/* * Program: Dodecahedron.java * Purpose: Solid 3D Objects * Author: George Aroush * Date: 1/1/1998 * Change Log: None * * Full description of Program: * Use of "painter's algorithm" to display filled in dodecahedron */ import java.applet.*; import java.awt.*; public class Dodecahedron extends Applet { final int NP = 21; /* number of points */ final int NF = 12; /* number of faces */ final int MAX_V = 5; /* largest number of vertices in a face */ final int ARRAYSIZE = (5 + MAX_V); /* number of values in a face array */ final int CX = 320; /* center of screen */ final int CY = 200; /* edges of screen */ final int MAXX = 640; final int MAXY = 400; /* index into our 3D array */ final int X = 0; final int Y = 1; final int Z = 2; /* positions (or offsets) in face array */ final int QTY = 0; /* number of vertices in face */ final int COLOR_R = 1; /* color of face - Red */ final int COLOR_G = 2; /* color of face - Green */ final int COLOR_B = 3; /* color of face - Blue */ final int FAR_Z = 4; /* most distant vertex in face */ final int VERT = 5; /* start of vertex numbers */ public void paint(Graphics g) { /* coordinates of 20 vertices of dodecahedron */ float oCoord[][] = {{-30, 78, 0}, { 30, 78, 0}, {48, 48, 48}, { 0, 30, 78}, {-48, 48, 48}, { 48, 48, -48}, { 0, 30, -78}, {-48, 48, -48}, {-78, 0, 30}, {-78, 0, -30}, {78, 0, 30}, { 78, 0, -30}, {-48, -48, 48}, { 0, -30, 78}, {48, -48, 48}, {-48, -48, -48}, {-30, -78, 0}, { 48, -48, -48}, { 0, -30, -78}, { 30, -78, 0}, { 0, 0, 0}}; /* 21st vertex added for center of dodecahedron */ /* to hold temporary values of vertices */ float coord[][] = new float[NP][3]; /* The twelve faces */ int faces[][] = { {5, /* number of vertices in face */ 0, 0, 255, /* color of face */ 0, /* place for farthest z */ 0, 1, 5, 6, 7}, /* vertices */ {5, 0, 255, 255, 0, 1, 0, 4, 3, 2}, {5, 64, 64, 64, 0, 16, 15, 18, 17, 19}, {5, 128, 128, 128, 0, 16, 19, 14, 13, 12}, {5, 0, 255, 0, 0, 9, 8, 4, 0, 7}, {5, 192, 192, 192, 0, 10, 11, 5, 1, 2}, {5, 255, 0, 255, 0, 8, 9, 15, 16, 12}, {5, 255, 200, 0, 0, 11, 10, 14, 19, 17}, {5, 255, 175, 175, 0, 18, 6, 5, 11, 17}, {5, 255, 0, 0, 0, 7, 6, 18, 15, 9}, {5, 255, 255, 255, 0, 3, 4, 8, 12, 13}, {5, 255, 255, 0, 0, 3, 13, 14, 10, 2} }; /* the location of the object in 3D space */ float trans[] = {0, 0, 900}; /* velocity along X, Y, & Z axes*/ float vel[] = {20, 20, 20}; /* the size of the object */ float scal[] = {2, 2, 2}; /* current angles of rotation of object */ float angle[] = {0, 0, 0}; /* rates of rotation of object */ float ang_inc[] = {0.08f, 0.05f, 0.0722f}; /* minimum and maximum X Y & Z values for vertex 21 */ float limits[][] = { {-500, 500}, {-500, 500}, { 700, 5000} }; /* holds the projected (2D) object */ int proj[][] = new int[NP][2]; /* screen distance */ float sd = 300; /* for looping */ int i, j; /* * Copy dodecahedron from unchanging, original arrays, * scale and rotate around three axes move it, project * vertices, determine farthest Z-coordinate for each * face, sort the faces from back to front, & draw them * in that order */ for (j = 0; j < 10000; j++) { Copy3D(oCoord, coord, NP); Scale3D(coord, scal, NP); Rotate3D(coord, Y, Z, NP, angle[X]); Rotate3D(coord, Z, X, NP, angle[Y]); Rotate3D(coord, X, Y, NP, angle[Z]); Translate3D(coord, trans, NP); /* * Test center of icosahedron and reverse direction * of velocity if it has crossed a limit */ for (i = X; i <= Z; i++) { if (coord[NP - 1][i] < limits[i][0] || coord[NP - 1][i] > limits[i][1]) vel[i] *= -1.0; trans[i] += vel[i]; /* change location of object */ angle[i] += ang_inc[i]; /* change angles of rotation */ if (angle[i] > 2 * Math.PI) angle[i] -= 2 * Math.PI; } Project3D(coord, proj, NP, sd); /* Find farthest z of each face, store in FAR_Z position in its array */ FarthestZ(coord, faces, NF); /* Sort faces from back to front, using BubbleSort() algorithm */ BubbleSort(faces, NF, ARRAYSIZE); FDisplay3D(proj, faces, NF, g); Delay(100); g.clearRect(0, 0, 640, 480); } } /* * void FarthestZ() * * Determines farthest z-coordinate in each face */ void FarthestZ(float v[][], int f[][], int nf) { int i, j; for (i = 0; i < nf; i++) { f[i][FAR_Z] = 0; /* assume it's zero */ for (j = 0; j < f[i][QTY]; j++) { /* * Vertex numbers start at f[i][VERT], so j is added to * get desired vertex number. This vertex number is * plugged into v[][Z] to get the actual Z-coordinate */ /* * Compare each Z-coordinate to current far_z. If a * Z-coordinate is farther, use its value for far_z */ if (f[i][FAR_Z] < (int) v[f[i][VERT + j]][Z]) f[i][FAR_Z] = (int) v[f[i][VERT + j]][Z]; } } } /* * void FDisplay() * * Displays filled faces of object. Uses values in faces[][] to set * color and fill x[] and y[] with projected values to be filled with area(). */ void FDisplay3D(int proj[][], int faces[][], int nf, Graphics g) { boolean on; int x[] = new int[MAX_V]; int y[] = new int[MAX_V]; int f, v; /* faces should have been sorted from front to back */ for (f = 0; f < nf; f++) { on = true; /* * This loop continues while v is less than # of vertices, * and on = 1, meaning all the points are on the screen */ for (v = 0; v < faces[f][QTY]; v++) { /* * vertex numbers start at faces[f][VERT], so v is added * to get desired vertex number. This vertex number is * plugged into proj[][] to get projected X and Y-coord */ x[v] = proj[ faces[f][ VERT + v] ][X]; y[v] = proj[ faces[f][ VERT + v] ][Y]; /* make sure this point is on screen */ if (x[v] < 0 || x[v] > MAXX || y[v] < 0 || y[v] > MAXY) on = false; } if (on == true) { Color c = new Color(faces[f][COLOR_R], faces[f][COLOR_G], faces[f][COLOR_B]); g.setColor(c); /* get color from face array */ g.fillPolygon(x, y, faces[f][QTY]); /* fill face */ /* Delay(1000); */ /* uncomment this line to see the drawing in action */ } } } /* * void BubbleSort() * * Sorts an array using the Bubble Sort algorithm */ void BubbleSort(int faces[][], int nf, int faceSize) { int faceDataA[] = new int[faceSize], faceDataB[] = new int[faceSize]; int facesIndexA, facesIndexB; int nDiff; int i, j; while (nf > 1) { bIsDone = true; facesIndexA = 0; for (i = 0; i < nf - 1; i++) /* walk throuh faces and move things up/down as needed */ { /* get a face off the list */ for (j = 0; j < faceSize; j++) faceDataA[j] = faces[facesIndexA][j]; facesIndexB = facesIndexA + 1; /* get the second face */ for (j = 0; j < faceSize; j++) faceDataB[j] = faces[facesIndexB][j]; /* check the 'far-z' of those faces */ if (faceDataA[FAR_Z] == faceDataB[FAR_Z]) nDiff = 0; else { if (faceDataA[FAR_Z] > faceDataB[FAR_Z]) nDiff = 1; else nDiff = -1; } /* if they are not equal the we must swap them */ if (nDiff != 0) { if (nDiff < 0) { /* we will swap now */ for (j = 0; j < faceSize; j++) faces[facesIndexA][j] = faceDataB[j]; for (j = 0; j < faceSize; j++) faces[facesIndexB][j] = faceDataA[j]; } } facesIndexA++; /* get the next element in the array */ } nf--; } } /* * void Project3D() * * Projects coordinate array onto screen at given screen distance * storing result as x and y coordinates in proj[][2] array. */ void Project3D(float coord[][], int proj[][], int np, float sd) { int i; /* * scale each x and y by the ratio of the the screen * distance to the Z-coordinate -- add coordinates of * center of screen to shift origin to center of screen */ for (i = 0; i < np; i++) { if (coord[i][Z] != 0.0f) { proj[i][X] = CX + (int) (coord[i][X] * sd / coord[i][Z]); proj[i][Y] = CY + (int) (coord[i][Y] * sd / coord[i][Z]); } else proj[i][X] = proj[i][Y] = 0; } } /* * void Translate3D() * * Add three values of trans[3] to each vertex in coord[][3] thus * moving vertices along all three axes */ void Translate3D(float coord[][], float trans[], int np) { int i, j; for (i = 0; i < np; i++) /* loop in the array */ { for (j = 0; j < 3; j++) /* loop in the vertex */ coord[i][j] += trans[j]; } } /* * void Copy3D() * * Copy X, Y & Z coordinates from original arrays to temp arrays */ void Copy3D(float orig[][], float coord[][], int np) { int i, j; for (i = 0; i < np; i++) { for (j = 0; j < 3; j++) coord[i][j] = orig[i][j]; } } /* * void Scale3D() * * Multiplies each X, Y & Z coordinate by corresponding element in the array s[] */ void Scale3D(float coord[][], float s[], int np) { int i, j; for (i = 0; i < np; i++) { for (j = 0; j < 3; j++) coord[i][j] *= s[j]; } } /* * void Rotate3D() * * Rotate vertices around an axis by number of radians in angle: * for X axis rotation: c1 = Y and c2 = Z * for Y axis rotation: c1 = Z and c2 = X * for Z axis rotation: c1 = X and c2 = Y */ void Rotate3D(float coord[][], int c1, int c2, int np, float angle) { int i; float t, s, c; s = (float) Math.sin(angle); c = (float) Math.cos(angle); for (i = 0; i < np; i++) { /* temporarily store new value of coordinate 1 */ t = c * coord[i][c1] + s * coord[i][c2]; coord[i][c2] = c * coord[i][c2] - s * coord[i][c1]; coord[i][c1] = t; } } /* * void Display3D() * * Displays wire frame of object. Uses values in edge[][2] to find starting and * ending vertex for each edge */ void Display3D(int proj[][], int edge[][], int ne, Graphics g) { int e; int s, f; int x1, y1, x2, y2; for (e = 0; e < ne; e++) { s = edge[e][0]; /* s -- is the starting vertex */ f = edge[e][1]; /* f -- is the ending vertex */ x1 = proj[s][X]; /* stating point of a line */ y1 = proj[s][Y]; x2 = proj[f][X]; /* ending point of a line */ y2 = proj[f][Y]; g.drawLine(x1, y1, x2, y2); } } /* * void Delay() * * Simply pauses for some time */ public void Delay(int delayTime) { try { Thread.sleep(delayTime); /* call Java's sleep method */ } catch (InterruptedException e) { /* when the sleep() call above is over, Java will */ /* be interuppted and we fall into this block of code */ /* because our intention is simply slow down things */ /* wed do nothing in our exception code and just get out */ } } }