em>).
     * @param  x the <em>x</em>-coordinate of the text
     * @param  y the <em>y</em>-coordinate of the text
     * @param  text the text
     * @throws IllegalArgumentException if {@code text} is {@code null}
     * @throws IllegalArgumentException if {@code x} or {@code y} is either NaN or infinite
     */
    public void textLeft(double x, double y, String text) {
        validate(x, "x");
        validate(y, "y");
        validateNotNull(text, "text");

        offscreen.setFont(font);
        FontMetrics metrics = offscreen.getFontMetrics();
        double xs = scaleX(x);
        double ys = scaleY(y);
        // int ws = metrics.stringWidth(text);
        int hs = metrics.getDescent();
        offscreen.drawString(text, (float) xs, (float) (ys + hs));
        draw();
    }

    /**
     * Writes the given text string in the current font, right-aligned at (<em>x</em>, <em>y</em>).
     *
     * @param  x the <em>x</em>-coordinate of the text
     * @param  y the <em>y</em>-coordinate of the text
     * @param  text the text to write
     * @throws IllegalArgumentException if {@code text} is {@code null}
     * @throws IllegalArgumentException if {@code x} or {@code y} is either NaN or infinite
     */
    public void textRight(double x, double y, String text) {
        validate(x, "x");
        validate(y, "y");
        validateNotNull(text, "text");

        offscreen.setFont(font);
        FontMetrics metrics = offscreen.getFontMetrics();
        double xs = scaleX(x);
        double ys = scaleY(y);
        int ws = metrics.stringWidth(text);
        int hs = metrics.getDescent();
        offscreen.drawString(text, (float) (xs - ws), (float) (ys + hs));
        draw();
    }

    /**
     * Copies the offscreen buffer to the onscreen buffer, pauses for t milliseconds
     * and enables double buffering.
     * @param t number of milliseconds
     * @throws IllegalArgumentException if {@code t} is negative
     * @deprecated replaced by {@link #enableDoubleBuffering()}, {@link #show()}, and {@link #pause(int t)}
     */
    @Deprecated
    public void show(int t) {
        show();
        pause(t);
        enableDoubleBuffering();
    }

    /**
     * Pause for t milliseconds. This method is intended to support computer animations.
     * @param t number of milliseconds
     * @throws IllegalArgumentException if {@code t} is negative
     */
    public void pause(int t) {
        try {
            Thread.sleep(t);
        }
        catch (InterruptedException e) {
            System.out.println("Error sleeping");
        }
    }

    /**
     * Copies offscreen buffer to onscreen buffer. There is no reason to call
     * this method unless double buffering is enabled.
     */
    public void show() {
        onscreen.setBackground(backgroundColor);
        onscreen.clearRect(0, 0, 2*width, 2*height);
        onscreen.drawImage(offscreenImage, 0, 0, null);

        // make frame visible upon first call to show()
        if (frame.isVisible() != isJFrameVisible) {
            frame.setVisible(isJFrameVisible);
        }

        frame.repaint();
    }

    // draw onscreen if defer is false
    private void draw() {
        if (!defer) show();
    }

    /**
     * Enable double buffering. All subsequent calls to
     * drawing methods such as {@code line()}, {@code circle()},
     * and {@code square()} will be deferred until the next call
     * to show(). Useful for animations.
     */
    public void enableDoubleBuffering() {
        defer = true;
    }

    /**
     * Disable double buffering. All subsequent calls to
     * drawing methods such as {@code line()}, {@code circle()},
     * and {@code square()} will be displayed on screen when called.
     * This is the default.
     */
    public void disableDoubleBuffering() {
        defer = false;
    }

    /**
     * Saves the drawing to a file in a supported file format
     * (typically JPEG, PNG, GIF, TIFF, and BMP).
     * The filetype extension must be {@code .jpg}, {@code .png}, {@code .gif},
     * {@code .bmp}, or {@code .tif}.
     *
     * @param  filename the name of the file
     * @throws IllegalArgumentException if {@code filename} is {@code null}
     * @throws IllegalArgumentException if {@code filename} is the empty string
     * @throws IllegalArgumentException if {@code filename} has invalid filetype extension
     * @throws IllegalArgumentException if cannot write the file {@code filename}
     */
    public void save(String filename) {
        validateNotNull(filename, "filename");
        if (filename.length() == 0) {
            throw new IllegalArgumentException("argument to save() is the empty string");
        }

        File file = new File(filename);
        String suffix = filename.substring(filename.lastIndexOf('.') + 1);
        if (!filename.contains(".") || suffix.length() == 0) {
            throw new IllegalArgumentException("the filename '" + filename + "' has no file extension, such as .jpg or .png");
        }

        try {
            // if the file format supports transparency (such as PNG or GIF)
            if (ImageIO.write(onscreenImage, suffix, file)) return;

            // if the file format does not support transparency (such as JPEG or BMP)
            BufferedImage saveImage = new BufferedImage(2*width, 2*height, BufferedImage.TYPE_INT_RGB);
            saveImage.createGraphics().drawImage(onscreenImage, 0, 0, Color.WHITE, null);
            if (ImageIO.write(saveImage, suffix, file)) return;

            // failed to save the file; probably wrong format
            throw new IllegalArgumentException("the filetype '" + suffix + "' is not supported");
        }
        catch (IOException e) {
            throw new IllegalArgumentException("could not write the file + " + filename, e);
        }
    }

    /**
     * This method cannot be called directly.
     */
    @Override
    public void actionPerformed(ActionEvent event) {
        FileDialog chooser = new FileDialog(frame, "Use a .png or .jpg extension", FileDialog.SAVE);
        chooser.setVisible(true);
        String selectedDirectory = chooser.getDirectory();
        String selectedFilename = chooser.getFile();
        if (selectedDirectory != null && selectedFilename != null) {
            try {
                save(selectedDirectory + selectedFilename);
            }
            catch (IllegalArgumentException e) {
                System.err.println(e.getMessage());
            }
        }
    }



   /***************************************************************************
    *  Event-based interactions.
    ***************************************************************************/

    /**
     * Adds a {@link DrawListener} to listen to keyboard and mouse events.
     *
     * @param listener the {\tt DrawListener} argument
     */
    public void addListener(DrawListener listener) {
        // ensure there is a window for listening to events
        show();
        listeners.add(listener);
    }




   /***************************************************************************
    *  Mouse interactions.
    ***************************************************************************/

    /**
     * Returns true if the mouse is being pressed.
     *
     * @return {@code true} if the mouse is being pressed;
     *         {@code false} otherwise
     */
    public boolean isMousePressed() {
        synchronized (mouseLock) {
            return isMousePressed;
        }
    }

    /**
     * Returns true if the mouse is being pressed.
     *
     * @return {@code true} if the mouse is being pressed;
     *         {@code false} otherwise
     * @deprecated replaced by {@link #isMousePressed()}
     */
    @Deprecated
    public boolean mousePressed() {
        synchronized (mouseLock) {
            return isMousePressed;
        }
    }

    /**
     * Returns the x-coordinate of the mouse.
     * @return the x-coordinate of the mouse
     */
    public double mouseX() {
        synchronized (mouseLock) {
            return mouseX;
        }
    }

    /**
     * Returns the y-coordinate of the mouse.
     *
     * @return the y-coordinate of the mouse
     */
    public double mouseY() {
        synchronized (mouseLock) {
            return mouseY;
        }
    }



    /**
     * This method cannot be called directly.
     */
    @Override
    public void mouseEntered(MouseEvent event) {
        // this body is intentionally left empty
    }

    /**
     * This method cannot be called directly.
     */
    @Override
    public void mouseExited(MouseEvent event) {
        // this body is intentionally left empty
    }

    /**
     * This method cannot be called directly.
     */
    @Override
    public void mousePressed(MouseEvent event) {
        synchronized (mouseLock) {
            mouseX = userX(event.getX());
            mouseY = userY(event.getY());
            isMousePressed = true;
        }
        if (event.getButton() == MouseEvent.BUTTON1) {
            for (DrawListener listener : listeners)
                listener.mousePressed(userX(event.getX()), userY(event.getY()));
        }

    }

    /**
     * This method cannot be called directly.
     */
    @Override
    public void mouseReleased(MouseEvent event) {
        synchronized (mouseLock) {
            isMousePressed = false;
        }
        if (event.getButton() == MouseEvent.BUTTON1) {
            for (DrawListener listener : listeners)
                listener.mouseReleased(userX(event.getX()), userY(event.getY()));
        }
    }

    /**
     * This method cannot be called directly.
     */
    @Override
    public void mouseClicked(MouseEvent event) {
        if (event.getButton() == MouseEvent.BUTTON1) {
            for (DrawListener listener : listeners)
                listener.mouseClicked(userX(event.getX()), userY(event.getY()));
        }
    }


    /**
     * This method cannot be called directly.
     */
    @Override
    public void mouseDragged(MouseEvent event)  {
        synchronized (mouseLock) {
            mouseX = userX(event.getX());
            mouseY = userY(event.getY());
        }
        // doesn't seem to work if a button is specified
        for (DrawListener listener : listeners)
            listener.mouseDragged(userX(event.getX()), userY(event.getY()));
    }

    /**
     * This method cannot be called directly.
     */
    @Override
    public void mouseMoved(MouseEvent event) {
        synchronized (mouseLock) {
            mouseX = userX(event.getX());
            mouseY = userY(event.getY());
        }
    }


   /***************************************************************************
    *  Keyboard interactions.
    ***************************************************************************/

    /**
     * Returns true if the user has typed a key.
     *
     * @return {@code true} if the user has typed a key; {@code false} otherwise
     */
    public boolean hasNextKeyTyped() {
        synchronized (keyLock) {
            return !keysTyped.isEmpty();
        }
    }

    /**
     * The next key typed by the user.
     *
     * @return the next key typed by the user
     */
    public char nextKeyTyped() {
        synchronized (keyLock) {
            return keysTyped.removeLast();
        }
    }

   /**
     * Returns true if the keycode is being pressed.
     * <p>
     * This method takes as an argument the keycode (corresponding to a physical key).
     * It can handle action keys (such as F1 and arrow keys) and modifier keys
     * (such as shift and control).
     * See {@link KeyEvent} for a description of key codes.
     *
     * @param  keycode the keycode to check
     * @return {@code true} if {@code keycode} is currently being pressed;
     *         {@code false} otherwise
     */
    public boolean isKeyPressed(int keycode) {
        synchronized (keyLock) {
            return keysDown.contains(keycode);
        }
    }

    /**
     * This method cannot be called directly.
     */
    @Override
    public void keyTyped(KeyEvent event) {
        synchronized (keyLock) {
            keysTyped.addFirst(event.getKeyChar());
        }

        // notify all listeners
        for (DrawListener listener : listeners)
            listener.keyTyped(event.getKeyChar());
    }

    /**
     * This method cannot be called directly.
     */
    @Override
    public void keyPressed(KeyEvent event) {
        synchronized (keyLock) {
            keysDown.add(event.getKeyCode());
        }

        // notify all listeners
        for (DrawListener listener : listeners)
            listener.keyPressed(event.getKeyCode());
    }

    /**
     * This method cannot be called directly.
     */
    @Override
    public void keyReleased(KeyEvent event) {
        synchronized (keyLock) {
            keysDown.remove(event.getKeyCode());
        }

        // notify all listeners
        for (DrawListener listener : listeners)
            listener.keyReleased(event.getKeyCode());
    }

   /***************************************************************************
    *  Timer events.
    ***************************************************************************/

   /**
     * Sets a timer that calls update() method a specified number of times
     * per second.
     * <p>
     * @param  callsPerSecond calls per second
     */
    public void enableTimer(int callsPerSecond) {
        disableTimer();
        timer = new Timer();
        timer.schedule(new MyTimerTask(), 0, (int) Math.round(1000.0 / callsPerSecond));
    }

    public void disableTimer() {
        if (timer != null) timer.cancel();
    }

    private class MyTimerTask extends TimerTask {
        public void run() {
            for (DrawListener listener : listeners)
                listener.update();
        }
    }

   /***************************************************************************
    *  For improved resolution on Mac Retina displays.
    ***************************************************************************/

    private static class RetinaImageIcon extends ImageIcon {

        public RetinaImageIcon(Image image) {
            super(image);
        }

        public int getIconWidth() {
            return super.getIconWidth() / 2;
        }

        /**
         * Returns the height of the icon.
         *
         * @return the height in pixels of this icon
         */
        public int getIconHeight() {
            return super.getIconHeight() / 2;
        }

        public synchronized void paintIcon(Component c, Graphics g, int x, int y) {
            Graphics2D g2 = (Graphics2D) g.create();
            g2.setRenderingHint(RenderingHints.KEY_INTERPOLATION, RenderingHints.VALUE_INTERPOLATION_BICUBIC);
            g2.setRenderingHint(RenderingHints.KEY_RENDERING,     RenderingHints.VALUE_RENDER_QUALITY);
            g2.setRenderingHint(RenderingHints.KEY_ANTIALIASING,  RenderingHints.VALUE_ANTIALIAS_ON);
            g2.scale(0.5, 0.5);
            super.paintIcon(c, g2, x * 2, y * 2);
            g2.dispose();
        }
    }

    /**
     * Test client.
     *
     * @param args the command-line arguments
     */
    public static void main(String[] args) {

        // create one drawing window
        Draw draw1 = new Draw();
        draw1.setTitle("Test client 1");
        draw1.square(0.2, 0.8, 0.1);
        draw1.filledSquare(0.8, 0.8, 0.2);
        draw1.circle(0.8, 0.2, 0.2);
        draw1.setPenColor(Draw.MAGENTA);
        draw1.setPenRadius(0.02);
        draw1.arc(0.8, 0.2, 0.1, 200, 45);


        // create another one
        Draw draw2 = new Draw();
        draw2.setCanvasSize(900, 200);
        draw2.setTitle("Test client 2");
        // draw a blue diamond
        draw2.setPenRadius();
        draw2.setPenColor(Draw.BLUE);
        double[] x = { 0.1, 0.2, 0.3, 0.2 };
        double[] y = { 0.2, 0.3, 0.2, 0.1 };
        draw2.filledPolygon(x, y);

        // text
        draw2.setPenColor(Draw.BLACK);
        draw2.text(0.2, 0.5, "black text");
        draw2.setPenColor(Draw.WHITE);
        draw2.text(0.2, 0.2, "white text");
    }

}