import java.io.*;
 import java.net.*;
 import java.awt.*;
 import java.awt.geom.*;
 import java.awt.event.*;
 import java.awt.image.*;
 import javax.swing.*;
 import javax.imageio.ImageIO;
 import java.util.LinkedList;
 
 /**
  *  <i>Standard draw</i>. 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.
  *  <p>
  *  For additional documentation, see <a href="http://www.cs.princeton.edu/introcs/15inout">Section 1.5</a> of
  *  <i>Introduction to Programming in Java: An Interdisciplinary Approach</i> by Robert Sedgewick and Kevin Wayne.
  */
 public final class StdDraw implements ActionListener, MouseListener, MouseMotionListener, KeyListener {
 
     // pre-defined colors
     public static final Color BLACK      = Color.BLACK;
     public static final Color BLUE       = Color.BLUE;
     public static final Color CYAN       = Color.CYAN;
     public static final Color DARK_GRAY  = Color.DARK_GRAY;
     public static final Color GRAY       = Color.GRAY;
     public static final Color GREEN      = Color.GREEN;
     public static final Color LIGHT_GRAY = Color.LIGHT_GRAY;
     public static final Color MAGENTA    = Color.MAGENTA;
     public static final Color ORANGE     = Color.ORANGE;
     public static final Color PINK       = Color.PINK;
     public static final Color RED        = Color.RED;
     public static final Color WHITE      = Color.WHITE;
     public static final Color YELLOW     = Color.YELLOW;
 
     /**
      * Shade of blue used in Introduction to Programming in Java.
      * It is Pantone Pantone 300U. The RGB values are approximately (9, 90, 266).
      */
     public static final Color BOOK_BLUE       = new Color(  9,  90, 166);
     public static final Color BOOK_LIGHT_BLUE = new Color(103, 198, 243);
 
     /**
      * Shade of red used in Algorithms 4th edition.
      * It is Pantone 1805U. The approximate RGB values are (150, 35, 31).
      */
     public static final Color BOOK_RED = new Color(150, 35, 31);
 
     // default colors
     private static final Color DEFAULT_PEN_COLOR   = BLACK;
     private static final Color DEFAULT_CLEAR_COLOR = WHITE;
 
     // current pen color
     private static Color penColor;
 
     // default canvas size is SIZE-by-SIZE
     private static final int DEFAULT_SIZE = 512;
     private static int width  = DEFAULT_SIZE;
     private static int height = DEFAULT_SIZE;
 
     // default pen radius
     private static final double DEFAULT_PEN_RADIUS = 0.002;
 
     // current pen radius
     private static double penRadius;
 
     // show we draw immediately or wait until next show?
     private static boolean defer = false;
 
     // boundary of drawing canvas, 5% border
     private static final double BORDER = 0.05;
     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;
     private static double xmin, ymin, xmax, ymax;
 
     // for synchronization
     private static Object mouseLock = new Object();
     private static Object keyLock = new Object();
 
     // default font
     private static final Font DEFAULT_FONT = new Font("SansSerif", Font.PLAIN, 16);
 
     // current font
     private static Font font;
 
     // double buffered graphics
     private static BufferedImage offscreenImage, onscreenImage;
     private static Graphics2D offscreen, onscreen;
 
     // singleton for callbacks: avoids generation of extra .class files
     private static StdDraw std = new StdDraw();
 
     // the frame for drawing to the screen
     private static JFrame frame;
 
     // mouse state
     private static boolean mousePressed = false;
     private static double mouseX = 0;
     private static double mouseY = 0;
 
     // keyboard state
     private static LinkedList<Character> keysTyped = new LinkedList<Character>();
 
     // not instantiable
     private StdDraw() { }
 
 
     // static initializer
     static { init(); }
 
     /**
      * Set the window size to w-by-h pixels.
      *
      * @param w the width as a number of pixels
      * @param h the height as a number of pixels
      * @throws a RunTimeException if the width or height is 0 or negative
      */
     public static void setCanvasSize(int w, int h) {
         if (w < 1 || h < 1) throw new RuntimeException("width and height must be positive");
         width = w;
         height = h;
         init();
     }
 
     // init
     private static void init() {
         if (frame != null) frame.setVisible(false);
         frame = new JFrame();
         offscreenImage = new BufferedImage(width, height, BufferedImage.TYPE_INT_ARGB);
         onscreenImage  = new BufferedImage(width, height, BufferedImage.TYPE_INT_ARGB);
         offscreen = offscreenImage.createGraphics();
         onscreen  = onscreenImage.createGraphics();
         setXscale();
         setYscale();
         offscreen.setColor(DEFAULT_CLEAR_COLOR);
         offscreen.fillRect(0, 0, width, height);
         setPenColor();
         setPenRadius();
         setFont();
         clear();
 
         // add antialiasing
         RenderingHints hints = new RenderingHints(RenderingHints.KEY_ANTIALIASING,
                                                   RenderingHints.VALUE_ANTIALIAS_ON);
         hints.put(RenderingHints.KEY_RENDERING, RenderingHints.VALUE_RENDER_QUALITY);
         offscreen.addRenderingHints(hints);
 
         // frame stuff
         ImageIcon icon = new ImageIcon(onscreenImage);
         JLabel draw = new JLabel(icon);
 
         draw.addMouseListener(std);
         draw.addMouseMotionListener(std);
 
         frame.setContentPane(draw);
         frame.addKeyListener(std);    // JLabel cannot get keyboard focus
         frame.setResizable(false);
         frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);            // closes all windows
         // frame.setDefaultCloseOperation(JFrame.DISPOSE_ON_CLOSE);      // closes only current window
         frame.setTitle("Standard Draw");
         frame.setJMenuBar(createMenuBar());
         frame.pack();
         frame.requestFocusInWindow();
         frame.setVisible(true);
     }
 
     // create the menu bar (changed to private)
     private static JMenuBar createMenuBar() {
         JMenuBar menuBar = new JMenuBar();
         JMenu menu = new JMenu("File");
         menuBar.add(menu);
         JMenuItem menuItem1 = new JMenuItem(" Save...   ");
         menuItem1.addActionListener(std);
         menuItem1.setAccelerator(KeyStroke.getKeyStroke(KeyEvent.VK_S,
                                 Toolkit.getDefaultToolkit().getMenuShortcutKeyMask()));
         menu.add(menuItem1);
         return menuBar;
     }
 
 
    /*************************************************************************
     *  User and screen coordinate systems
     *************************************************************************/
 
     /**
      * Set the x-scale to be the default (between 0.0 and 1.0).
      */
     public static void setXscale() { setXscale(DEFAULT_XMIN, DEFAULT_XMAX); }
 
     /**
      * Set the y-scale to be the default (between 0.0 and 1.0).
      */
     public static void setYscale() { setYscale(DEFAULT_YMIN, DEFAULT_YMAX); }
 
     /**
      * Set the x-scale (a 10% border is added to the values)
      * @param min the minimum value of the x-scale
      * @param max the maximum value of the x-scale
      */
     public static void setXscale(double min, double max) {
         double size = max - min;
         xmin = min - BORDER * size;
         xmax = max + BORDER * size;
     }
 
     /**
      * Set the y-scale (a 10% border is added to the values).
      * @param min the minimum value of the y-scale
      * @param max the maximum value of the y-scale
      */
     public static void setYscale(double min, double max) {
         double size = max - min;
         ymin = min - BORDER * size;
         ymax = max + BORDER * size;
     }
 
     // helper functions that scale from user coordinates to screen coordinates and back
     private static double  scaleX(double x) { return width  * (x - xmin) / (xmax - xmin); }
     private static double  scaleY(double y) { return height * (ymax - y) / (ymax - ymin); }
     private static double factorX(double w) { return w * width  / Math.abs(xmax - xmin);  }
     private static double factorY(double h) { return h * height / Math.abs(ymax - ymin);  }
     private static double   userX(double x) { return xmin + x * (xmax - xmin) / width;    }
     private static double   userY(double y) { return ymax - y * (ymax - ymin) / height;   }
 
 
     /**
      * Clear the screen to the default color (white).
      */
     public static void clear() { clear(DEFAULT_CLEAR_COLOR); }
     /**
      * Clear the screen to the given color.
      * @param color the Color to make the background
      */
     public static void clear(Color color) {
         offscreen.setColor(color);
         offscreen.fillRect(0, 0, width, height);
         offscreen.setColor(penColor);
         draw();
     }
 
     /**
      * Get the current pen radius.
      */
     public static double getPenRadius() { return penRadius; }
 
     /**
      * Set the pen size to the default (.002).
      */
     public static void setPenRadius() { setPenRadius(DEFAULT_PEN_RADIUS); }
     /**
      * Set the radius of the pen to the given size.
      * @param r the radius of the pen
      * @throws RuntimeException if r is negative
      */
     public static void setPenRadius(double r) {
         if (r < 0) throw new RuntimeException("pen radius must be positive");
         penRadius = r * DEFAULT_SIZE;
         BasicStroke stroke = new BasicStroke((float) penRadius, BasicStroke.CAP_ROUND, BasicStroke.JOIN_ROUND);
         // BasicStroke stroke = new BasicStroke((float) penRadius);
         offscreen.setStroke(stroke);
     }
 
     /**
      * Get the current pen color.
      */
     public static Color getPenColor() { return penColor; }
 
     /**
      * Set the pen color to the default color (black).
      */
     public static void setPenColor() { setPenColor(DEFAULT_PEN_COLOR); }
     /**
      * Set the pen color to the given color. The available pen colors are
      * BLACK, BLUE, CYAN, DARK_GRAY, GRAY, GREEN, LIGHT_GRAY, MAGENTA,
      * ORANGE, PINK, RED, WHITE, and YELLOW.
      * @param color the Color to make the pen
      */
     public static void setPenColor(Color color) {
         penColor = color;
         offscreen.setColor(penColor);
     }
 
     /**
      * Get the current font.
      */
     public static Font getFont() { return font; }
 
     /**
      * Set the font to the default font (sans serif, 16 point).
      */
     public static void setFont() { setFont(DEFAULT_FONT); }
 
     /**
      * Set the font to the given value.
      * @param f the font to make text
      */
     public static void setFont(Font f) { font = f; }
 
 
    /*************************************************************************
     *  Drawing geometric shapes.
     *************************************************************************/
 
     /**
      * Draw 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
      */
     public static void line(double x0, double y0, double x1, double y1) {
         offscreen.draw(new Line2D.Double(scaleX(x0), scaleY(y0), scaleX(x1), scaleY(y1)));
         draw();
     }
 
     /**
      * Draw one pixel at (x, y).
      * @param x the x-coordinate of the pixel
      * @param y the y-coordinate of the pixel
      */
     private static void pixel(double x, double y) {
         offscreen.fillRect((int) Math.round(scaleX(x)), (int) Math.round(scaleY(y)), 1, 1);
     }
 
     /**
      * Draw a point at (x, y).
      * @param x the x-coordinate of the point
      * @param y the y-coordinate of the point
      */
     public static void point(double x, double 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();
     }
 
     /**
      * Draw a circle of radius r, centered on (x, y).
      * @param x the x-coordinate of the center of the circle
      * @param y the y-coordinate of the center of the circle
      * @param r the radius of the circle
      * @throws RuntimeException if the radius of the circle is negative
      */
     public static void circle(double x, double y, double r) {
         if (r < 0) throw new RuntimeException("circle radius can't be negative");
         double xs = scaleX(x);
         double ys = scaleY(y);
         double ws = factorX(2*r);
         double hs = factorY(2*r);
         if (ws <= 1 && hs <= 1) pixel(x, y);
         else offscreen.draw(new Ellipse2D.Double(xs - ws/2, ys - hs/2, ws, hs));
         draw();
     }
 
     /**
      * Draw filled circle of radius r, centered on (x, y).
      * @param x the x-coordinate of the center of the circle
      * @param y the y-coordinate of the center of the circle
      * @param r the radius of the circle
      * @throws RuntimeException if the radius of the circle is negative
      */
     public static void filledCircle(double x, double y, double r) {
         if (r < 0) throw new RuntimeException("circle radius can't be negative");
         double xs = scaleX(x);
         double ys = scaleY(y);
         double ws = factorX(2*r);
         double hs = factorY(2*r);
         if (ws <= 1 && hs <= 1) pixel(x, y);
         else offscreen.fill(new Ellipse2D.Double(xs - ws/2, ys - hs/2, ws, hs));
         draw();
     }
 
 
     /**
      * Draw an ellipse with given semimajor and semiminor axes, centered on (x, y).
      * @param x the x-coordinate of the center of the ellipse
      * @param y the y-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 RuntimeException if either of the axes are negative
      */
     public static void ellipse(double x, double y, double semiMajorAxis, double semiMinorAxis) {
         if (semiMajorAxis < 0) throw new RuntimeException("ellipse semimajor axis can't be negative");
         if (semiMinorAxis < 0) throw new RuntimeException("ellipse semiminor axis can't be negative");
         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();
     }
 
     /**
      * Draw an ellipse with given semimajor and semiminor axes, centered on (x, y).
      * @param x the x-coordinate of the center of the ellipse
      * @param y the y-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 RuntimeException if either of the axes are negative
      */
     public static void filledEllipse(double x, double y, double semiMajorAxis, double semiMinorAxis) {
         if (semiMajorAxis < 0) throw new RuntimeException("ellipse semimajor axis can't be negative");
         if (semiMinorAxis < 0) throw new RuntimeException("ellipse semiminor axis can't be negative");
         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();
     }
 
 
     /**
      * Draw an arc of radius r, centered on (x, y), from angle1 to angle2 (in degrees).
      * @param x the x-coordinate of the center of the circle
      * @param y the y-coordinate of the center of the circle
      * @param r 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 RuntimeException if the radius of the circle is negative
      */
     public static void arc(double x, double y, double r, double angle1, double angle2) {
         if (r < 0) throw new RuntimeException("arc radius can't be negative");
         while (angle2 < angle1) angle2 += 360;
         double xs = scaleX(x);
         double ys = scaleY(y);
         double ws = factorX(2*r);
         double hs = factorY(2*r);
         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();
     }
 
     /**
      * Draw a square of side length 2r, centered on (x, y).
      * @param x the x-coordinate of the center of the square
      * @param y the y-coordinate of the center of the square
      * @param r radius is half the length of any side of the square
      * @throws RuntimeException if r is negative
      */
     public static void square(double x, double y, double r) {
         if (r < 0) throw new RuntimeException("square side length can't be negative");
         double xs = scaleX(x);
         double ys = scaleY(y);
         double ws = factorX(2*r);
         double hs = factorY(2*r);
         if (ws <= 1 && hs <= 1) pixel(x, y);
         else offscreen.draw(new Rectangle2D.Double(xs - ws/2, ys - hs/2, ws, hs));
         draw();
     }
 
     /**
      * Draw a filled square of side length 2r, centered on (x, y).
      * @param x the x-coordinate of the center of the square
      * @param y the y-coordinate of the center of the square
      * @param r radius is half the length of any side of the square
      * @throws RuntimeException if r is negative
      */
     public static void filledSquare(double x, double y, double r) {
         if (r < 0) throw new RuntimeException("square side length can't be negative");
         double xs = scaleX(x);
         double ys = scaleY(y);
         double ws = factorX(2*r);
         double hs = factorY(2*r);
         if (ws <= 1 && hs <= 1) pixel(x, y);
         else offscreen.fill(new Rectangle2D.Double(xs - ws/2, ys - hs/2, ws, hs));
         draw();
     }
 
 
     /**
      * Draw a rectangle of given half width and half height, centered on (x, y).
      * @param x the x-coordinate of the center of the rectangle
      * @param y the y-coordinate of the center of the rectangle
      * @param halfWidth is half the width of the rectangle
      * @param halfHeight is half the height of the rectangle
      * @throws RuntimeException if halfWidth or halfHeight is negative
      */
     public static void rectangle(double x, double y, double halfWidth, double halfHeight) {
         if (halfWidth  < 0) throw new RuntimeException("half width can't be negative");
         if (halfHeight < 0) throw new RuntimeException("half height can't be negative");
         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();
     }
 
     /**
      * Draw a filled rectangle of given half width and half height, centered on (x, y).
      * @param x the x-coordinate of the center of the rectangle
      * @param y the y-coordinate of the center of the rectangle
      * @param halfWidth is half the width of the rectangle
      * @param halfHeight is half the height of the rectangle
      * @throws RuntimeException if halfWidth or halfHeight is negative
      */
     public static void filledRectangle(double x, double y, double halfWidth, double halfHeight) {
         if (halfWidth  < 0) throw new RuntimeException("half width can't be negative");
         if (halfHeight < 0) throw new RuntimeException("half height can't be negative");
         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();
     }
 
 
     /**
      * Draw a polygon with the given (x[i], y[i]) coordinates.
      * @param x an array of all the x-coordindates of the polygon
      * @param y an array of all the y-coordindates of the polygon
      */
     public static void polygon(double[] x, double[] y) {
         int N = x.length;
         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();
     }
 
     /**
      * Draw a filled polygon with the given (x[i], y[i]) coordinates.
      * @param x an array of all the x-coordindates of the polygon
      * @param y an array of all the y-coordindates of the polygon
      */
     public static void filledPolygon(double[] x, double[] y) {
         int N = x.length;
         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) {
 
         // to read from file
         ImageIcon icon = new ImageIcon(filename);
 
         // try to read from URL
         if ((icon == null) || (icon.getImageLoadStatus() != MediaTracker.COMPLETE)) {
             try {
                 URL url = new URL(filename);
                 icon = new ImageIcon(url);
             } catch (Exception e) { /* not a url */ }
         }
 
         // in case file is inside a .jar
         if ((icon == null) || (icon.getImageLoadStatus() != MediaTracker.COMPLETE)) {
             URL url = StdDraw.class.getResource(filename);
             if (url == null) throw new RuntimeException("image " + filename + " not found");
             icon = new ImageIcon(url);
         }
 
         return icon.getImage();
     }
 
     /**
      * Draw picture (gif, jpg, or png) centered on (x, y).
      * @param x the center x-coordinate of the image
      * @param y the center y-coordinate of the image
      * @param s the name of the image/picture, e.g., "ball.gif"
      * @throws RuntimeException if the image is corrupt
      */
     public static void picture(double x, double y, String s) {
         Image image = getImage(s);
         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 RuntimeException("image " + s + " is corrupt");
 
         offscreen.drawImage(image, (int) Math.round(xs - ws/2.0), (int) Math.round(ys - hs/2.0), null);
         draw();
     }
 
     /**
      * Draw picture (gif, jpg, or png) centered on (x, y),
      * rotated given number of degrees
      * @param x the center x-coordinate of the image
      * @param y the center y-coordinate of the image
      * @param s the name of the image/picture, e.g., "ball.gif"
      * @param degrees is the number of degrees to rotate counterclockwise
      * @throws RuntimeException if the image is corrupt
      */
     public static void picture(double x, double y, String s, double degrees) {
         Image image = getImage(s);
         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 RuntimeException("image " + s + " 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();
     }
 
     /**
      * Draw picture (gif, jpg, or png) centered on (x, y), rescaled to w-by-h.
      * @param x the center x coordinate of the image
      * @param y the center y coordinate of the image
      * @param s the name of the image/picture, e.g., "ball.gif"
      * @param w the width of the image
      * @param h the height of the image
      * @throws RuntimeException if the width height are negative
      * @throws RuntimeException if the image is corrupt
      */
     public static void picture(double x, double y, String s, double w, double h) {
         Image image = getImage(s);
         double xs = scaleX(x);
         double ys = scaleY(y);
         if (w < 0) throw new RuntimeException("width is negative: " + w);
         if (h < 0) throw new RuntimeException("height is negative: " + h);
         double ws = factorX(w);
         double hs = factorY(h);
         if (ws < 0 || hs < 0) throw new RuntimeException("image " + s + " 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();
     }
 
 
     /**
      * Draw picture (gif, jpg, or png) centered on (x, y), rotated
      * given number of degrees, rescaled to w-by-h.
      * @param x the center x-coordinate of the image
      * @param y the center y-coordinate of the image
      * @param s the name of the image/picture, e.g., "ball.gif"
      * @param w the width of the image
      * @param h the height of the image
      * @param degrees is the number of degrees to rotate counterclockwise
      * @throws RuntimeException if the image is corrupt
      */
     public static void picture(double x, double y, String s, double w, double h, double degrees) {
         Image image = getImage(s);
         double xs = scaleX(x);
         double ys = scaleY(y);
         double ws = factorX(w);
         double hs = factorY(h);
         if (ws < 0 || hs < 0) throw new RuntimeException("image " + s + " 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.
     *************************************************************************/
 
     /**
      * Write the given text string in the current font, centered on (x, y).
      * @param x the center x-coordinate of the text
      * @param y the center y-coordinate of the text
      * @param s the text
      */
     public static void text(double x, double y, String s) {
         offscreen.setFont(font);
         FontMetrics metrics = offscreen.getFontMetrics();
         double xs = scaleX(x);
         double ys = scaleY(y);
         int ws = metrics.stringWidth(s);
         int hs = metrics.getDescent();
         offscreen.drawString(s, (float) (xs - ws/2.0), (float) (ys + hs));
         draw();
     }
 
     /**
      * Write the given text string in the current font, centered on (x, y) and
      * rotated by the specified number of degrees  
      * @param x the center x-coordinate of the text
      * @param y the center y-coordinate of the text
      * @param s the text
      * @param degrees is the number of degrees to rotate counterclockwise
      */
     public static void text(double x, double y, String s, double degrees) {
         double xs = scaleX(x);
         double ys = scaleY(y);
         offscreen.rotate(Math.toRadians(-degrees), xs, ys);
         text(x, y, s);
         offscreen.rotate(Math.toRadians(+degrees), xs, ys);
     }
 
 
     /**
      * Write the given text string in the current font, left-aligned at (x, y).
      * @param x the x-coordinate of the text
      * @param y the y-coordinate of the text
      * @param s the text
      */
     public static void textLeft(double x, double y, String s) {
         offscreen.setFont(font);
         FontMetrics metrics = offscreen.getFontMetrics();
         double xs = scaleX(x);
         double ys = scaleY(y);
         int ws = metrics.stringWidth(s);
         int hs = metrics.getDescent();
         offscreen.drawString(s, (float) (xs), (float) (ys + hs));
         show();
     }
 
     /**
      * Write the given text string in the current font, right-aligned at (x, y).
      * @param x the x-coordinate of the text
      * @param y the y-coordinate of the text
      * @param s the text
      */
     public static void textRight(double x, double y, String s) {
         offscreen.setFont(font);
         FontMetrics metrics = offscreen.getFontMetrics();
         double xs = scaleX(x);
         double ys = scaleY(y);
         int ws = metrics.stringWidth(s);
         int hs = metrics.getDescent();
         offscreen.drawString(s, (float) (xs - ws), (float) (ys + hs));
         show();
     }
 
 
 
     /**
      * Display on screen, pause for t milliseconds, and turn on
      * <em>animation mode</em>: subsequent calls to
      * drawing methods such as <tt>line()</tt>, <tt>circle()</tt>, and <tt>square()</tt>
      * will not be displayed on screen until the next call to <tt>show()</tt>.
      * This is useful for producing animations (clear the screen, draw a bunch of shapes,
      * display on screen for a fixed amount of time, and repeat). It also speeds up
      * drawing a huge number of shapes (call <tt>show(0)</tt> to defer drawing
      * on screen, draw the shapes, and call <tt>show(0)</tt> to display them all
      * on screen at once).
      * @param t number of milliseconds
      */
     public static void show(int t) {
         defer = false;
         draw();
         try { Thread.currentThread().sleep(t); }
         catch (InterruptedException e) { System.out.println("Error sleeping"); }
         defer = true;
     }
 
 
     /**
      * Display on-screen and turn off animation mode:
      * subsequent calls to
      * drawing methods such as <tt>line()</tt>, <tt>circle()</tt>, and <tt>square()</tt>
      * will be displayed on screen when called. This is the default.
      */
     public static void show() {
         defer = false;
         draw();
     }
 
     // draw onscreen if defer is false
     private static void draw() {
         if (defer) return;
         onscreen.drawImage(offscreenImage, 0, 0, null);
         frame.repaint();
     }
 
 
    /*************************************************************************
     *  Save drawing to a file.
     *************************************************************************/
 
     /**
      * Save to file - suffix must be png, jpg, or gif.
      * @param filename the name of the file with one of the required suffixes
      */
     public static void save(String filename) {
         File file = new File(filename);
         String suffix = filename.substring(filename.lastIndexOf('.') + 1);
 
         // png files
         if (suffix.toLowerCase().equals("png")) {
             try { ImageIO.write(offscreenImage, suffix, file); }
             catch (IOException e) { e.printStackTrace(); }
         }
 
         // need to change from ARGB to RGB for jpeg
         // reference: http://archives.java.sun.com/cgi-bin/wa?A2=ind0404&L=java2d-interest&D=0&P=2727
         else if (suffix.toLowerCase().equals("jpg")) {
             WritableRaster raster = offscreenImage.getRaster();
             WritableRaster newRaster;
             newRaster = raster.createWritableChild(0, 0, width, height, 0, 0, new int[] {0, 1, 2});
             DirectColorModel cm = (DirectColorModel) offscreenImage.getColorModel();
             DirectColorModel newCM = new DirectColorModel(cm.getPixelSize(),
                                                           cm.getRedMask(),
                                                           cm.getGreenMask(),
                                                           cm.getBlueMask());
             BufferedImage rgbBuffer = new BufferedImage(newCM, newRaster, false,  null);
             try { ImageIO.write(rgbBuffer, suffix, file); }
             catch (IOException e) { e.printStackTrace(); }
         }
 
         else {
             System.out.println("Invalid image file type: " + suffix);
         }
     }
 
 
     /**
      * This method cannot be called directly.
      */
     public void actionPerformed(ActionEvent e) {
         FileDialog chooser = new FileDialog(StdDraw.frame, "Use a .png or .jpg extension", FileDialog.SAVE);
         chooser.setVisible(true);
         String filename = chooser.getFile();
         if (filename != null) {
             StdDraw.save(chooser.getDirectory() + File.separator + chooser.getFile());
         }
     }
 
 
    /*************************************************************************
     *  Mouse interactions.
     *************************************************************************/
 
     /**
      * Is the mouse being pressed?
      * @return true or false
      */
     public static boolean mousePressed() {
         synchronized (mouseLock) {
             return mousePressed;
         }
     }
 
     /**
      * What is the x-coordinate of the mouse?
      * @return the value of the x-coordinate of the mouse
      */
     public static double mouseX() {
         synchronized (mouseLock) {
             return mouseX;
         }
     }
 
     /**
      * What is the y-coordinate of the mouse?
      * @return the value of the y-coordinate of the mouse
      */
     public static double mouseY() {
         synchronized (mouseLock) {
             return mouseY;
         }
     }
 
 
     /**
      * This method cannot be called directly.
      */
     public void mouseClicked(MouseEvent e) { }
 
     /**
      * This method cannot be called directly.
      */
     public void mouseEntered(MouseEvent e) { }
 
     /**
      * This method cannot be called directly.
      */
     public void mouseExited(MouseEvent e) { }
 
     /**
      * This method cannot be called directly.
      */
     public void mousePressed(MouseEvent e) {
         synchronized (mouseLock) {
             mouseX = StdDraw.userX(e.getX());
             mouseY = StdDraw.userY(e.getY());
             mousePressed = true;
         }
     }
 
     /**
      * This method cannot be called directly.
      */
     public void mouseReleased(MouseEvent e) {
         synchronized (mouseLock) {
             mousePressed = false;
         }
     }
 
     /**
      * This method cannot be called directly.
      */
     public void mouseDragged(MouseEvent e)  {
         synchronized (mouseLock) {
             mouseX = StdDraw.userX(e.getX());
             mouseY = StdDraw.userY(e.getY());
         }
     }
 
     /**
      * This method cannot be called directly.
      */
     public void mouseMoved(MouseEvent e) {
         synchronized (mouseLock) {
             mouseX = StdDraw.userX(e.getX());
             mouseY = StdDraw.userY(e.getY());
         }
     }
 
 
    /*************************************************************************
     *  Keyboard interactions.
     *************************************************************************/
 
     /**
      * Has the user typed a key?
      * @return true if the user has typed a key, false otherwise
      */
     public static boolean hasNextKeyTyped() {
         synchronized (keyLock) {
             return !keysTyped.isEmpty();
         }
     }
 
     /**
      * What is the next key that was typed by the user?
      * @return the next key typed
      */
     public static char nextKeyTyped() {
         synchronized (keyLock) {
             return keysTyped.removeLast();
         }
     }
 
     /**
      * This method cannot be called directly.
      */
     public void keyTyped(KeyEvent e) {
         synchronized (keyLock) {
             keysTyped.addFirst(e.getKeyChar());
         }
     }
 
     /**
      * This method cannot be called directly.
      */
     public void keyPressed(KeyEvent e) { }
 
     /**
      * This method cannot be called directly.
      */
     public void keyReleased(KeyEvent e) { }
 
 
 
 
     /**
      * Test client.
      */
     public static void main(String[] args) {
         StdDraw.square(.2, .8, .1);
         StdDraw.filledSquare(.8, .8, .2);
         StdDraw.circle(.8, .2, .2);
 
         StdDraw.setPenColor(StdDraw.BOOK_RED);
         StdDraw.setPenRadius(.02);
         StdDraw.arc(.8, .2, .1, 200, 45);
 
         // draw a blue diamond
         StdDraw.setPenRadius();
         StdDraw.setPenColor(StdDraw.BOOK_BLUE);
         double[] x = { .1, .2, .3, .2 };
         double[] y = { .2, .3, .2, .1 };
         StdDraw.filledPolygon(x, y);
 
         // text
         StdDraw.setPenColor(StdDraw.BLACK);
         StdDraw.text(0.2, 0.5, "black text");
         StdDraw.setPenColor(StdDraw.WHITE);
         StdDraw.text(0.8, 0.8, "white text");
     }
 
 }