2 1 Java 1.1: (paint, update) Frame Canvas java.awt.canvas java.awt.component java.lang.object paint Canvas Graphics update Canvas ( ) paint Graphics

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1 1 1 Java 1.1 (graphics) (graph) ( ) ( ) (discretization, sampling) (pixel) 1 (raster) (0, 0) x y (quantization) ( ) ( ) CRT(Cathode-Ray Tube) (LCD: Liquid-Crystal Display) ( ) ( ) ( / ) imac , , Frame Frame ( ) OS java.awt.frame java.awt.window java.awt.container java.awt.component java.lant.object Canvas Canvas ( )

2 2 1 Java 1.1: (paint, update) Frame Canvas java.awt.canvas java.awt.component java.lang.object paint Canvas Graphics update Canvas ( ) paint Graphics Graphics ( ) Canvas Graphics java.awt.graphics java.lang.object - Crossline.java (2 ) import java.awt.*; import java.awt.event.*; public class CrossLine extends Canvas { private static final int width = 400; // Canvas

3 private static final int height = 300; // Canvas private CrossLine() { super(); setsize(width, height); setbackground(color.white); setforeground(color.black); // Canvas // ( ) // ( ) Frame f = new Frame("CrossLine"); // Frame f.add(this); // Frame Canva f.pack(); // f.addwindowlistener(new WindowAdapter() { public void windowclosing(windowevent e) { System.exit(0); ); f.setvisible(true); // Frame public void paint(graphics g) { g.drawline(0, 0, width-1, height-1); // : g.drawline(0, height-1, width-1, 0); // : g.drawstring("hello, Graphics.", width/2, height/2); // : public static void main(string[] args) { new CrossLine(); // Canvas - Lines.java import java.awt.*; import java.awt.event.*; public class Lines extends Canvas { private static final int width = 600; private static final int height = 600; protected static final int[][] points = // Canvas // Canvas

4 4 1 Java (0,0) 600 (599,75) (599,150) 600 (599,300) (300,599) (599,599) 1.2: {{10, 599, {30, 599, {75, 599, {150, 599, {300, 599, {599, 599, ; {599, 300, {599, 150, {599, 75, {599, 30, {599, 10 protected Lines(String name) { super(); setsize(width, height); setbackground(color.white); setforeground(color.black); // Canvas // ( ) // ( ) Frame f = new Frame(name); // Frame f.add(this); // Frame Canva f.pack(); // f.addwindowlistener(new WindowAdapter() { public void windowclosing(windowevent e) { System.exit(0); ); f.setvisible(true); // Frame public void paint(graphics g) { for (int i = 0; i < points.length; i++) { g.drawline(0, 0, points[i][0], points[i][1]); //

5 public static void main(string[] args) { new Lines("Lines"); // Canvas - DotLines.java import java.awt.*; public class DotLines extends Lines { private DotLines(String name) { super(name); // Lines public void paint(graphics g) { for (int i = 0; i < points.length; i++) { if (points[i][0] >= points[i][1]) { // x >= y ( ) int n = points[i][0]; // : n = x double d = ((double)points[i][1])/n; // 1 for (int x = 0; x <= n; x++) { // n g.fillrect(x, (int)(d*x+0.5), 1, 1); // else { // x < y ( ) int n = points[i][1]; // : n = y double d = ((double)points[i][0])/n; // 1 for (int y = 0; y <= n; y++) { // n g.fillrect((int)(d*y+0.5), y, 1, 1); // public static void main(string[] args) { new DotLines("DotLines"); // Canvas 4 - DDALines.java

6 6 1 Java DDA(Digital Differential Analyzer) ( ) import java.awt.*; public class DDALines extends Lines { private DDALines(String name) { super(name); // Lines public void paint(graphics g) { for (int i = 0; i < points.length; i++) { if (points[i][0] >= points[i][1]) { // x >= y ( ) int n = points[i][0]; // : n = x int dn = points[i][1] << 1; // * 2n int dr = dn - (n << 1); // ( -1) * 2n int e = dn - n; // ( -0.5) * 2n for (int x = 0, y = 0; x <= n; x++) { // n g.fillrect(x, y, 1, 1); // if (e > 0) { // (y 1 ) y++; e += dr; // & else { // (y ) e += dn; // else { // x < y ( ) int n = points[i][1]; // : n = y int dn = points[i][0] << 1; // * 2n int dr = dn - (n << 1); // ( -1) * 2n int e = dn - n; // ( -0.5) * 2n for (int x = 0, y = 0; y <= n; y++) { // n g.fillrect(x, y, 1, 1); // if (e > 0) { // (x 1 ) x++; e += dr; // & else { // (x ) e += dn; //

7 x (x o, y o) r y 1.3: public static void main(string[] args) { new DDALines("DDALines"); // Canvas 5 ( ) - Circle.java ( ) (x o, y o ) r x = r cos θ + x o, y = r sin θ + y o (θ [ π, π]) import java.awt.*; import java.awt.event.*; public class Circle extends Canvas { private static final int width = 600; private static final int height = 600; private static final int centerx = 300; private static final int centery = 299; private static final int radius = 250; protected int[][] points; // Canvas // Canvas // x // y // //

8 8 1 Java protected Circle(String name, int numberofpoints) { super(); // Canvas setsize(width, height); setbackground(color.white); // ( ) setforeground(color.black); // ( ) points = new int[numberofpoints+1][]; : n+1 for (int i = 0; i <= numberofpoints; i++) {// P_0 = p_n double theta = 2.0 * Math.PI * i / numberofpoints; // : n points[i] = new int[2]; points[i][0] = (int)(radius * Math.cos(theta)) + centerx; points[i][1] = (int)(radius * Math.sin(theta)) + centery; Frame f = new Frame(name); // Frame f.add(this); // Frame Canva f.pack(); // f.addwindowlistener(new WindowAdapter() { public void windowclosing(windowevent e) { System.exit(0); ); f.setvisible(true); // Frame public void paint(graphics g) { for (int i = 0; i < points.length - 1; i++) { g.drawline(points[i][0], points[i][1], // P_i P_i+1 points[i+1][0], points[i+1][1]); public static void main(string[] args) { if (args.length == 0) System.err.println("Usage: java Circle #"); else new Circle("Circle", Integer.parseInt(args[0])); // Canvas

9 ( ) ( ) (cone) (rod) (cone) ( ) ( ) RGB(Red Green Blue) ( 3 ) RGB ( 1.0) RGB Color ( R G B ) Red ( ) Green ( ) Blue ( ) Cyan ( ) Magenta ( ) Yellow ( ) White ( ) Black ( )

10 10 1 Java Black (0 0 0) Red (1 0 0) x=300, y=225 Green (0 1 0) x=213.4, y=375 Yellow Magenta (1 1 0) (1 0 1) White (1 1 1) Cyan (0 1 1) Blue (0 0 1) x=386.6, y= : 3 (RGB ) 3 CMY (Cyan Magenta Yellow) ( 3 ) CMY ( ) ( 1.0) CMY Color ( C M Y ) Cyan ( ) Magenta ( ) Yellow ( ) Red ( ) Green ( ) Blue ( ) Black ( ) White ( ) RGB CMY ( R G B ) = ( ) ( C M Y ) (1.1) HSB(HSV ) H, S, B 3 H, S, B (Hue) (Saturation) (Brightness/Value) RGB HSB 1 ( ) Java ( (300,225),(213.4,375),(386.6,375)

11 ) R = ( ), G = ( ), B = ( ) 3 3 import java.awt.*; import java.awt.event.*; public class AdditiveColor extends Canvas { protected static final int width = 600; // Canvas protected static final int height = 600; // Canvas protected static final double radius2 = * 180.0; // 2 protected double[][] centers = // {{300.0, 225.0, {213.4, 375.0, {386.6, 375.0; protected AdditiveColor(String name) { super(); setsize(width, height); // Canvas Frame f = new Frame(name); // Frame f.add(this); // Frame Canva f.pack(); // f.addwindowlistener(new WindowAdapter() { public void windowclosing(windowevent e) { System.exit(0); ); f.setvisible(true); // Frame public void paint(graphics g) { for (int y = 0; y < height; y++) { // y for (int x = 0; x < width; x++) { // x float[] color = new float[3]; // RGB for (int i = 0; i < 3; i++) { // RGB double dist2 = (x - centers[i][0]) * (x - centers[i][0]) + (y - centers[i][1]) * (y - centers[i][1]); color[i] = (dist2 > radius2)? 0.0f : 1.0f; 1 / 0

12 12 1 Java Cyan (0 1 1) Blue (0 0 1) R=0 G=1~0 B=1 R=0 G=1 B=0~1 Green (0 1 0) Magenta (1 0 1) R=0~1 G=0 B=1 R=1 G=0 B=1~0 R=1~0 G=1 B=0 y R=1 G=0~1 B=0 Yellow (1 1 0) Red (1 0 0) x 1.5: g.setcolor(new Color(color[0], color[1], color[2])); // (RGB ) g.fillrect(x, y, 1, 1); // 1 public static void main(string[] args) { new AdditiveColor("Additive Color");// Canvas π θ [0, ) : Red ( ) Yellow ( ) θ [ π, 2π ) : Yellow ( ) Green ( ) θ [ 2π, π) : Green ( ) Cyan ( ) 4π θ [π, ) : Cyan ( ) Blue ( ) θ [ 4π, 5π) : Blue ( ) Magenta ( ) θ [ 5π, 2π] : Magenta ( ) Red ( ) import java.awt.*;

13 import java.awt.event.*; public class ColorRingRGB extends Canvas { protected static final int width = 600; protected static final int height = 600; protected static final int centerx = 300; protected static final int centery = 299; protected static final int radius = 250; protected Color[] colors; protected int[][] points; // Canvas // Canvas // x // y // // // protected ColorRingRGB(String name, int numberofpoints) { super(); // Canvas setsize(width, height); setbackground(color.black); // ( ) setdata(numberofpoints); Frame f = new Frame(name); // Frame f.add(this); // Frame Canva f.pack(); // f.addwindowlistener(new WindowAdapter() { public void windowclosing(windowevent e) { System.exit(0); ); f.setvisible(true); // Frame protected void setdata(int numberofpoints) { final float onesixth = 1.0f / 6.0f; final float twosixth = 2.0f / 6.0f; final float threesixth = 3.0f / 6.0f; final float foursixth = 4.0f / 6.0f; final float fivesixth = 5.0f / 6.0f; final float six = 6.0f; colors = new Color[numberOfPoints+1]; : n+1 points = new int[numberofpoints+1][]; : n+1 for (int i = 0; i <= numberofpoints; i++) { float ratio = (float)i / numberofpoints;

14 14 1 Java // if (ratio <= onesixth) { // 0 <= t <= 1/6 colors[i] = new Color(1.0f, ratio*six, 0.0f); else if (ratio <= twosixth) { // 1/6 < t <= 2/6 colors[i] = new Color((twoSixth-ratio)*six, 1.0f, 0.0f); else if (ratio <= threesixth) { // 2/6 < t <= 3/6 colors[i] = new Color(0.0f, 1.0f, (ratio-twosixth)*six); else if (ratio <= foursixth) { // 3/6 < t <= 4/6 colors[i] = new Color(0.0f, (foursixth-ratio)*six, 1.0f); else if (ratio <= fivesixth) { // 4/6 < t <= 5/6 colors[i] = new Color((ratio-fourSixth)*six, 0.0f, 1.0f); else { // 5/6 < t <= 1 colors[i] = new Color(1.0f, 0.0f, (1.0f-ratio)*six); double theta = 2.0 * Math.PI * ratio; // (radian) points[i] = new int[2]; points[i][0] = (int)(radius * Math.cos(theta)) + centerx; points[i][1] = (int)(radius * Math.sin(theta)) + centery; public void paint(graphics g) { for (int i = 0; i < points.length - 1; i++) { g.setcolor(colors[i]); // (RGB ) g.drawline(points[i][0], points[i][1], points[i+1][0], points[i+1][1]); // P_i P_i+1 public static void main(string[] args) { if (args.length == 0) System.err.println("Usage: java ColorRingRGB #"); else new ColorRingRGB("ColorRingRGB", Integer.parseInt(args[0])); HSB

15 HSB import java.awt.*; import java.awt.event.*; public class ColorDisk extends Canvas { protected static final int width = 600; protected static final int height = 600; protected static final int centerx = 300; protected static final int centery = 299; protected static final int radius = 250; // Canvas // Canvas // x // y // protected ColorDisk(String name) { super(); setsize(width, height); // Canvas Frame f = new Frame(name); // Frame f.add(this); // Frame Canva f.pack(); // f.addwindowlistener(new WindowAdapter() { public void windowclosing(windowevent e) { System.exit(0); ); f.setvisible(true); // Frame public void paint(graphics g) { for (int y = 0; y < height; y++) { // y for (int x = 0; x < width; x++) { // x double dx = (double)(x-centerx); // x double dy = (double)(y-centery); // y float h = (float)(math.atan2(dy, dx) / (2.0 * Math.PI)); // x / 2PI float s = (float)(math.sqrt(dx*dx + dy*dy) / radius); // float b = (s > 1.0f)? 0.0f : 1.0f; // 1 / 0 if (s > 1.0f) s = 0.0f; // s 1 g.setcolor(color.gethsbcolor(h, s, b)); // (HSB )

16 16 1 Java g.fillrect(x, y, 1, 1); // 1 public static void main(string[] args) { new ColorDisk("ColorDisk"); // Canvas 1.3 (interactive; ) (event) ( ) (event driven) (event source) ( ) Canvas Canvas ( ) EventListener ( ) EventListener( ) EventListener Canvas Component addeventlistener EventListener Java EventListener EventAdapter ( ) EventListener EventAdapter EventAdapter Canvas EventAdapter

17 MouseEvent Java ( ) MouseEvent MouseEvent MouseEvent EventListener/Adapter MOUSE CLICKED MouseListener/Adapter mouseclicked MOUSE ENTERED MouseListener/Adapter mouseentered MOUSE EXITED MouseListener/Adapter mouseexited MOUSE PRESSED MouseListener/Adapter mousepressed MOUSE RELEASED MouseListener/Adapter mousereleased MOUSE DRAGGED MouseMotionListener/Adapter mousedragged MOUSE MOVED MouseMotionListener/Adapter mousemoved MouseEvent ( ) getmodifiers MouseEvent getx gety - Background.java Canvas MouseEvent Canvas Background EventListener MouseAdapter BAMouseAdapter MouseEvent BAMouseAdapter mousepressed mousereleased Background mousepressed mousereleased MouseEvent BAMouseAdapter Backround ba import java.awt.*; import java.awt.event.*; public class Background extends Canvas { private static final int width = 200; private static final int height = 200; // Canvas // Canvas private Background() { super(); // Canvas setsize(width, height); setbackground(color.green); // ( ) addmouselistener(new BgMouseAdapter(this)); Frame f = new Frame("Background"); f.add(this); // Frame // Frame Canva

18 18 1 Java f.pack(); // f.setvisible(true); // Frame f.addwindowlistener(new WindowAdapter() { public void windowclosing(windowevent e) { System.exit(0); ); protected void mousepressed(mouseevent me) { setbackground(color.red); repaint(); // ( ) (update) protected void mousereleased(mouseevent me) { setbackground(color.green); // ( ) repaint(); (update) public static void main(string[] args) { new Background(); // Canvas class BgMouseAdapter extends MouseAdapter { private Background bg; public BgMouseAdapter(Background bg) { this.bg = bg; public void mousepressed(mouseevent me) { bg.mousepressed(me); public void mousereleased(mouseevent me) { bg.mousereleased(me); ( ) - BackgroundListener.java MouseAdapter MouseLinstener (

19 ) Background MouseListener EventListener import java.awt.*; import java.awt.event.*; public class BackgroundListener extends Canvas implements MouseListener { private static final int width = 200; // Canvas private static final int height = 200; // Canvas private BackgroundListener() { super(); setsize(width, height); setbackground(color.green); addmouselistener(this); // Canvas // ( ) Frame f = new Frame("BackgroundListener"); // Frame f.add(this); // Frame Canva f.pack(); // f.setvisible(true); // Frame f.addwindowlistener(new WindowAdapter() { public void windowclosing(windowevent e) { System.exit(0); ); public void mousepressed(mouseevent me) { setbackground(color.red); repaint(); public void mousereleased(mouseevent me) { setbackground(color.green); repaint(); public void mouseentered(mouseevent me) { public void mouseexited(mouseevent me) { // ( ) (update) // ( ) (update)

20 20 1 Java public void mouseclicked(mouseevent me) { public static void main(string[] args) { new BackgroundListener(); // Canvas ( ) - BackgroundInner.java MouseAdapter BgMouseAdapter BackgroundInner BackgroundInner BackgroundInner setbackground repaint BgMouseAdapter import java.awt.*; import java.awt.event.*; public class BackgroundInner extends Canvas { private static final int width = 200; private static final int height = 200; // Canvas // Canvas private BackgroundInner() { super(); // Canvas setsize(width, height); setbackground(color.green); // ( ) addmouselistener(new BgMouseAdapter()); Frame f = new Frame("BackgroundInner"); // Frame f.add(this); // Frame Canva f.pack(); // f.setvisible(true); // Frame f.addwindowlistener(new WindowAdapter() { public void windowclosing(windowevent e) { System.exit(0); ); class BgMouseAdapter extends MouseAdapter { public void mousepressed(mouseevent me) { setbackground(color.red); // ( )

21 repaint(); (update) public void mousereleased(mouseevent me) { setbackground(color.green); // ( ) repaint(); (update) public static void main(string[] args) { new BackgroundInner(); // Canvas ( ) - BackgroundAnonymous.java MouseAdapter f.addwindowlistener WindowAdapter import java.awt.*; import java.awt.event.*; public class BackgroundAnonymous extends Canvas { private static final int width = 200; // Canvas private static final int height = 200; // Canvas private BackgroundAnonymous() { super(); // Canvas setsize(width, height); setbackground(color.green); // ( ) addmouselistener(new MouseAdapter() { public void mousepressed(mouseevent me) { setbackground(color.red); // ( ) repaint(); (update) public void mousereleased(mouseevent me) { setbackground(color.green); // ( ) repaint(); (update) );

22 22 1 Java Frame f = new Frame("BackgroundAnonymous"); // Frame f.add(this); // Frame Canva f.pack(); // f.setvisible(true); // Frame f.addwindowlistener(new WindowAdapter() { public void windowclosing(windowevent e) { System.exit(0); ); public static void main(string[] args) { new BackgroundAnonymous(); // Canvas - Marker.java getmodifiers int getx gety repaint update import java.awt.*; import java.awt.event.*; public class Marker extends Canvas { private static final int width = 400; private static final int height = 400; private static final int SIZE = 10; // Canvas // Canvas // 1 private Marker() { super(); // Canvas setsize(width, height); setbackground(color.white); // ( ) addmouselistener(new MouseAdapter () { public void mousepressed(mouseevent me) { int modifiers = me.getmodifiers(); //

23 ); Graphics g = getgraphics(); // Graphics if ((modifiers & MouseEvent.BUTTON3_MASK)!= 0) g.setcolor(color.blue); // 3( ) // else if ((modifiers & MouseEvent.BUTTON2_MASK)!= 0) // g.setcolor(color.blue); // 2( ) Mac else g.setcolor(color.red); // ( ) int x = me.getx(); // x int y = me.gety(); // y g.fillrect(x - (SIZE/2), y - (SIZE/2), SIZE, SIZE); // Frame f = new Frame("Marker"); // Frame f.add(this); // Frame Canva f.pack(); // f.setvisible(true); // Frame f.addwindowlistener(new WindowAdapter() { public void windowclosing(windowevent e) { System.exit(0); ); public static void main(string[] args) { new Marker(); // Canvas - Rubberband.java MouseListener MuoseMotionListener ( ) ( ) import java.awt.*; import java.awt.event.*; public class Rubberband extends Canvas { private static final int width = 400; private static final int height = 400; private int startx; // Canvas // Canvas // x

24 24 1 Java private int starty; // y private Rubberband() { super(); // Canvas setsize(width, height); setbackground(color.white); // ( ) setforeground(color.black); // ( ) addmouselistener(new MouseAdapter() { public void mousepressed(mouseevent me) { startx = me.getx(); // x ( ) starty = me.gety(); // y ( ) ); addmousemotionlistener(new MouseMotionAdapter() { public void mousedragged(mouseevent me) { Graphics g = getgraphics(); // Graphics update(g); // int x = me.getx(); // x int y = me.gety(); // y g.drawline(startx, starty, x, y); // ); Frame f = new Frame("Rubberband"); // Frame f.add(this); // Frame Canva f.pack(); // f.setvisible(true); // Frame f.addwindowlistener(new WindowAdapter() { public void windowclosing(windowevent e) { System.exit(0); ); public static void main(string[] args) { new Rubberband(); // Canvas - Draw.java

25 import java.awt.*; import java.awt.event.*; public class Draw extends Canvas { private static final int width = 400; private static final int height = 400; private int oldx; private int oldy; // Canvas // Canvas // x // y private Draw() { super(); // Canvas setsize(width, height); setbackground(color.white); // ( ) setforeground(color.black); // ( ) addmouselistener(new MouseAdapter() { public void mousepressed(mouseevent me) { oldx = me.getx(); // x ( ) oldy = me.gety(); // y ( ) ); addmousemotionlistener(new MouseMotionAdapter() { public void mousedragged(mouseevent me) { int x = me.getx(); // x int y = me.gety(); // y getgraphics().drawline(oldx, oldy, x, y);// oldx = x; oldy = y; ); Frame f = new Frame("Draw"); // Frame f.add(this); // Frame Canva f.pack(); // f.setvisible(true); // Frame f.addwindowlistener(new WindowAdapter() { public void windowclosing(windowevent e) { System.exit(0); );

26 26 1 Java public static void main(string[] args) { new Draw(); // Canvas 1.4 ( ) 2 Canvas (tolerance) 2 ( ) - Tolerance.java public class Tolerance { public final static double EPSILON = 1.0e-6; 2 2 (x, y) 2 - Vector2D.java import java.util.*; public class Vector2D { private double x, y; public Vector2D(double x, double y) { ( ) this.x = x; this.y = y; public Vector2D(Vector2D v) { ( ) this.x = v.x; this.y = v.y; public Vector2D(String str) { ( ) StringTokenizer st = new StringTokenizer(str);

27 1.4. ( ) 2 27 this.x = Double.parseDouble(st.nextToken()); this.y = Double.parseDouble(st.nextToken()); public double x() { // x return this.x; public double y() { // y return this.y; public double norm() { // ( ) return Math.sqrt(this.x * this.x + this.y * this.y); public Vector2D add(vector2d v) { // return new Vector2D(this.x + v.x, this.y + v.y); public Vector2D subtract(vector2d v) { // return new Vector2D(this.x - v.x, this.y - v.y); public Vector2D scale(double d) { // ( ) return new Vector2D(this.x * d, this.y * d); public Vector2D normalize() { // double norm = this.norm(); if (norm > Tolerance.EPSILON) return this.scale(1.0 / norm); else return (new Vector2D(0.0, 0.0)); public String tostring() { // return "(" + x + ", " + y + ")"; (affine transformation) p = Mp + v M ( 2 2 ) v ( ) 2

28 28 1 Java - x, y s x, s y [ sx 0 M = 0 s y ] - θ [ cos θ sin θ M = sin θ cos θ ] - v = [ t x t y ] T v = [ ] tx t y Matrix2X2.java public class Matrix2X2 { private double xx, xy, yx, yy; // public Matrix2X2(double xx, double xy, double yx, double yy) { this.xx = xx; this.xy = xy; ( ) this.yx = yx; this.yy = yy; public Matrix2X2(Matrix2X2 m) { ( ) this.xx = m.xx; this.xy = m.xy; this.yx = m.yx; this.yy = m.yy; public Vector2D apply(vector2d v) { return new Vector2D(xx*v.x() + xy*v.y(), yx*v.x() + yy*v.y()); public Matrix2X2 multiply(matrix2x2 m) { // return new Matrix2X2((xx*m.xx + xy*m.yx), (xx*m.xy + xy*m.yy), (yx*m.xx + yy*m.yx), (yx*m.xy + yy*m.yy)); public static Matrix2X2 rotate(double t) { return new Matrix2X2(Math.cos(t), -Math.sin(t), Math.sin(t), Math.cos(t)); public static Matrix2X2 scale(double s) { return new Matrix2X2(s, 0.0, 0.0, s);

29 1.4. ( ) 2 29 Canvas - CGCanvas.java CGCanvas x, y 1 import java.awt.*; import java.awt.event.*; public class CGCanvas extends Canvas { private Frame f; private double x, y; private int width = 600; private int height = 600; private int originx = 300; private int originy = 299; protected double range = 2.0; protected double scale = width/range; protected int markersize = 5; // Frame // Canvas // Canvas // x // y ( ) // Canvas // ( ) public CGCanvas(String name) { super(); setsize(width, height); setbackground(color.white); setforeground(color.black); // Canvas // ( ) // ( ) f = new Frame(name); // Frame f.add(this); // Frame Canva f.pack(); // f.addwindowlistener(new WindowAdapter() { public void windowclosing(windowevent e) { System.exit(0); ); public void showframe() { f.setvisible(true); // Frame public void setorigin(int x, int y) { originx = x; originy = y; public void setrange(double r) {

30 30 1 Java Dimension d = getsize(); // Canvas width = d.width; height = d.height; range = r; scale = Math.min(width, height) / range; public void drawline(graphics g, Vector2D from, Vector2D to) { g.drawline(x(from), y(from), x(to), y(to)); // public void drawpoint(graphics g, Vector2D point) { g.fillrect(x(point), y(point), 1, 1); // public void drawpolygon(graphics g, Vector2D[] points) { int[] x = new int[points.length]; // ( ) int[] y = new int[points.length]; for (int i = 0; i < points.length; i++) { x[i] = x(points[i]); y[i] = y(points[i]); g.drawpolygon(x, y, points.length); public void drawcircle(graphics g, Vector2D point, int radius) { int dr = (int) (radius * scale); // g.drawoval(x(point) - dr, y(point) - dr, dr * 2, dr * 2); public void drawstring(graphics g, Vector2D point, String str) { g.drawstring(str, x(point), y(point)); // public void fillmarker(graphics g, Vector2D point) { g.fillrect(x(point) - markersize / 2, y(point) - markersize / 2, markersize, markersize); // ( ) public void fillpolygon(graphics g, Vector2D[] points) { int[] x = new int[points.length]; // ( ) int[] y = new int[points.length]; for (int i = 0; i < points.length; i++) { x[i] = x(points[i]); y[i] = y(points[i]); g.fillpolygon(x, y, points.length);

31 1.4. ( ) 2 31 public Vector2D point(int x, int y) { return new Vector2D((x - originx) / scale, (originy - y) / scale); // Canvas protected final int x(vector2d point) { return (int) (scale * point.x()) + originx; // Canvas x protected final int y(vector2d point) { return -(int) (scale * point.y()) + originy; // Canvas y protected final boolean inside(vector2d point) { int x = (int) (scale * point.x()) + originx; if (x < 0 x >= width) return false; int y = -(int) (scale * point.y()) + originy; if (y < 0 y >= height) return false; return true; ( ) - CGDiamondPattern.java CGCanvas import java.awt.*; public class CGDiamondPattern extends CGCanvas { private final static double radius = 0.8; // private Vector2D[] points; private CGDiamondPattern(int numberofpoints) { super("cgdiamondpattern"); // CGCanvas points = new Vector2D[numberOfPoints]; // for (int i = 0; i < numberofpoints; i++) { // double theta = 2.0 * Math.PI * i / numberofpoints; points[i] = new Vector2D(radius*Math.cos(theta), radius*math.sin(theta)); public void paint(graphics g) {

32 32 1 Java for (int i = 0; i < points.length - 1; i++) for (int j = i + 1; j < points.length; j++) drawline(g, points[i], points[j]); // 2 public static void main(string[] args) { if (args.length == 0) System.err.println("Usage: java CGDiamondPattern #"); else (new CGDiamondPattern(Integer.parseInt(args[0]))).showFrame(); 1.5 (Fractal) (self-similarity) (Hausdorff dimension) ( ) (1 ) (2 ) (3 ) n ( ) 1/s s n (Iterated Function System: IFS) Koch.java /3 4 log 3 4 = import java.awt.*; public class Koch extends CGCanvas { private int times; private Vector2D initp0; private Vector2D initp1;

33 : private Matrix2X2[] m; private Vector2D[] v; private Koch(int times) { super("koch"); this.times = times; setorigin(50, 299); setrange(1.2); initp0 = new Vector2D(0.0, 0.0); initp1 = new Vector2D(1.0, 0.0); // CGCanvas // // ( ) // m = new Matrix2X2[4]; v = new Vector2D[4]; m[0] = Matrix2X2.scale(1.0/3.0); // m[1] = Matrix2X2.scale(1.0/3.0). multiply(matrix2x2.rotate(math.pi/3.0)); m[2] = Matrix2X2.scale(1.0/3.0). multiply(matrix2x2.rotate(-math.pi/3.0)); m[3] = Matrix2X2.scale(1.0/3.0);

34 34 1 Java v[0] = new Vector2D(0.0, 0.0); v[1] = m[0].apply(new Vector2D(1.0, 0.0)).add(v[0]); v[2] = m[1].apply(new Vector2D(1.0, 0.0)).add(v[1]); v[3] = m[2].apply(new Vector2D(1.0, 0.0)).add(v[2]); public void paint(graphics g) { drawsegment(g, initp0, initp1, times); private void drawsegment(graphics g, Vector2D p0, Vector2D p1, int l) { if (l > 0) // for (int i = 0; i < m.length; i++) drawsegment(g, m[i].apply(p0).add(v[i]), m[i].apply(p1).add(v[i]), l-1); else // drawline(g, p0, p1); public static void main(string[] args) { if (args.length!= 1) System.err.println("Usage: Koch #iteration"); else (new Koch(Integer.parseInt(args[0]))).showFrame(); - Sierpinski.java 2 4 1/2 3 log 2 3 = import java.awt.*; public class Sierpinski extends CGCanvas { private int times; private Vector2D[] initpoints; private Matrix2X2[] m; private Vector2D[] v; private Sierpinski(int times) {

35 super("sierpinski"); // CGCanvas this.times = times; // setorigin(300, 84); setrange(2.4); initpoints = new Vector2D[3]; // 3 initpoints[0] = new Vector2D( 0.0, 0.0); initpoints[1] = new Vector2D(-1.0, -Math.sqrt(3.0)); initpoints[2] = new Vector2D( 1.0, -Math.sqrt(3.0)); m = new Matrix2X2[3]; v = new Vector2D[3]; m[0] = Matrix2X2.scale(1.0/2.0); // m[1] = Matrix2X2.scale(1.0/2.0); m[2] = Matrix2X2.scale(1.0/2.0); v[0] = new Vector2D( 0.0, 0.0); v[1] = new Vector2D(-0.5, -Math.sqrt(3.0)/2.0); v[2] = new Vector2D( 0.5, -Math.sqrt(3.0)/2.0); public void paint(graphics g) { drawtriangle(g, initpoints, times); private void drawtriangle(graphics g, Vector2D[] points, int l) { if (l > 0) { // for (int i = 0; i < m.length; i++) { Vector2D[] newpoints = new Vector2D[3]; for (int j = 0; j < 3; j++) newpoints[j] = m[i].apply(points[j]).add(v[i]); drawtriangle(g, newpoints, l-1); else { // g.setcolor(color.lightgray); fillpolygon(g, points); g.setcolor(color.black); drawpolygon(g, points);

36 36 1 Java public static void main(string[] args) { if (args.length!= 1) System.err.println("Usage: Sierpinski #iteration"); else (new Sierpinski(Integer.parseInt(args[0]))).showFrame(); 1.6 ( )t ( / ) 1 (parametric curve) x = g(t), y = h(t) { x = r cos t y = r sin t x = 2rt 1+t 2 y = r(1 t2 ) 1+t 2 CG (implicit curve) f(x, y) = 0 x 2 + y 2 r 2 = 0 (function curve) y x y = f(x) y = r 2 x 2 - ParametricCurve.java public interface ParametricCurve { public Vector2D evaluate(double t); public double begin(); public double end(); // - CurveCanvas.java import java.awt.*; public class CurveCanvas extends CGCanvas {

37 final static int NOP = 128; final static double RATIO = 8.0; protected ParametricCurve[] curves; // protected CurveCanvas(String name){ super(name); // CGCanvas protected void drawcurve(graphics g, ParametricCurve curve, double ts, double te, int nofpoints, double borderratio) { double delta = (te - ts)/nofpoints; // te -> ts Vector2D prev = null; // (prev ) boolean previn = false; // (prev ) for (int i = 0; i <= nofpoints; i++) { // nofpoints Vector2D point = curve.evaluate(ts + delta * i); // boolean in = inside(point); // if (prev!= null && (previn in)) drawline(g, prev, point); // 1 prev = point; // previn = in; protected void drawcurve(graphics g, ParametricCurve curve) { drawcurve(g, curve, curve.begin(), curve.end(), NOP, RATIO); public void paint(graphics g) { if (curves!= null) // curves for (int i = 0; i < curves.length; i++) if (curves[i]!= null) drawcurve(g, curves[i]); - DiagonalCanvas.java import java.awt.*; public class DiagonalCanvas extends CurveCanvas {

38 38 1 Java public DiagonalCanvas() { super("diagonal Canvas"); // CurveCanvas setrange(8.0); curves = new ParametricCurve[3]; curves[0] = new Sine(-Math.PI, 0.0); curves[1] = new Cosine(-Math.PI, 0.0); curves[2] = new Tangent(-Math.PI, 0.0); public void paint(graphics g) { g.setcolor(color.blue); // ( ) super.paint(g); // g.setcolor(color.black); // ( ) drawline(g, new Vector2D(-Math.PI, 4.0), new Vector2D(-Math.PI, -4.0)); drawline(g, new Vector2D(-4.0, 0.0), new Vector2D(4.0, 0.0)); // public static void main(string[] args) { new DiagonalCanvas().showFrame(); abstract class Diagonal implements ParametricCurve { protected Vector2D translation; Diagonal(double x, double y) { translation = new Vector2D(x, y); public double begin() { return -0.5 * Math.PI; public double end() { return 2.5 * Math.PI; class Sine extends Diagonal { Sine(double x, double y) { super(x, y); // ParametricCurve

39 public Vector2D evaluate(double t) { // return (new Vector2D(t, Math.sin(t))).add(translation); class Cosine extends Diagonal { Cosine(double x, double y) { super(x, y); // ParametricCurve public Vector2D evaluate(double t) { // return (new Vector2D(t, Math.cos(t))).add(translation); class Tangent extends Diagonal { Tangent(double x, double y) { super(x, y); // ParametricCurve public Vector2D evaluate(double t) { // return (new Vector2D(t, Math.tan(t))).add(translation); (Bézier curve) P 0, P 1,, P n 3 ( 3) P(t) = (1 t) 3 P 0 + 3(1 t) 2 tp 1 + 3(1 t)t 2 P 2 + t 3 P 3 0 t 1 1 (1 t) 3 + 3(1 t) 2 t + 3(1 t)t 2 + t 3 = ((1 t) + t) 3 = 1 t = 0, 1 P(0) = P 0, P(1) = P 3, dp dt (0) = 3(P 1 P 0 ), dp dt (1) = 3(P 3 P 2 ) 3 - CubicBezier.java public class CubicBezier implements ParametricCurve { private Vector2D[] points; //

40 40 1 Java public CubicBezier(Vector2D[] points) { this.points = points; // public Vector2D[] points() { return points; // public Vector2D evaluate(double t) { // double[] ts = new double[4]; ( ) double u = t; ts[0] = u*u*u; ts[1] = 3.0*u*u*t; ts[2] = 3.0*u*t*t; ts[3] = t*t*t; Vector2D point = new Vector2D(0.0, 0.0); for (int j = 0; j <= 3; j++) // 4 point = point.add(points[j].scale(ts[j])); return point; public double begin() { return 0.0; public double end() { return 1.0; - CubicBezierCanvas.java import java.awt.*; public class CubicBezierCanvas extends CurveCanvas { public CubicBezierCanvas() { ( ) super("cubic Bezier Canvas"); public CubicBezierCanvas(Vector2D[] points) { super("cubic Bezier Canvas"); ( ) curves = new ParametricCurve[1]; curves[0] = new CubicBezier(points);

41 public void paint(graphics g) { super.paint(g); // if (curves!= null) // for (int i = 0; i < curves.length; i++) drawpoints(g, ((CubicBezier)curves[i]).points()); private void drawpoints(graphics g, Vector2D[] points) { if (points!= null) { // Color tmpcolor = g.getcolor(); // (tmp) g.setcolor(color.blue); // ( ) fillmarker(g, points[0]); // 1 for (int i = 1; i < points.length; i++) { fillmarker(g, points[i]); drawline(g, points[i - 1], points[i]); g.setcolor(tmpcolor); // (tmp) public static void main(string[] args) { if (args.length!= 8) System.err.println( "Usage: java CubicBezierCanvas x0 y0 x1 y1 x2 y2 x3 y3"); else { Vector2D[] points = new Vector2D[4]; for (int i = 0; i < 4; i++) points[i] = new Vector2D(Double.parseDouble(args[2*i]), Double.parseDouble(args[2*i+1])); (new CubicBezierCanvas(points)).showFrame();

42 42 1 Java 1.7 JOGL OpenGL 3 ( ) C C++ Java JOGL JNI(Java Native Interface) JOGL Java (SDK) JOGL jogl.jar C/C++ JNI (OS ) OS JNI-jar JNI MacOS X jogl-natives-macosx.jar libjogl.jnilib, libjogl cg.jnilib Windows jogl-natives-win32.jar jogl.dll, jogl cg.dll JNI jar JNI-jar MacOS jogl.jar JNI /Library /Java/Extensions ca10101$ jar xf jogl-natives-macosx.jar ca10101$ mkdir ~/Library/Java ca10101$ mkdir ~/Library/Java/Extensions ca10101$ cp jogl.jar ~/Library/Java/Extensions ca10101$ cp libjogl.jnilib ~/Library/Java/Extensions ca10101$ cp libjogl_cg.jnilib ~/Library/Java/Extensions ca10101$ javac File.java ca10101$ java File ( ) 3 OpenGL/JOGL CFIVE jogl.jar JNI (MacOS )

43 : 1. / 3 2. (clipping) 3 (viewing volume) 3 (viewing frustum) (perspective transformation) (window-viewport transformation)

44 44 1 Java 1.8: 7. (rasterization) (JOGL/OpenGL ) ( ) ( ) 1.8 OpenGL void gluperspective(double fieldofview, double aspect, double near, double far); (GL_PROJECTION ) fieldofview y ( ) ( ) aspect xy near far void glulookat(double ex, double ey, double ez, double rx, double ry, double rz, double upx, double upy, double upz); (GL_MODEL_VIEW )

45 ex,ey,ez rx,ry,rz ( ) upx,upy,upz glbegin( ) glend() ( ) GL_POINTS GL_LINES 2 1 GL_LINE_STRIP GL_LINE_LOOP ( ) GL_TRIANGLES 3 1 GL_QUADS 4 1 GL_POLYGON GL_QUAD_STRIP ( ) GL_TRIANGLE_STRIP ( ) GL_TRIANGLE_FAN gl{vertex,color,normal{3,4{i,f,d[v] Vertex,Color,Normal:,, 3,4 : 3 4 i,f,d : int, float, double v : Z ( ) (RGB) (Z) ( ) ( ) JOGL(OpenGL) Z glenable(gl DEPTH TEST) ( glenable(gl CULL FACE)) Z JOGL(OpenGL)

46 46 1 Java P V P 2 P 2 P 3 P 3 P 1 P 1 P 0 P 0 1.9: 1.10: ( ) V 0 = [x 0 y 0 z 0 ] T, V 1 = [x 1 y 1 z 1 ] T V 0 V 1 = x 0 x 1 + y 0 y 1 + z 0 z 1 > 0 V 0, V 1 π 2 V 0 V 1 = 0 < 0 V 0, V 1 π 2 V 0, V 1 π 2 ( ) V 0 = [x 0 y 0 z 0 ] T, V 1 = [x 1 y 1 z 1 ] T y 0 z 1 y 1 z 0 V 0 V 1 = z 0 x 1 z 1 x 0 x 0 y 1 x 1 y 0 V 0, V 1 - CubePosition.java

47 vertices faces y import java.awt.*; import java.awt.event.*; import net.java.games.jogl.*; // jogl public class CubePosition implements GLEventListener { private Frame f; // Frame protected GL gl; // GL protected GLU glu; // GLU protected double eye_x = 4.0, eye_y = 3.0, eye_z = 7.0; // protected CubePosition(String name) { GLCanvas canvas = // JOGL GLCanvas GLDrawableFactory.getFactory(). createglcanvas(new GLCapabilities()); canvas.addgleventlistener(this); // GL f = new Frame(name); // Frame f.add(canvas); // Frame GLCanvas f.setsize(500, 500); f.addwindowlistener(new WindowAdapter() { public void windowclosing(windowevent e) { System.exit(0); ); protected CubePosition(String name, String[] args) { this(name); eye_x = Double.parseDouble(args[0]); // (x ) eye_y = Double.parseDouble(args[1]); // (y ) eye_z = Double.parseDouble(args[2]); // (z ) protected void showframe() { f.setvisible(true); // Frame

48 48 1 Java public void init(gldrawable drawable) { // gl = drawable.getgl(); // GL glu = drawable.getglu(); // GLU gl.glclearcolor(0.0f, 0.0f, 0.0f, 1.0f); // gl.glenable(gl.gl_depth_test); gl.glenable(gl.gl_cull_face); // public void reshape(gldrawable drawable, int x, int y, int w, int h) { final double fieldofview = 25.0, near = 1.0, far = 20.0; // ( ), / double aspect = (double) w / (double) h; // gl.glmatrixmode(gl.gl_projection); // gl.glloadidentity(); // glu.gluperspective(fieldofview, aspect, near, far); gl.glmatrixmode(gl.gl_modelview); // gl.glloadidentity(); // glu.glulookat(eye_x, eye_y, eye_z, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0); public void display(gldrawable drawable) { // gl.glclear(gl.gl_color_buffer_bit GL.GL_DEPTH_BUFFER_BIT); cube(); ( ) void cube() { // float[][] vertices = { { -1.0f, -1.0f, -1.0f, { 1.0f, -1.0f, -1.0f, { 1.0f, 1.0f, -1.0f, { -1.0f, 1.0f, -1.0f, { -1.0f, -1.0f, 1.0f, { 1.0f, -1.0f, 1.0f, { 1.0f, 1.0f, 1.0f, { -1.0f, 1.0f, 1.0f ; // int[][] faces = { { 1, 2, 6, 5, { 2, 3, 7, 6, { 4, 5, 6, 7, { 0, 4, 7, 3, { 0, 1, 5, 4, { 0, 3, 2, 1 ; float[][] colors = { { 0.0f, 1.0f, 1.0f, { 1.0f, 0.0f, 1.0f, { 1.0f, 1.0f, 0.0f, { 0.0f, 0.5f, 0.5f, { 0.5f, 0.0f, 0.5f, { 0.5f, 0.5f, 0.0f ; //

49 1.9. (homogeneous coordinates) 49 gl.glbegin(gl.gl_quads); for (int i = 0; i < faces.length; i++) { gl.glcolor3fv(colors[i]); // for (int j = 0; j < faces[i].length; j++) gl.glvertex3fv(vertices[faces[i][j]]); gl.glend(); public void displaychanged(gldrawable drawable, boolean modechanged, boolean devicechanged) { ( ) public static void main(string[] args) { if (args.length == 3) // (new CubePosition("CubePosition Demo", args)).showframe(); else // (new CubePosition("CubePosition Demo")).showFrame(); 1.9 (homogeneous coordinates) P (3) = [x (3) y (3) z (3) ] T R 3 4 P = [x y z w] T R 4 P (3) P x = x (3) w, y = y (3) w, y = y (3) w, w 0 2 [x y z w] T [ x z w w 1]T 3 [ x (3) y (3) z (3) ] T w w w ( ) ( ) M ( ) x P y = z = MP = 1 y w s x s y s y x y z 1 = s x x s y y s z z 1

50 50 1 Java θ x P = x y z 1 = MP = cos θ sin θ 0 0 sin θ cos θ x y z 1 = x y cos θ z sin θ y sin θ + z cos θ 1 y P = x y z 1 = MP = cos θ 0 sin θ sin θ 0 cos θ x y z 1 = x cos θ + z sin θ y x sin θ + z cos θ 1 z P = x y z 1 = MP = cos θ sin θ 0 0 sin θ cos θ x y z 1 = x cos θ y sin θ x sin θ + y cos θ z 1 ( ) P = x y z 1 = MP = t x t y t z x y z 1 = x + t x y + t y z + t z 1 ( ) z x y z P = x y z 1 = MP = d d 0 x y z 1 = x y z 1 d z d xd z yd z d 1 z 1 M 1 M 2 M 3 P = M 1 (M 2 (M 3 P)) = (M 1 M 2 M 3 )P (identity matrix) 1

51 1.9. (homogeneous coordinates) 51 IP = x y z 1 = x y z 1 = P - CubeMatrix.java 1.8 CubePosition GL_MODEL_VIEW 1 import net.java.games.jogl.*; // jogl public class CubeMatrix extends CubePosition { protected CubeMatrix(String name) { super(name); protected CubeMatrix(String name, String[] args) { super(name, args); public void reshape(gldrawable drawable, int x, int y, int w, int h) { final double fieldofview = 25.0, near = 1.0, far = 20.0; // ( ), / double aspect = (double) w / (double) h; // gl.glmatrixmode(gl.gl_projection); // gl.glloadidentity(); // glu.gluperspective(fieldofview, aspect, near, far); gl.glmatrixmode(gl.gl_modelview); // gl.glloadidentity(); // double eye_xz = Math.sqrt(eye_x * eye_x + eye_z * eye_z); double eye_xyz = Math.sqrt(eye_xz * eye_xz + eye_y * eye_y); double[] translate = { // (z ) 1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, -eye_xyz, 1.0f ; gl.glmultmatrixd(translate);

52 52 1 Java double sinp = eye_y / eye_xyz, cosp = eye_xz / eye_xyz; double[] rotatex = { // (x ) 1.0f, 0.0f, 0.0f, 0.0f, 0.0f, cosp, sinp, 0.0f, 0.0f, -sinp, cosp, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f ; gl.glmultmatrixd(rotatex); double sint = eye_x / eye_xz, cost = eye_z / eye_xz; double[] rotatey = { // (y ) cost, 0.0f, sint, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, -sint, 0.0f, cost, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f ; gl.glmultmatrixd(rotatey); public static void main(string[] args) { if (args.length == 3) // (new CubeMatrix("CubeMatrix Demo", args)).showframe(); else // (new CubeMatrix("CubeMatrix Demo")).showFrame(); ( ) OpenGL 1 (GL_PROJECTION GL_MODEL_VIEW ) OpenGL ( ) ( A + B) 3. push A pop 4. push B pop A A B B 1.10

53 1.9. (homogeneous coordinates) 53 - CubeAngle.java 10 import net.java.games.jogl.*; // jogl public class CubeAngle extends CubePosition { private double fieldofview = 25.0, near = 1.0, far = 20.0; // ( ), / private float rotx = 20.0f, roty = -30.0f, rotz = 0.0f; // x,y,z CubeAngle(String name) { super(name); CubeAngle(String name, String[] args) { super(name); switch (args.length) { case 1: // fieldofview = Double.parseDouble(args[0]); break; case 2: near = Double.parseDouble(args[0]); far = Double.parseDouble(args[1]); break; case 3: // rotx = Float.parseFloat(args[0]); // x roty = Float.parseFloat(args[1]); // y rotz = Float.parseFloat(args[2]); // z public void reshape(gldrawable drawable, int x, int y, int w, int h) { double aspect = (double) w / (double) h; // gl.glmatrixmode(gl.gl_projection); // gl.glloadidentity(); // glu.gluperspective(fieldofview, aspect, near, far); gl.glmatrixmode(gl.gl_modelview); // gl.glloadidentity(); // gl.gltranslatef(0.0f, 0.0f, -10.0f); // (z )

54 54 1 Java public void display(gldrawable drawable) { // gl.glclear(gl.gl_color_buffer_bit GL.GL_DEPTH_BUFFER_BIT); ( ) gl.glpushmatrix(); // ( ) gl.glrotatef(rotx, 1.0f, 0.0f, 0.0f); // (x ) gl.glrotatef(roty, 0.0f, 1.0f, 0.0f); // (y ) gl.glrotatef(rotz, 0.0f, 0.0f, 1.0f); // (z ) cube(); // gl.glpopmatrix(); public static void main(string[] args) { if (args.length > 0 && args.length < 4) // (new CubeAngle("CubeAngle Demo", args)).showframe(); else // (new CubeAngle("CubeAngle Demo")).showFrame(); 1.10 JOGL Animator Animator (display ) JOGL ( ) JOGL repaint ( ) ( ) ( ) - ObjectRotate.java object()

55 import java.awt.*; import java.awt.event.*; import net.java.games.jogl.*; // jogl public abstract class ObjectRotate implements GLEventListener { private Frame f; // Frame protected GL gl; // GL protected GLU glu; // GLU private double fieldofview = 25.0, near = 1.0, far = 20.0; // ( ), / protected float rotx = 0.0f, roty = 0.0f, rotz = 0.0f; // x,y,z private int prevmousex, prevmousey; private int object; protected abstract void object(); public ObjectRotate(String name) { GLCanvas canvas = // JOGL GLCanvas GLDrawableFactory.getFactory(). createglcanvas(new GLCapabilities()); canvas.addgleventlistener(this); // GL f = new Frame(name); // Frame f.add(canvas); // Frame GLCanvas f.setsize(500, 500); final Animator animator = new Animator(canvas); // Animator f.addwindowlistener(new WindowAdapter() { public void windowclosing(windowevent e) { animator.stop(); // Animator System.exit(0); ); animator.start(); // Animator protected void showframe() { f.setvisible(true); // Frame

56 56 1 Java public void init(gldrawable drawable) { // gl = drawable.getgl(); // GL glu = drawable.getglu(); // GLU gl.glclearcolor(0.0f, 0.0f, 0.0f, 1.0f); // gl.glenable(gl.gl_depth_test); gl.glenable(gl.gl_cull_face); // object = gl.glgenlists(1); gl.glnewlist(object, GL.GL_COMPILE); // object(); // gl.glendlist(); // drawable.addmouselistener(new MouseAdapter() { public void mousepressed(mouseevent e) { prevmousex = e.getx(); prevmousey = e.gety(); ); drawable.addmousemotionlistener(new MouseMotionAdapter() { public void mousedragged(mouseevent e) { int x = e.getx(); int y = e.gety(); Dimension size = e.getcomponent().getsize(); float thetay = 360.0f*((float)(x-prevMouseX)/size.width); float thetax = 360.0f*((float)(prevMouseY-y)/size.height); rotx -= thetax; roty += thetay; prevmousex = x; prevmousey = y; ); public void reshape(gldrawable drawable, int x, int y, int w, int h) { double aspect = (double) w / (double) h; // gl.glmatrixmode(gl.gl_projection); // gl.glloadidentity(); // glu.gluperspective(fieldofview, aspect, near, far);

57 gl.glmatrixmode(gl.gl_modelview); // gl.glloadidentity(); // gl.gltranslatef(0.0f, 0.0f, -10.0f); // (z ) public void display(gldrawable drawable) { // gl.glclear(gl.gl_color_buffer_bit GL.GL_DEPTH_BUFFER_BIT); ( ) gl.glpushmatrix(); // ( ) gl.glrotatef(rotx, 1.0f, 0.0f, 0.0f); // (x ) gl.glrotatef(roty, 0.0f, 1.0f, 0.0f); // (y ) gl.glrotatef(rotz, 0.0f, 0.0f, 1.0f); // (z ) gl.glcalllist(object); gl.glpopmatrix(); public void displaychanged(gldrawable drawable, boolean modechanged, boolean devicechanged) { ( ) - CubeRotate.java ObjectRotate import net.java.games.jogl.*; // jogl public class CubeRotate extends ObjectRotate { public CubeRotate(String name) { super(name); rotx = 20.0f; // (x ) roty = -30.0f; // (y ) protected void object() { // float[][] vertices = { { -1.0f, -1.0f, -1.0f, { 1.0f, -1.0f, -1.0f, { 1.0f, 1.0f, -1.0f, { -1.0f, 1.0f, -1.0f, { -1.0f, -1.0f, 1.0f, { 1.0f, -1.0f, 1.0f, { 1.0f, 1.0f, 1.0f, { -1.0f, 1.0f, 1.0f ; //

58 58 1 Java int[][] faces = { { 1, 2, 6, 5, { 2, 3, 7, 6, { 4, 5, 6, 7, { 0, 4, 7, 3, { 0, 1, 5, 4, { 0, 3, 2, 1 ; float[][] colors = { { 0.0f, 1.0f, 1.0f, { 1.0f, 0.0f, 1.0f, { 1.0f, 1.0f, 0.0f, { 0.0f, 0.5f, 0.5f, { 0.5f, 0.0f, 0.5f, { 0.5f, 0.5f, 0.0f ; // gl.glbegin(gl.gl_quads); for (int i = 0; i < faces.length; i++) { gl.glcolor3fv(colors[i]); // for (int j = 0; j < faces[i].length; j++) gl.glvertex3fv(vertices[faces[i][j]]); gl.glend(); public static void main(string[] args) { (new CubeRotate("Cube Rotate")).showFrame(); - ConesWire.java gl.glpushmatrix() gl.glpopmatrix() ( ) Z import net.java.games.jogl.*; // jogl public class ConesWire extends ObjectRotate { public ConesWire(String name) { super(name); protected void object() { final int NOP = 16; // float[] foreground = { 1.0f, 1.0f, 0.0f ; // ( ) gl.glcolor3fv(foreground); // for (int i = 0; i < NOP; i++) { double t = 2.0 * Math.PI * i / NOP; // 2PI n gl.glpushmatrix(); // ( ) gl.gltranslated(1.6*math.cos(t), 1.6*Math.sin(t), 0.0);

59 gl.glscalef(0.3f, 0.3f, 1.4f); conewire(); gl.glpopmatrix(); // 1.6 // protected void conewire() { final int NOP = 16; float[] apex = { 0.0f, 0.0f, 1.0f ; float[][] circle = new float[nop][]; for (int i = 0; i < NOP; i++) { double t = 2.0 * Math.PI * i / NOP; // 2PI n circle[i] = new float[3]; circle[i][0] = (float)math.cos(t); circle[i][1] = (float)math.sin(t); circle[i][2] = -1.0f; gl.glbegin(gl.gl_line_loop); for (int i = 0; i < NOP; i++) gl.glvertex3fv(circle[nop-i-1]); gl.glend(); gl.glbegin(gl.gl_lines); for (int i = 0; i < NOP; i++) { gl.glvertex3fv(apex); // gl.glvertex3fv(circle[i]); // gl.glend(); public static void main(string[] args) { (new ConesWire("Cones Wire")).showFrame(); Z Z - ConesHiddenLine.java

60 60 1 Java ConesWire ( ) import net.java.games.jogl.*; // jogl public class ConesHiddenLine extends ConesWire { public ConesHiddenLine(String name) { super(name); public void init(gldrawable drawable) { // super.init(drawable); gl.glenable(gl.gl_polygon_offset_fill); gl.glpolygonoffset(1.0f, 1.0f); protected void object() { final int NOP = 16; // float[] background = { 0.0f, 0.0f, 0.0f ; // ( ) float[] foreground = { 1.0f, 1.0f, 0.0f ; // ( ) for (int i = 0; i < NOP; i++) { double t = 2.0 * Math.PI * i / NOP; // 2PI n gl.glpushmatrix(); // ( ) gl.gltranslated(1.6*math.cos(t), 1.6*Math.sin(t), 0.0); // 1.6 gl.glscalef(0.3f, 0.3f, 1.4f); // gl.glcolor3fv(foreground); // conewire(); gl.glcolor3fv(background); // conepolygon(); // gl.glpopmatrix(); private void conepolygon() { final int NOP = 16; float[] apex = { 0.0f, 0.0f, 1.0f ; float[][] circle = new float[nop+1][]; for (int i = 0; i <= NOP; i++) { double t = 2.0 * Math.PI * i / NOP; // 2PI n

61 circle[i] = new float[3]; circle[i][0] = (float)math.cos(t); circle[i][1] = (float)math.sin(t); circle[i][2] = -1.0f; gl.glbegin(gl.gl_polygon); for (int i = 0; i < NOP; i++) gl.glvertex3fv(circle[nop-i-1]); // gl.glend(); gl.glbegin(gl.gl_triangle_fan); gl.glvertex3fv(apex); // for (int i = 0; i <= NOP; i++) { // gl.glvertex3fv(circle[i]); // gl.glend(); public static void main(string[] args) { (new ConesHiddenLine("Cones HiddenLine")).showFrame(); JOGL(OpenGL) 3 RGB CMY HSB(HSV) RGB - ColorCube.java import net.java.games.jogl.*; // jogl public class ColorCube extends ObjectRotate { public ColorCube(String name) { super(name); protected void object() { // RGB float[][] vertices = { { -1.0f, -1.0f, -1.0f, { 1.0f, -1.0f, -1.0f, { 1.0f, 1.0f, -1.0f,

62 62 1 Java { -1.0f, 1.0f, -1.0f, { -1.0f, -1.0f, 1.0f, { 1.0f, -1.0f, 1.0f, { 1.0f, 1.0f, 1.0f, { -1.0f, 1.0f, 1.0f ; // float[][] colors = { { 0.0f, 0.0f, 0.0f, { 1.0f, 0.0f, 0.0f, { 1.0f, 1.0f, 0.0f, { 0.0f, 1.0f, 0.0f, { 0.0f, 0.0f, 1.0f, { 1.0f, 0.0f, 1.0f, { 1.0f, 1.0f, 1.0f, { 0.0f, 1.0f, 1.0f ; int[][] faces = { { 1, 2, 6, 5, { 2, 3, 7, 6, { 4, 5, 6, 7, { 0, 4, 7, 3, { 0, 1, 5, 4, { 0, 3, 2, 1 ; // gl.glbegin(gl.gl_quads); for (int i = 0; i < faces.length; i++) { for (int j = 0; j < faces[i].length; j++){ gl.glcolor3fv(colors[faces[i][j]]); gl.glvertex3fv(vertices[faces[i][j]]); gl.glend(); public static void main(string[] args) { (new ColorCube("Color Cube")).showFrame(); 1.11 ( ) RGB (ambient)

63 L n M V 1.11: ( ) I a k a I a k a (diffuse) ( ) L n θ cos θ ( 1.11 ) 2 L, n ( ) (Lambert) I d k d cos θ = I d k d nl I d k d (specular) L n ( 1.11 ) M = (L + V)/ L + V n α cos α 2 I s k s cos n α = I s k s (nm) n I s k s n (shininess ) ( ) OpenGL ( ) RGB I a k a + I d k d nl + I s k s (nm) n

64 64 1 Java void gllightfv(enum light, enum pname, const float *params); light (GL_LIGHTi) pname (GL.GL_AMBIENT, GL.GL_DIFFUSE, GL.GL_SPECULAR ) params void glmaterialfv(enum face, enum pname, const float *params); ( vertex ) face (GL.GL_FRONT, GL.GL_BACK, GL.GL_FRONT_AND_BACK) pname (GL.GL_AMBIENT, GL.GL_DIFFUSE, GL.GL_SPECULAR ) params void glnormal3dv(double v[3]); ( vertex ) v ( ) gl.glenable(gl.gl_normalize) - ObjectShade.java ObjectRotate object() import net.java.games.jogl.*; // jogl public abstract class ObjectShade extends ObjectRotate { protected float[] lightposition = { 5.0f, 5.0f, 10.0f, 0.0f ; // protected float[] lightambient = { 0.2f, 0.2f, 0.2f, 1.0f ; protected float[] lightdiffuse = { 1.0f, 1.0f, 1.0f, 1.0f ; protected float[] lightspecular = { 0.9f, 0.9f, 0.9f, 1.0f ; public ObjectShade(String name) { super(name); public void init(gldrawable drawable) { // super.init(drawable); // init gl.gllightfv(gl.gl_light0, GL.GL_POSITION, lightposition); // gl.gllightfv(gl.gl_light0, GL.GL_AMBIENT, lightambient);

65 // gl.gllightfv(gl.gl_light0, GL.GL_DIFFUSE, lightdiffuse); // gl.gllightfv(gl.gl_light0, GL.GL_SPECULAR, lightspecular); // gl.glenable(gl.gl_lighting); gl.glenable(gl.gl_light0); // gl.glenable(gl.gl_normalize); - CubeShade.java ObjectShade (material) import net.java.games.jogl.*; // jogl public class CubeShade extends ObjectShade { public CubeShade(String name) { super(name); rotx = 20.0f; // (x ) roty = -30.0f; // (y ) protected void object() { // float[][] vertices = { { -1.0f, -1.0f, -1.0f, { 1.0f, -1.0f, -1.0f, { 1.0f, 1.0f, -1.0f, { -1.0f, 1.0f, -1.0f, { -1.0f, -1.0f, 1.0f, { 1.0f, -1.0f, 1.0f, { 1.0f, 1.0f, 1.0f, { -1.0f, 1.0f, 1.0f ; // int[][] faces = { { 1, 2, 6, 5, { 2, 3, 7, 6, { 4, 5, 6, 7, { 0, 4, 7, 3, { 0, 1, 5, 4, { 0, 3, 2, 1 ; float[][] normals = { { 1.0f, 0.0f, 0.0f, { 0.0f, 1.0f, 0.0f, { 0.0f, 0.0f, 1.0f, { -1.0f, 0.0f, 0.0f, { 0.0f, -1.0f, 0.0f, { 0.0f, 0.0f, -1.0f ; float[] diffuse = { 0.8f, 0.8f, 0.2f, 1.0f ; float[] specular = { 0.9f, 0.9f, 0.9f, 1.0f ;

66 66 1 Java gl.glmaterialfv(gl.gl_front, GL.GL_AMBIENT_AND_DIFFUSE, diffuse); gl.glmaterialfv(gl.gl_front, GL.GL_SPECULAR, specular); gl.glmaterialf(gl.gl_front, GL.GL_SHININESS, 100.0f); // shininess gl.glshademodel(gl.gl_flat); gl.glbegin(gl.gl_quads); for (int i = 0; i < faces.length; i++) { gl.glnormal3fv(normals[i]); // ( ) for (int j = 0; j < faces[i].length; j++) gl.glvertex3fv(vertices[faces[i][j]]); gl.glend(); public static void main(string[] args) { (new CubeShade("Cube Shade")).showFrame(); 20 - IcosahedronShade.java ObjectShade import net.java.games.jogl.*; // jogl public class IcosahedronShade extends ObjectShade { public IcosahedronShade(String name) { super(name); protected void object() { // 20 float[] diffuse = { 0.8f, 0.3f, 0.8f, 1.0f ; float[] specular = { 0.9f, 0.9f, 0.9f, 1.0f ; gl.glmaterialfv(gl.gl_front, GL.GL_AMBIENT_AND_DIFFUSE, diffuse); gl.glmaterialfv(gl.gl_front, GL.GL_SPECULAR, specular); gl.glmaterialf(gl.gl_front, GL.GL_SHININESS, 100.0f);

67 // shininess final float R = (float)math.sqrt(2.0); // final float X = (float)((math.sqrt(5.0) + 1.0) / 2.0); final float Y = (float)(r / Math.sqrt(1.0 + X*X)); final float Z = (float)(x * Y); float[][] vertices = // 20 { { 0.0f, Y, Z, { 0.0f, -Y, Z, { 0.0f, -Y, -Z, { 0.0f, Y, -Z, { Z, 0.0f, Y, { Z, 0.0f, -Y, { -Z, 0.0f, -Y, { -Z, 0.0f, Y, { Y, Z, 0.0f, { -Y, Z, 0.0f, { -Y, -Z, 0.0f, { Y, -Z, 0.0f ; int[][] faces = { { 0, 1, 4, { 0, 4, 8, { 0, 8, 9, { 0, 9, 7, { 0, 7, 1, { 1, 10, 11, { 1, 11, 4, { 4, 11, 5, { 4, 5, 8, { 8, 5, 3, { 8, 3, 9, { 9, 3, 6, { 9, 6, 7, { 7, 6, 10, { 7, 10, 1, { 2, 10, 6, { 2, 6, 3, { 2, 3, 5, { 2, 5, 11, { 2, 11, 10 ; gl.glshademodel(gl.gl_flat); gl.glbegin(gl.gl_triangles); for (int i = 0; i < faces.length; i++) { gl.glnormal3fv(normal(vertices[faces[i][0]], vertices[faces[i][1]], vertices[faces[i][2]])); // ( ) for (int j = 0; j < faces[i].length; j++) gl.glvertex3fv(vertices[faces[i][j]]); gl.glend(); private float[] normal(float[] pnt0, float[] pnt1, float[] pnt2) { return crossproduct(subtract(pnt1, pnt0), subtract(pnt2, pnt0)); - 2 private float[] subtract(float[] vec0, float[] vec1) { float[] answer = new float[3]; for (int i = 0; i < 3; i++) answer[i] = vec0[i] - vec1[i]; return answer; private float[] crossproduct(float[] vec0, float[] vec1) {

68 68 1 Java float[] answer = new float[3]; answer[0] = vec0[1] * vec1[2] - vec0[2] * vec1[1]; answer[1] = vec0[2] * vec1[0] - vec0[0] * vec1[2]; answer[2] = vec0[0] * vec1[1] - vec0[1] * vec1[0]; return answer; public static void main(string[] args) { (new IcosahedronShade("Icosahedron Shade")).showFrame(); - SubdivideShade.java ( ) import net.java.games.jogl.*; // jogl public class SubdivideShade extends ObjectShade { static int depth = 0; public SubdivideShade(String name) { super(name); protected void object() { float[] diffuse = { 0.8f, 0.3f, 0.8f, 1.0f ; float[] specular = { 0.9f, 0.9f, 0.9f, 1.0f ; gl.glmaterialfv(gl.gl_front, GL.GL_AMBIENT_AND_DIFFUSE, diffuse); gl.glmaterialfv(gl.gl_front, GL.GL_SPECULAR, specular); gl.glmaterialf(gl.gl_front, GL.GL_SHININESS, 100.0f); // shininess final float R = (float)math.sqrt(2.0); // final float X = (float)((math.sqrt(5.0) + 1.0) / 2.0);

69 final float Y = (float)(r / Math.sqrt(1.0 + X*X)); final float Z = (float)(x * Y); float[][] vertices = // 20 { { 0.0f, Y, Z, { 0.0f, -Y, Z, { 0.0f, -Y, -Z, { 0.0f, Y, -Z, { Z, 0.0f, Y, { Z, 0.0f, -Y, { -Z, 0.0f, -Y, { -Z, 0.0f, Y, { Y, Z, 0.0f, { -Y, Z, 0.0f, { -Y, -Z, 0.0f, { Y, -Z, 0.0f ; int[][] faces = { { 0, 1, 4, { 0, 4, 8, { 0, 8, 9, { 0, 9, 7, { 0, 7, 1, { 1, 10, 11, { 1, 11, 4, { 4, 11, 5, { 4, 5, 8, { 8, 5, 3, { 8, 3, 9, { 9, 3, 6, { 9, 6, 7, { 7, 6, 10, { 7, 10, 1, { 2, 10, 6, { 2, 6, 3, { 2, 3, 5, { 2, 5, 11, { 2, 11, 10 ; for (int i = 0; i < faces.length; i++) { subdivide(vertices[faces[i][0]], vertices[faces[i][1]], vertices[faces[i][2]], depth); // 20 protected void subdivide (float[] pnt0, float[] pnt1, float[] pnt2, int depth) { if (depth == 0) { // gl.glshademodel(gl.gl_flat); gl.glbegin(gl.gl_triangles); gl.glnormal3fv(normal(pnt0, pnt1, pnt2)); // gl.glvertex3fv(pnt0); // gl.glvertex3fv(pnt1); gl.glvertex3fv(pnt2); gl.glend(); else { float[] pnt01 = split(pnt0, pnt1); // 2 float[] pnt12 = split(pnt1, pnt2); float[] pnt20 = split(pnt2, pnt0); subdivide(pnt0, pnt01, pnt20, depth-1); subdivide(pnt1, pnt12, pnt01, depth-1); subdivide(pnt2, pnt20, pnt12, depth-1); subdivide(pnt01, pnt12, pnt20, depth-1); // 4

70 70 1 Java private float[] normal(float[] pnt0, float[] pnt1, float[] pnt2) { float[] answer = new float[3]; for (int i = 0; i < 3; i++) answer[i] = pnt0[i] + pnt1[i] + pnt2[i]; return answer; protected float[] split(float[] pnt0, float[] pnt1) { float[] ans = new float[3]; // for (int i = 0; i < 3; i++) ans[i] = pnt0[i] + pnt1[i]; float ratio = (float)(math.sqrt(2.0) / Math.sqrt(ans[0]*ans[0]+ans[1]*ans[1]+ans[2]*ans[2])); for (int i = 0; i < 3; i++) ans[i] *= ratio; return ans; public static void main(string[] args) { if (args.length == 1) depth = Integer.parseInt(args[0]); (new SubdivideShade("Subdivide Shade")).showFrame(); ( ) ( ) ( ) (Phong) ( ) (Gouraud) 2 OpenGL ( ) - SphereShade.java 4 20 import net.java.games.jogl.*;

71 public class SphereShade extends SubdivideShade { public SphereShade(String name) { super(name); protected void subdivide (float[] pnt0, float[] pnt1, float[] pnt2, int depth) { if (depth == 0) { // gl.glshademodel(gl.gl_smooth); gl.glbegin(gl.gl_triangles); gl.glnormal3fv(pnt0); // ( ) gl.glvertex3fv(pnt0); // gl.glnormal3fv(pnt1); gl.glvertex3fv(pnt1); gl.glnormal3fv(pnt2); gl.glvertex3fv(pnt2); gl.glend(); else { float[] pnt01 = split(pnt0, pnt1); // 2 float[] pnt12 = split(pnt1, pnt2); float[] pnt20 = split(pnt2, pnt0); subdivide(pnt0, pnt01, pnt20, depth-1); subdivide(pnt1, pnt12, pnt01, depth-1); subdivide(pnt2, pnt20, pnt12, depth-1); subdivide(pnt01, pnt12, pnt20, depth-1); // 4 public static void main(string[] args) { if (args.length == 1) depth = Integer.parseInt(args[0]); (new SphereShade("Sphere Shade")).showFrame();

72

73 73 2 V , 2, 3, 4, n n 2 (1.1 x y 2.1:

74 74 2 V

75 , 2, ( /CMY ) (CMY ) (RGB ) 1.4 ( (1.1) 5 ) White (0 0 0) Cyan (1 0 0) x=300, y=225 Magenta (0 1 0) x=213.4, y=375 Blue Green (1 1 0) (1 0 1) Black (1 1 1) Red (0 1 1) Yellow (0 0 1) x=386.6, y= : 3 (CMY ) 2.5 HSB HSB (S = 1, B = 1 ) HSB HSB HSB 2.3

76 76 2 V 2.3: