/*- * morph3d.c - Shows 3D morphing objects * * Converted to GLUT by brianp on 1/1/98 * * This program was inspired on a WindowsNT(R)'s screen saver. It was written * from scratch and it was not based on any other source code. * * Porting it to xlock (the final objective of this code (float)Math.since the moment I * decided to create it) was possible by comparing the original Mesa's gear * demo with it's ported version, so thanks for Danny Sung for his indirect * help (look at gear.c in xlock source tree). NOTE: At the moment this code * was sent to Brian Paul for package inclusion, the XLock Version was not * available. In fact, I'll wait it to appear on the next Mesa release (If you * are reading this, it means THIS release) to send it for xlock package * inclusion). It will probably there be a GLUT version too. * * Thanks goes also to Brian Paul for making it possible and inexpensive * to use OpenGL at home. * * Since I'm not a native english speaker, my apologies for any gramatical * mistake. * * My e-mail addresses are * * vianna@cat.cbpf.br * and * marcelo@venus.rdc.puc-rio.br * * Marcelo F. Vianna (Feb-13-1997) */ /* This document is VERY incomplete, but tries to describe the mathematics used in the program. At this moment it just describes how the polyhedra are generated. On futhurer versions, this document will be probabbly improved. Since I'm not a native english speaker, my apologies for any gramatical mistake. Marcelo Fernandes Vianna - Undergraduate in Computer Engeneering at Catholic Pontifical University - of Rio de Janeiro (PUC-Rio) Brasil. - e-mail: vianna@cat.cbpf.br or marcelo@venus.rdc.puc-rio.br - Feb-13-1997 POLYHEDRA GENERATION For the purpose of this program it's not sufficient to know the polyhedra vertexes coordinates. Since the morphing algorithm applies a nonlinear transformation over the surfaces (faces) of the polyhedron, each face has to be divided into smaller ones. The morphing algorithm needs to transform each vertex of these smaller faces individually. It's a very time consoming task. In order to reduce calculation overload, and (float)Math.since all the macro faces of the polyhedron are transformed by the same way, the generation is made by creating only one face of the polyhedron, morphing it and then rotating it around the polyhedron center. What we need to know is the face radius of the polyhedron (the radius of the inscribed sphere) and the angle between the center of two adjacent faces u(float)Math.sing the center of the sphere as the angle's vertex. The face radius of the regular polyhedra are known values which I decided to not waste my time calculating. Following is a table of face radius for the regular polyhedra with edge length = 1: TETRAHEDRON : 1/(2*(float)Math.sqrt(2))/(float)Math.sqrt(3) CUBE : 1/2 OCTAHEDRON : 1/(float)Math.sqrt(6) DODECAHEDRON : T^2 * (float)Math.sqrt((T+2)/5) / 2 -> where T=((float)Math.sqrt(5)+1)/2 ICOSAHEDRON : (3*(float)Math.sqrt(3)+(float)Math.sqrt(15))/12 I've not found any reference about the mentioned angles, so I needed to calculate them, not a trivial task until I figured out how :) Curiously these angles are the same for the tetrahedron and octahedron. A way to obtain this value is inscribing the tetrahedron inside the cube by matching their vertexes. So you'll notice that the remaining unmatched vertexes are in the same straight line starting in the cube/tetrahedron center and cros(float)Math.sing the center of each tetrahedron's face. At this point it's easy to obtain the bigger angle of the isosceles triangle formed by the center of the cube and two opposite vertexes on the same cube face. The edges of this triangle have the following lenghts: (float)Math.sqrt(2) for the base and (float)Math.sqrt(3)/2 for the other two other edges. So the angle we want is: +-----------------------------------------------------------+ | 2*ARCSIN((float)Math.sqrt(2)/(float)Math.sqrt(3)) = 109.47122063449069174f degrees | +-----------------------------------------------------------+ For the cube this angle is obvious, but just for formality it can be easily obtained because we also know it's isosceles edge lenghts: (float)Math.sqrt(2)/2 for the base and 1/2 for the other two edges. So the angle we want is: +-----------------------------------------------------------+ | 2*ARCSIN(((float)Math.sqrt(2)/2)/1) = 90.000000000000000000f degrees | +-----------------------------------------------------------+ For the octahedron we use the same idea used for the tetrahedron, but now we inscribe the cube inside the octahedron so that all cubes's vertexes matches excatly the center of each octahedron's face. It's now clear that this angle is the same of the thetrahedron one: +-----------------------------------------------------------+ | 2*ARCSIN((float)Math.sqrt(2)/(float)Math.sqrt(3)) = 109.47122063449069174f degrees | +-----------------------------------------------------------+ For the dodecahedron it's a little bit harder because it's only relationship with the cube is useless to us. So we need to solve the problem by another way. The concept of Face radius also exists on 2D polygons with the name Edge radius: Edge Radius For Pentagon (ERp) ERp = (1/2)/TAN(36 degrees) * VRp = 0.6881909602355867905f (VRp is the pentagon's vertex radio). Face Radius For Dodecahedron FRd = T^2 * (float)Math.sqrt((T+2)/5) / 2 = 1.1135163644116068404f Why we need ERp? Well, ERp and FRd segments forms a 90 degrees angle, completing this triangle, the lesser angle is a half of the angle we are looking for, so this angle is: +-----------------------------------------------------------+ | 2*ARCTAN(ERp/FRd) = 63.434948822922009981f degrees | +-----------------------------------------------------------+ For the icosahedron we can use the same method used for dodecahedron (well the method used for dodecahedron may be used for all regular polyhedra) Edge Radius For Triangle (this one is well known: 1/3 of the triangle height) ERt = (float)Math.sin(60)/3 = (float)Math.sqrt(3)/6 = 0.2886751345948128655f Face Radius For Icosahedron FRi= (3*(float)Math.sqrt(3)+(float)Math.sqrt(15))/12 = 0.7557613140761707538f So the angle is: +-----------------------------------------------------------+ | 2*ARCTAN(ERt/FRi) = 41.810314895778596167f degrees | +-----------------------------------------------------------+ */ import java.applet.*; import java.awt.*; import java.awt.event.*; import java.lang.*; import java.util.*; import java.io.*; import java.util.*; import gl4java.GLContext; import gl4java.awt.GLCanvas; import gl4java.awt.GLAnimCanvas; import gl4java.applet.SimpleGLAnimApplet1; import gl4java.utils.textures.*; public class morph3d extends SimpleGLAnimApplet1 { static final float Scale =0.3f; static final float tetraangle = 109.47122063449069174f; static final float cubeangle = 90.000000000000000000f; static final float octaangle = 109.47122063449069174f; static final float dodecaangle = 63.434948822922009981f; static final float icoangle = 41.810314895778596167f; static final float Pi = 3.1415926535897932385f; static final float SQRT2 = 1.4142135623730951455f; static final float SQRT3 = 1.7320508075688771932f; static final float SQRT5 = 2.2360679774997898051f; static final float SQRT6 = 2.4494897427831778813f; static final float SQRT15 = 3.8729833462074170214f; static final float cossec36_2 = 0.8506508083520399322f; static final float cos72 = 0.3090169943749474241f; static final float sin72 = 0.9510565162951535721f; static final float cos36 = 0.8090169943749474241f; static final float sin36 = 0.5877852522924731292f; static final float TAU = (SQRT5+1f)/2.0f; /* Initialize the applet */ boolean isAnApplet = true; public morph3d() { super(); } public void init() { super.init(); Dimension d = getSize(); canvas = new morph3dCanvas(d.width, d.height); add("Center", canvas); } public static void main( String args[] ) { Frame mainFrame = new Frame("morph3d"); mainFrame.addWindowListener( new WindowAdapter() { public void windowClosed(WindowEvent e) { System.exit(0); } public void windowClosing(WindowEvent e) { windowClosed(e); } } ); GLContext.gljNativeDebug = true; GLContext.gljClassDebug = true; morph3d applet = new morph3d(); applet.isAnApplet = false; applet.setSize(400, 400); applet.init(); applet.start(); mainFrame.add(applet); mainFrame.pack(); mainFrame.setVisible(true); } /* Local GLCanvas extension class */ private class morph3dCanvas extends GLAnimCanvas implements MouseListener, ActionListener { private PopupMenu menu = null; private boolean menu_showing = false; private boolean save_suspended = false; private final String MENUE_0 = "Tetrahedron"; private final String MENUE_1 = "Hexahedron (Cube)"; private final String MENUE_2 = "Octahedron"; private final String MENUE_3 = "Dodecahedron"; private final String MENUE_4 = "Icosahedron"; private final String MENUE_5 = "Toggle colored faces"; private final String MENUE_6 = "Toggle smooth/flat shading"; private final String MENU_SNAPSHOT = "Snapshot"; TGATextureGrabber textgrab = null; boolean doSnapshot=false; /* Increasing this values produces better image quality, the price is speed. */ /* Very low values produces erroneous/incorrect plotting */ int tetradivisions = 23; int cubedivisions = 20; int octadivisions = 21; int dodecadivisions = 10; int icodivisions = 15; boolean mono=false; boolean smooth=true; int WindH, WindW; float step=0; float seno; int object; int edgedivisions; float Magnitude; // float *MaterialColor[20]; float MaterialColor[][]; float front_shininess[] = {60.0f}; float front_specular[] = { 0.7f, 0.7f, 0.7f, 1.0f }; float ambient[] = { 0.0f, 0.0f, 0.0f, 1.0f }; float diffuse[] = { 1.0f, 1.0f, 1.0f, 1.0f }; float position0[] = { 1.0f, 1.0f, 1.0f, 0.0f }; float position1[] = {-1.0f,-1.0f, 1.0f, 0.0f }; float lmodel_ambient[] = { 0.5f, 0.5f, 0.5f, 1.0f }; float lmodel_twoside[] = {1.0f}; float MaterialRed[] = { 0.7f, 0.0f, 0.0f, 1.0f }; float MaterialGreen[] = { 0.1f, 0.5f, 0.2f, 1.0f }; float MaterialBlue[] = { 0.0f, 0.0f, 0.7f, 1.0f }; float MaterialCyan[] = { 0.2f, 0.5f, 0.7f, 1.0f }; float MaterialYellow[] = { 0.7f, 0.7f, 0.0f, 1.0f }; float MaterialMagenta[] = { 0.6f, 0.2f, 0.5f, 1.0f }; float MaterialWhite[] = { 0.7f, 0.7f, 0.7f, 1.0f }; float MaterialGray[] = { 0.2f, 0.2f, 0.2f, 1.0f }; public morph3dCanvas(int w, int h) { super(w, h); setAnimateFps(30.0); } public void preInit() { doubleBuffer = true; stereoView = false; rgba = true; } final float VectMulX(float Y1,float Z1,float Y2,float Z2) { return (Y1)*(Z2)-(Z1)*(Y2); } final float VectMulY(float X1,float Z1,float X2,float Z2) { return (Z1)*(X2)-(X1)*(Z2); } final float VectMulZ(float X1,float Y1,float X2,float Y2) { return (X1)*(Y2)-(Y1)*(X2); } final float sqr(float A) { return (A)*(A); } final void TRIANGLE(float Edge, float Amp, int Divisions, float Z) { float Xf,Yf,Xa,Yb,Xf2,Yf2; float Factor,Factor1,Factor2; float VertX,VertY,VertZ,NeiAX,NeiAY,NeiAZ,NeiBX,NeiBY,NeiBZ; float Ax,Ay,Bx; int Ri,Ti; float Vr=(Edge)*SQRT3/3; float AmpVr2=(Amp)/sqr(Vr); float Zf=(Edge)*(Z); Ax=(Edge)*(+0.5f/(Divisions)); Ay=(Edge)*(-SQRT3/(2*Divisions)); Bx=(Edge)*(-0.5f/(Divisions)); for (Ri=1; Ri<=(Divisions); Ri++) { gl.glBegin(GL_TRIANGLE_STRIP); for (Ti=0; Ti