package com.mwc.cosc610.project6; import java.awt.*; import java.awt.image.*; import java.awt.event.*; import java.applet.*; import java.util.*; import com.mwc.util.*; /** * A simple 3D animation applet. * * This is based off of my readings of the * following books and web sites: * * 1) Elementary Linear Algebra (Applications Version) * Anton, Rorres * Chapter 11.11, Page 626 * * 2) Build Your Own Flight Sim in C++ * Michael Radtke, Chris Lampton and Andr Lamothe * * 3) http://www.javaworld.com/javaworld/jw-07-1997/jw-07-howto-p2.html * * @author Matthew W. Coan (10:04 PM 12/3/2002) */ public class Project6 extends Applet implements ImageObserver, Runnable { class Prj6KeyListner implements KeyListener { public void keyPressed(KeyEvent e) { } public void keyReleased(KeyEvent e) { switch(Character.toLowerCase(e.getKeyChar())) { case 'x': synchronized(_xRot) { _xOn = !_xOn; } break; case 'y': synchronized(_yRot) { _yOn = !_yOn; } break; case 'z': synchronized(_zRot) { _zOn = !_zOn; } break; } } public void keyTyped(KeyEvent e) { } } public Matrix getCentroid(Polygon ts) { return new Matrix(new double[][]{ {(_vertexArray[ts.vertexArray[0]].get(0,0) + _vertexArray[ts.vertexArray[1]].get(0,0) + _vertexArray[ts.vertexArray[2]].get(0,0)) / 3.0}, {(_vertexArray[ts.vertexArray[0]].get(1,0) + _vertexArray[ts.vertexArray[1]].get(1,0) + _vertexArray[ts.vertexArray[2]].get(1,0)) / 3.0}, {(_vertexArray[ts.vertexArray[0]].get(2,0) + _vertexArray[ts.vertexArray[1]].get(2,0) + _vertexArray[ts.vertexArray[2]].get(2,0)) / 3.0}, }, 3, 1); } public Matrix getNormal(Polygon ts) { Matrix coords = new Matrix(3,1); coords.set(0,0, ((_vertexArray[ts.vertexArray[0]].get(1,0) - _vertexArray[ts.vertexArray[1]].get(1,0)) * (_vertexArray[ts.vertexArray[0]].get(2,0) + _vertexArray[ts.vertexArray[1]].get(2,0))) + ((_vertexArray[ts.vertexArray[1]].get(1,0) - _vertexArray[ts.vertexArray[2]].get(1,0)) * (_vertexArray[ts.vertexArray[1]].get(2,0) + _vertexArray[ts.vertexArray[2]].get(2,0))) + ((_vertexArray[ts.vertexArray[2]].get(1,0) - _vertexArray[ts.vertexArray[0]].get(1,0)) * (_vertexArray[ts.vertexArray[2]].get(2,0) + _vertexArray[ts.vertexArray[0]].get(2,0)))); coords.set(1,0, ((_vertexArray[ts.vertexArray[0]].get(2,0) - _vertexArray[ts.vertexArray[1]].get(0,0)) * (_vertexArray[ts.vertexArray[1]].get(2,0) + _vertexArray[ts.vertexArray[2]].get(2,0))) + ((_vertexArray[ts.vertexArray[1]].get(2,0) - _vertexArray[ts.vertexArray[2]].get(0,0)) * (_vertexArray[ts.vertexArray[1]].get(0,0) + _vertexArray[ts.vertexArray[2]].get(0,0))) + ((_vertexArray[ts.vertexArray[2]].get(2,0) - _vertexArray[ts.vertexArray[0]].get(2,0)) * (_vertexArray[ts.vertexArray[1]].get(0,0) + _vertexArray[ts.vertexArray[0]].get(0,0)))); coords.set(2,0, ((_vertexArray[ts.vertexArray[0]].get(0,0) - _vertexArray[ts.vertexArray[1]].get(0,0)) * (_vertexArray[ts.vertexArray[0]].get(1,0) + _vertexArray[ts.vertexArray[1]].get(1,0))) + ((_vertexArray[ts.vertexArray[1]].get(0,0) - _vertexArray[ts.vertexArray[2]].get(0,0)) * (_vertexArray[ts.vertexArray[1]].get(1,0) + _vertexArray[ts.vertexArray[2]].get(1,0))) + ((_vertexArray[ts.vertexArray[2]].get(0,0) - _vertexArray[ts.vertexArray[0]].get(0,0)) * (_vertexArray[ts.vertexArray[2]].get(1,0) + _vertexArray[ts.vertexArray[0]].get(1,0)))); double length = Math.sqrt((coords.get(0,0) * coords.get(0,0)) + (coords.get(1,0) * coords.get(1,0)) + (coords.get(2,0) * coords.get(2,0))); coords.set(0,0, coords.get(0,0) / length); coords.set(1,0, coords.get(1,0) / length); coords.set(2,0, coords.get(2,0) / length); return coords; } public Matrix getLine(Matrix coords1, Matrix coords2) { Matrix coords = new Matrix(new double [][]{ {coords1.get(0,0) - coords2.get(0,0)}, {coords1.get(1,0) - coords2.get(1,0)}, {coords1.get(2,0) - coords2.get(2,0)}}, 3, 1); double length = Math.sqrt((coords.get(0,0) * coords.get(0,0)) + (coords.get(1,0) * coords.get(1,0)) + (coords.get(2,0) * coords.get(2,0))); coords.set(0,0, coords.get(0,0) / length); coords.set(1,0, coords.get(1,0) / length); coords.set(2,0, coords.get(2,0) / length); return coords; } public double dot(Matrix coords1, Matrix coords2) { return coords1.get(0,0) * coords2.get(0,0) + coords1.get(1,0) * coords2.get(1,0) + coords1.get(2,0) * coords2.get(2,0); } /** * The width of the applet. */ public static final int WIDTH = 600; /** * The height of the applet. */ public static final int HEIGHT = 400; /** * Middle of the applet on the horizontal. */ public static final int XORIGIN = 300; /** * Middle of the applet on the vertical. */ public static final int YORIGIN = 200; // light source private Matrix _light = new Matrix(new double[][]{{-180.0},{180.0},{0.0}}, 3, 1); // rotation flags private boolean _xOn = true; private boolean _yOn = true; private boolean _zOn = false; // X rotation private Matrix _xRot; // Y rotation private Matrix _yRot; // Z rotation private Matrix _zRot; // List of unique vertex colum vectors private Matrix _vertexArray[]; // List of graphical objects (each graphical object // composed of an array of polygons) private Polygon _objectArray[][]; // Stoping capability private Object _stopLock; private boolean _stopFlag; // My polygon class (Over-rides the java.awt.Polygon // class in this class scope) class Polygon { int vertexArray[]; Polygon(int vertexArray[]) { this.vertexArray = vertexArray; } boolean isBackface(Matrix vvertexArray[]) { Matrix v0 = vvertexArray[vertexArray[0]]; Matrix v1 = vvertexArray[vertexArray[1]]; Matrix v2 = vvertexArray[vertexArray[2]]; // cross product double z = (v1.get(0,0) - v0.get(0,0)) * (v2.get(1,0) - v0.get(1,0)) - (v1.get(1,0) - v0.get(1,0)) * (v2.get(0,0) - v0.get(0,0)); z = -z; return z >= 0.0; } } public boolean polygonComp(Polygon p1, Polygon p2) { double z1 = (_vertexArray[p1.vertexArray[0]].get(2,0) + _vertexArray[p1.vertexArray[1]].get(2,0) + _vertexArray[p1.vertexArray[2]].get(2,0)) / 3.0; double z2 = (_vertexArray[p2.vertexArray[0]].get(2,0) + _vertexArray[p2.vertexArray[1]].get(2,0) + _vertexArray[p2.vertexArray[2]].get(2,0)) / 3.0; return z1 < z2; } public void sort(Polygon [] rgo, int nLow0, int nHigh0) { int nLow = nLow0; int nHigh = nHigh0; Polygon oMid; if (nHigh0 > nLow0) { oMid = rgo[ (nLow0 + nHigh0) / 2 ]; while(nLow <= nHigh) { while((nLow < nHigh0) && polygonComp(rgo[nLow], oMid)) ++nLow; while((nLow0 < nHigh) && polygonComp(oMid, rgo[nHigh])) --nHigh; if(nLow <= nHigh) swap(rgo, nLow++, nHigh--); } if(nLow0 < nHigh) sort(rgo, nLow0, nHigh); if(nLow < nHigh0) sort(rgo, nLow, nHigh0); } } public void swap(Polygon [] rgo, int i, int j) { Polygon o; o = rgo[i]; rgo[i] = rgo[j]; rgo[j] = o; } void zSort(Polygon polygonArray[]) { sort(polygonArray, 0, polygonArray.length - 1); } // Project the vertex array on the applet // from some distance away Matrix[] project(double distance) { Matrix ret[] = new Matrix[_vertexArray.length]; for(int i = 0; i < _vertexArray.length; i++) { ret[i] = new Matrix( new double[][]{ {(distance * _vertexArray[i].get(0,0)) / (distance - _vertexArray[i].get(2,0))+XORIGIN}, {(distance * _vertexArray[i].get(1,0)) / (distance - _vertexArray[i].get(2,0))+YORIGIN}, {_vertexArray[i].get(2,0)} },3,1); } return ret; } private Matrix[] _scale(Matrix vertexArray[], double scaler) { Matrix[] ret = new Matrix[vertexArray.length]; Matrix T = new Matrix(new double[][]{ {scaler, 0.0, 0.0}, {0.0, scaler, 0.0}, {0.0, 0.0, scaler} }, 3, 3); for(int i = 0; i < vertexArray.length; i++) ret[i] = T.mul(vertexArray[i]); return ret; } private Matrix[] _translate(Matrix vertexArray[], double x, double y, double z) { Matrix[] ret = new Matrix[vertexArray.length]; Matrix T = new Matrix(new double[][]{ {x}, {y}, {z} }, 3, 1); for(int i = 0; i < vertexArray.length; i++) ret[i] = vertexArray[i].add(T); return ret; } /** * Init the applet. */ public void init() { _stopLock = new Object(); _stopFlag = true; _xRot = new Matrix(new double[][]{ {1.0, 0.0, 0.0}, {0.0, Math.cos(Math.PI/180.0), -Math.sin(Math.PI/180.0)}, {0.0, Math.sin(Math.PI/180.0), Math.cos(Math.PI/180.0)} }, 3, 3); _yRot = new Matrix(new double[][]{ {Math.cos(Math.PI/180.0), 0.0, Math.sin(Math.PI/180)}, {0.0, 1.0, 0.0}, {-Math.sin(Math.PI/180.0), 0.0, Math.cos(Math.PI/180.0)} }, 3, 3); _zRot = new Matrix(new double[][]{ {Math.cos(Math.PI/180.0), -Math.sin(Math.PI/180.0), 0,0}, {Math.sin(Math.PI/180.0), Math.cos(Math.PI/180.0), 0.0}, {0.0, 0.0, 1.0} }, 3, 3); _vertexArray = new Matrix[] { new Matrix(new double[][]{{-50.0},{50.0},{-50.0}},3,1), new Matrix(new double[][]{{50.0},{50.0},{-50.0}},3,1), new Matrix(new double[][]{{50.0},{50.0},{50.0}},3,1), new Matrix(new double[][]{{-50.0},{50.0},{50.0}},3,1), new Matrix(new double[][]{{-50.0},{-50.0},{-50.0}},3,1), new Matrix(new double[][]{{50.0},{-50.0},{-50.0}},3,1), new Matrix(new double[][]{{50.0},{-50.0},{50.0}},3,1), new Matrix(new double[][]{{-50.0},{-50.0},{50.0}},3,1), }; Matrix[] cube2 = _scale(_vertexArray, 0.4); cube2 = _translate(cube2, 150.0, 0.0, 0.0); Matrix[] cube3 = _scale(_vertexArray, 0.4); cube3 = _translate(cube3, 0.0, 150.0, 0.0); Matrix[] cube4 = _scale(_vertexArray, 0.4); cube4 = _translate(cube4, 0.0, 0.0, 150.0); Matrix[] cube5 = _scale(_vertexArray, 0.4); cube5 = _translate(cube5, -150.0, 0.0, 0.0); Matrix[] cube6 = _scale(_vertexArray, 0.4); cube6 = _translate(cube6, 0.0, -150.0, 0.0); Matrix[] cube7 = _scale(_vertexArray, 0.4); cube7 = _translate(cube7, 0.0, 0.0, -150.0); Matrix temp[] = new Matrix[_vertexArray.length + cube2.length + cube3.length + cube4.length + cube5.length + cube6.length + cube7.length ]; int index,j; for(index = 0; index < _vertexArray.length; index++) temp[index] = _vertexArray[index]; j = 0; while(index < (_vertexArray.length + cube2.length)) { temp[index] = cube2[j]; index++; j++; } j = 0; while(index < (_vertexArray.length + cube2.length + cube3.length)) { temp[index] = cube3[j]; index++; j++; } j = 0; while(index < (_vertexArray.length + cube2.length + cube3.length + cube4.length)) { temp[index] = cube4[j]; index++; j++; } j = 0; while(index < (_vertexArray.length + cube2.length + cube3.length + cube4.length + cube5.length)) { temp[index] = cube5[j]; index++; j++; } j = 0; while(index < (_vertexArray.length + cube2.length + cube3.length + cube4.length + cube5.length + cube6.length)) { temp[index] = cube6[j]; index++; j++; } j = 0; while(index < (_vertexArray.length + cube2.length + cube3.length + cube4.length + cube5.length + cube6.length + cube7.length)) { temp[index] = cube7[j]; index++; j++; } _vertexArray = temp; _objectArray = new Polygon[][] { { // Cube 1: new Polygon(new int[] {0, 1, 5, 4}), new Polygon(new int[] {5, 6, 7, 4}), new Polygon(new int[] {6, 2, 3, 7}), new Polygon(new int[] {2, 1, 0, 3}), new Polygon(new int[] {2, 6, 5, 1}), new Polygon(new int[] {4, 7, 3, 0}), }, { // Cube 2: new Polygon(new int[] {0+8, 1+8, 5+8, 4+8}), new Polygon(new int[] {5+8, 6+8, 7+8, 4+8}), new Polygon(new int[] {6+8, 2+8, 3+8, 7+8}), new Polygon(new int[] {2+8, 1+8, 0+8, 3+8}), new Polygon(new int[] {2+8, 6+8, 5+8, 1+8}), new Polygon(new int[] {4+8, 7+8, 3+8, 0+8}), }, { // Cube 3: new Polygon(new int[] {0+8+8, 1+8+8, 5+8+8, 4+8+8}), new Polygon(new int[] {5+8+8, 6+8+8, 7+8+8, 4+8+8}), new Polygon(new int[] {6+8+8, 2+8+8, 3+8+8, 7+8+8}), new Polygon(new int[] {2+8+8, 1+8+8, 0+8+8, 3+8+8}), new Polygon(new int[] {2+8+8, 6+8+8, 5+8+8, 1+8+8}), new Polygon(new int[] {4+8+8, 7+8+8, 3+8+8, 0+8+8}), }, { // Cube 4: new Polygon(new int[] {0+8+8+8, 1+8+8+8, 5+8+8+8, 4+8+8+8}), new Polygon(new int[] {5+8+8+8, 6+8+8+8, 7+8+8+8, 4+8+8+8}), new Polygon(new int[] {6+8+8+8, 2+8+8+8, 3+8+8+8, 7+8+8+8}), new Polygon(new int[] {2+8+8+8, 1+8+8+8, 0+8+8+8, 3+8+8+8}), new Polygon(new int[] {2+8+8+8, 6+8+8+8, 5+8+8+8, 1+8+8+8}), new Polygon(new int[] {4+8+8+8, 7+8+8+8, 3+8+8+8, 0+8+8+8}), }, { // Cube 5: new Polygon(new int[] {0+8+8+8+8, 1+8+8+8+8, 5+8+8+8+8, 4+8+8+8+8}), new Polygon(new int[] {5+8+8+8+8, 6+8+8+8+8, 7+8+8+8+8, 4+8+8+8+8}), new Polygon(new int[] {6+8+8+8+8, 2+8+8+8+8, 3+8+8+8+8, 7+8+8+8+8}), new Polygon(new int[] {2+8+8+8+8, 1+8+8+8+8, 0+8+8+8+8, 3+8+8+8+8}), new Polygon(new int[] {2+8+8+8+8, 6+8+8+8+8, 5+8+8+8+8, 1+8+8+8+8}), new Polygon(new int[] {4+8+8+8+8, 7+8+8+8+8, 3+8+8+8+8, 0+8+8+8+8}), }, { // Cube 6: new Polygon(new int[] {0+8+8+8+8+8, 1+8+8+8+8+8, 5+8+8+8+8+8, 4+8+8+8+8+8}), new Polygon(new int[] {5+8+8+8+8+8, 6+8+8+8+8+8, 7+8+8+8+8+8, 4+8+8+8+8+8}), new Polygon(new int[] {6+8+8+8+8+8, 2+8+8+8+8+8, 3+8+8+8+8+8, 7+8+8+8+8+8}), new Polygon(new int[] {2+8+8+8+8+8, 1+8+8+8+8+8, 0+8+8+8+8+8, 3+8+8+8+8+8}), new Polygon(new int[] {2+8+8+8+8+8, 6+8+8+8+8+8, 5+8+8+8+8+8, 1+8+8+8+8+8}), new Polygon(new int[] {4+8+8+8+8+8, 7+8+8+8+8+8, 3+8+8+8+8+8, 0+8+8+8+8+8}), }, { // Cube 7: new Polygon(new int[] {0+8+8+8+8+8+8, 1+8+8+8+8+8+8, 5+8+8+8+8+8+8, 4+8+8+8+8+8+8}), new Polygon(new int[] {5+8+8+8+8+8+8, 6+8+8+8+8+8+8, 7+8+8+8+8+8+8, 4+8+8+8+8+8+8}), new Polygon(new int[] {6+8+8+8+8+8+8, 2+8+8+8+8+8+8, 3+8+8+8+8+8+8, 7+8+8+8+8+8+8}), new Polygon(new int[] {2+8+8+8+8+8+8, 1+8+8+8+8+8+8, 0+8+8+8+8+8+8, 3+8+8+8+8+8+8}), new Polygon(new int[] {2+8+8+8+8+8+8, 6+8+8+8+8+8+8, 5+8+8+8+8+8+8, 1+8+8+8+8+8+8}), new Polygon(new int[] {4+8+8+8+8+8+8, 7+8+8+8+8+8+8, 3+8+8+8+8+8+8, 0+8+8+8+8+8+8}), } }; addKeyListener(new Prj6KeyListner()); } /** * Get the vector of X values for a polygon in the representation. */ protected int[] getX(Polygon poly, Matrix vertexArray[]) { int ret[] = new int[poly.vertexArray.length]; for(int k = 0; k < poly.vertexArray.length; k++) ret[k] = (int)Math.round(vertexArray[poly.vertexArray[k]].get(0,0)); return ret; } /** * Gthe the vector of Y values for a polygon in the representation. */ protected int[] getY(Polygon poly, Matrix vertexArray[]) { int ret[] = new int[poly.vertexArray.length]; for(int k = 0; k < poly.vertexArray.length; k++) ret[k] = (int)Math.round(vertexArray[poly.vertexArray[k]].get(1,0)); return ret; } private Polygon[] _makePolygonArray(Matrix vertexArray[]) { Vector ret = new Vector(); Polygon []object; Polygon poly; for(int objnum = 0; objnum < _objectArray.length; objnum++) { object = _objectArray[objnum]; for(int polynum = 0; polynum < object.length; polynum++) { poly = object[polynum]; if(!poly.isBackface(vertexArray)) ret.addElement(poly); } } Polygon array[] = new Polygon[ret.size()]; for(int index = 0; index < ret.size(); index++) array[index] = (Polygon)ret.elementAt(index); return array; } /** * Paint the array of 3D objects onto the 2D applet. */ public void paint(Graphics g) { // Clear: g.setColor(Color.white); g.fillRect(0, 0, WIDTH, HEIGHT); // Project: Matrix[] temp = project(400.0); // Paint: int x[], y[]; Polygon polygonArray[] = _makePolygonArray(temp); zSort(polygonArray); for(int j = 0; j < polygonArray.length; j++) { Matrix n0 = getCentroid(polygonArray[j]); Matrix n1 = getNormal(polygonArray[j]); Matrix n2 = getLine(n0, _light); float dot1 = (float)dot(n1, n2); float dot = (float)(dot1 / 6.0 + 0.5); x = getX(polygonArray[j], temp); y = getY(polygonArray[j], temp); g.setColor(new Color(0, dot, 0)); g.fillPolygon(x, y, x.length); g.setColor(new Color(dot, 0, dot)); g.drawPolygon(x, y, x.length); } } public boolean imageUpdate(Image img, int infoflags, int x, int y, int width, int height) { return true; } /** * Is the animation thread running? */ public boolean isRunning() { synchronized(_stopLock) { return !_stopFlag; } } /** * Stop the animation thread on applet stop. */ public void stop() { synchronized(_stopLock) { _stopFlag = true; } } /** * Stop the animation thread on applet destory. */ public void destroy() { synchronized(_stopLock) { _stopFlag = true; } } /** * Start the applet. */ public void start() { new Thread(this).start(); } /** * Main animation run method. */ public void run() { // Set the stop flag synchronized(_stopLock) { _stopFlag = false; } Graphics g; try { // Create the off screen image buffer Image offscreen = createImage(WIDTH, HEIGHT); // Paint the objects while the applet // is running while(isRunning()) { // Try to do close to 30 frames per second try { Thread.sleep(1000/30); } catch(InterruptedException ie) { } // Paint onto the image paint(offscreen.getGraphics()); // If the applet got stoped // in the body of this loop // getGraphics() will return // null. If it is null stop // the animation loop. if((g = getGraphics()) == null) break; // Paint the image onto the applet g.drawImage(offscreen, 0, 0, this); // Rotate about X,Y and Z one degree at a time // if the x,y or z keys are pressed. for(int i = 0; i < _vertexArray.length; i++) { synchronized(_xRot) { if(_xOn) { _vertexArray[i] = _xRot.mul(_vertexArray[i]); } } synchronized(_yRot) { if(_yOn) { _vertexArray[i] = _yRot.mul(_vertexArray[i]); } } synchronized(_zRot) { if(_zOn) { _vertexArray[i] = _zRot.mul(_vertexArray[i]); } } } // Rotate the outer cubes again for(int i = 1; i < _objectArray.length; i++) { for(int j = 0; j < _objectArray[i].length; j++) { Polygon p = _objectArray[i][j]; for(int k = 0; k < p.vertexArray.length; k++) { synchronized(_xRot) { if(_xOn) { _vertexArray[p.vertexArray[k]] = _xRot.mul(_vertexArray[p.vertexArray[k]]); } } synchronized(_yRot) { if(_yOn) _vertexArray[p.vertexArray[k]] = _yRot.mul(_vertexArray[p.vertexArray[k]]); } synchronized(_zRot) { if(_zOn) { _vertexArray[p.vertexArray[k]] = _zRot.mul(_vertexArray[p.vertexArray[k]]); } } } } } } } finally { // Set the stop flag synchronized(_stopLock) { _stopFlag = true; } } } }