michael@0: // 3D Cube Rotation
michael@0: // http://www.speich.net/computer/moztesting/3d.htm
michael@0: // Created by Simon Speich
michael@0: 
michael@0: var Q = new Array();
michael@0: var MTrans = new Array();  // transformation matrix
michael@0: var MQube = new Array();  // position information of qube
michael@0: var I = new Array();      // entity matrix
michael@0: var Origin = new Object();
michael@0: var Testing = new Object();
michael@0: var LoopTimer;
michael@0: 
michael@0: var DisplArea = new Object();
michael@0: DisplArea.Width = 300;
michael@0: DisplArea.Height = 300;
michael@0: 
michael@0: function DrawLine(From, To) {
michael@0:   var x1 = From.V[0];
michael@0:   var x2 = To.V[0];
michael@0:   var y1 = From.V[1];
michael@0:   var y2 = To.V[1];
michael@0:   var dx = Math.abs(x2 - x1);
michael@0:   var dy = Math.abs(y2 - y1);
michael@0:   var x = x1;
michael@0:   var y = y1;
michael@0:   var IncX1, IncY1;
michael@0:   var IncX2, IncY2;  
michael@0:   var Den;
michael@0:   var Num;
michael@0:   var NumAdd;
michael@0:   var NumPix;
michael@0: 
michael@0:   if (x2 >= x1) {  IncX1 = 1; IncX2 = 1;  }
michael@0:   else { IncX1 = -1; IncX2 = -1; }
michael@0:   if (y2 >= y1)  {  IncY1 = 1; IncY2 = 1; }
michael@0:   else { IncY1 = -1; IncY2 = -1; }
michael@0:   if (dx >= dy) {
michael@0:     IncX1 = 0;
michael@0:     IncY2 = 0;
michael@0:     Den = dx;
michael@0:     Num = dx / 2;
michael@0:     NumAdd = dy;
michael@0:     NumPix = dx;
michael@0:   }
michael@0:   else {
michael@0:     IncX2 = 0;
michael@0:     IncY1 = 0;
michael@0:     Den = dy;
michael@0:     Num = dy / 2;
michael@0:     NumAdd = dx;
michael@0:     NumPix = dy;
michael@0:   }
michael@0: 
michael@0:   NumPix = Math.round(Q.LastPx + NumPix);
michael@0: 
michael@0:   var i = Q.LastPx;
michael@0:   for (; i < NumPix; i++) {
michael@0:     Num += NumAdd;
michael@0:     if (Num >= Den) {
michael@0:       Num -= Den;
michael@0:       x += IncX1;
michael@0:       y += IncY1;
michael@0:     }
michael@0:     x += IncX2;
michael@0:     y += IncY2;
michael@0:   }
michael@0:   Q.LastPx = NumPix;
michael@0: }
michael@0: 
michael@0: function CalcCross(V0, V1) {
michael@0:   var Cross = new Array();
michael@0:   Cross[0] = V0[1]*V1[2] - V0[2]*V1[1];
michael@0:   Cross[1] = V0[2]*V1[0] - V0[0]*V1[2];
michael@0:   Cross[2] = V0[0]*V1[1] - V0[1]*V1[0];
michael@0:   return Cross;
michael@0: }
michael@0: 
michael@0: function CalcNormal(V0, V1, V2) {
michael@0:   var A = new Array();   var B = new Array(); 
michael@0:   for (var i = 0; i < 3; i++) {
michael@0:     A[i] = V0[i] - V1[i];
michael@0:     B[i] = V2[i] - V1[i];
michael@0:   }
michael@0:   A = CalcCross(A, B);
michael@0:   var Length = Math.sqrt(A[0]*A[0] + A[1]*A[1] + A[2]*A[2]); 
michael@0:   for (var i = 0; i < 3; i++) A[i] = A[i] / Length;
michael@0:   A[3] = 1;
michael@0:   return A;
michael@0: }
michael@0: 
michael@0: function CreateP(X,Y,Z) {
michael@0:   this.V = [X,Y,Z,1];
michael@0: }
michael@0: 
michael@0: // multiplies two matrices
michael@0: function MMulti(M1, M2) {
michael@0:   var M = [[],[],[],[]];
michael@0:   var i = 0;
michael@0:   var j = 0;
michael@0:   for (; i < 4; i++) {
michael@0:     j = 0;
michael@0:     for (; j < 4; j++) M[i][j] = M1[i][0] * M2[0][j] + M1[i][1] * M2[1][j] + M1[i][2] * M2[2][j] + M1[i][3] * M2[3][j];
michael@0:   }
michael@0:   return M;
michael@0: }
michael@0: 
michael@0: //multiplies matrix with vector
michael@0: function VMulti(M, V) {
michael@0:   var Vect = new Array();
michael@0:   var i = 0;
michael@0:   for (;i < 4; i++) Vect[i] = M[i][0] * V[0] + M[i][1] * V[1] + M[i][2] * V[2] + M[i][3] * V[3];
michael@0:   return Vect;
michael@0: }
michael@0: 
michael@0: function VMulti2(M, V) {
michael@0:   var Vect = new Array();
michael@0:   var i = 0;
michael@0:   for (;i < 3; i++) Vect[i] = M[i][0] * V[0] + M[i][1] * V[1] + M[i][2] * V[2];
michael@0:   return Vect;
michael@0: }
michael@0: 
michael@0: // add to matrices
michael@0: function MAdd(M1, M2) {
michael@0:   var M = [[],[],[],[]];
michael@0:   var i = 0;
michael@0:   var j = 0;
michael@0:   for (; i < 4; i++) {
michael@0:     j = 0;
michael@0:     for (; j < 4; j++) M[i][j] = M1[i][j] + M2[i][j];
michael@0:   }
michael@0:   return M;
michael@0: }
michael@0: 
michael@0: function Translate(M, Dx, Dy, Dz) {
michael@0:   var T = [
michael@0:   [1,0,0,Dx],
michael@0:   [0,1,0,Dy],
michael@0:   [0,0,1,Dz],
michael@0:   [0,0,0,1]
michael@0:   ];
michael@0:   return MMulti(T, M);
michael@0: }
michael@0: 
michael@0: function RotateX(M, Phi) {
michael@0:   var a = Phi;
michael@0:   a *= Math.PI / 180;
michael@0:   var Cos = Math.cos(a);
michael@0:   var Sin = Math.sin(a);
michael@0:   var R = [
michael@0:   [1,0,0,0],
michael@0:   [0,Cos,-Sin,0],
michael@0:   [0,Sin,Cos,0],
michael@0:   [0,0,0,1]
michael@0:   ];
michael@0:   return MMulti(R, M);
michael@0: }
michael@0: 
michael@0: function RotateY(M, Phi) {
michael@0:   var a = Phi;
michael@0:   a *= Math.PI / 180;
michael@0:   var Cos = Math.cos(a);
michael@0:   var Sin = Math.sin(a);
michael@0:   var R = [
michael@0:   [Cos,0,Sin,0],
michael@0:   [0,1,0,0],
michael@0:   [-Sin,0,Cos,0],
michael@0:   [0,0,0,1]
michael@0:   ];
michael@0:   return MMulti(R, M);
michael@0: }
michael@0: 
michael@0: function RotateZ(M, Phi) {
michael@0:   var a = Phi;
michael@0:   a *= Math.PI / 180;
michael@0:   var Cos = Math.cos(a);
michael@0:   var Sin = Math.sin(a);
michael@0:   var R = [
michael@0:   [Cos,-Sin,0,0],
michael@0:   [Sin,Cos,0,0],
michael@0:   [0,0,1,0],   
michael@0:   [0,0,0,1]
michael@0:   ];
michael@0:   return MMulti(R, M);
michael@0: }
michael@0: 
michael@0: function DrawQube() {
michael@0:   // calc current normals
michael@0:   var CurN = new Array();
michael@0:   var i = 5;
michael@0:   Q.LastPx = 0;
michael@0:   for (; i > -1; i--) CurN[i] = VMulti2(MQube, Q.Normal[i]);
michael@0:   if (CurN[0][2] < 0) {
michael@0:     if (!Q.Line[0]) { DrawLine(Q[0], Q[1]); Q.Line[0] = true; };
michael@0:     if (!Q.Line[1]) { DrawLine(Q[1], Q[2]); Q.Line[1] = true; };
michael@0:     if (!Q.Line[2]) { DrawLine(Q[2], Q[3]); Q.Line[2] = true; };
michael@0:     if (!Q.Line[3]) { DrawLine(Q[3], Q[0]); Q.Line[3] = true; };
michael@0:   }
michael@0:   if (CurN[1][2] < 0) {
michael@0:     if (!Q.Line[2]) { DrawLine(Q[3], Q[2]); Q.Line[2] = true; };
michael@0:     if (!Q.Line[9]) { DrawLine(Q[2], Q[6]); Q.Line[9] = true; };
michael@0:     if (!Q.Line[6]) { DrawLine(Q[6], Q[7]); Q.Line[6] = true; };
michael@0:     if (!Q.Line[10]) { DrawLine(Q[7], Q[3]); Q.Line[10] = true; };
michael@0:   }
michael@0:   if (CurN[2][2] < 0) {
michael@0:     if (!Q.Line[4]) { DrawLine(Q[4], Q[5]); Q.Line[4] = true; };
michael@0:     if (!Q.Line[5]) { DrawLine(Q[5], Q[6]); Q.Line[5] = true; };
michael@0:     if (!Q.Line[6]) { DrawLine(Q[6], Q[7]); Q.Line[6] = true; };
michael@0:     if (!Q.Line[7]) { DrawLine(Q[7], Q[4]); Q.Line[7] = true; };
michael@0:   }
michael@0:   if (CurN[3][2] < 0) {
michael@0:     if (!Q.Line[4]) { DrawLine(Q[4], Q[5]); Q.Line[4] = true; };
michael@0:     if (!Q.Line[8]) { DrawLine(Q[5], Q[1]); Q.Line[8] = true; };
michael@0:     if (!Q.Line[0]) { DrawLine(Q[1], Q[0]); Q.Line[0] = true; };
michael@0:     if (!Q.Line[11]) { DrawLine(Q[0], Q[4]); Q.Line[11] = true; };
michael@0:   }
michael@0:   if (CurN[4][2] < 0) {
michael@0:     if (!Q.Line[11]) { DrawLine(Q[4], Q[0]); Q.Line[11] = true; };
michael@0:     if (!Q.Line[3]) { DrawLine(Q[0], Q[3]); Q.Line[3] = true; };
michael@0:     if (!Q.Line[10]) { DrawLine(Q[3], Q[7]); Q.Line[10] = true; };
michael@0:     if (!Q.Line[7]) { DrawLine(Q[7], Q[4]); Q.Line[7] = true; };
michael@0:   }
michael@0:   if (CurN[5][2] < 0) {
michael@0:     if (!Q.Line[8]) { DrawLine(Q[1], Q[5]); Q.Line[8] = true; };
michael@0:     if (!Q.Line[5]) { DrawLine(Q[5], Q[6]); Q.Line[5] = true; };
michael@0:     if (!Q.Line[9]) { DrawLine(Q[6], Q[2]); Q.Line[9] = true; };
michael@0:     if (!Q.Line[1]) { DrawLine(Q[2], Q[1]); Q.Line[1] = true; };
michael@0:   }
michael@0:   Q.Line = [false,false,false,false,false,false,false,false,false,false,false,false];
michael@0:   Q.LastPx = 0;
michael@0: }
michael@0: 
michael@0: function Loop() {
michael@0:   if (Testing.LoopCount > Testing.LoopMax) return;
michael@0:   var TestingStr = String(Testing.LoopCount);
michael@0:   while (TestingStr.length < 3) TestingStr = "0" + TestingStr;
michael@0:   MTrans = Translate(I, -Q[8].V[0], -Q[8].V[1], -Q[8].V[2]);
michael@0:   MTrans = RotateX(MTrans, 1);
michael@0:   MTrans = RotateY(MTrans, 3);
michael@0:   MTrans = RotateZ(MTrans, 5);
michael@0:   MTrans = Translate(MTrans, Q[8].V[0], Q[8].V[1], Q[8].V[2]);
michael@0:   MQube = MMulti(MTrans, MQube);
michael@0:   var i = 8;
michael@0:   for (; i > -1; i--) {
michael@0:     Q[i].V = VMulti(MTrans, Q[i].V);
michael@0:   }
michael@0:   DrawQube();
michael@0:   Testing.LoopCount++;
michael@0:   Loop();
michael@0: }
michael@0: 
michael@0: function Init(CubeSize) {
michael@0:   // init/reset vars
michael@0:   Origin.V = [150,150,20,1];
michael@0:   Testing.LoopCount = 0;
michael@0:   Testing.LoopMax = 50;
michael@0:   Testing.TimeMax = 0;
michael@0:   Testing.TimeAvg = 0;
michael@0:   Testing.TimeMin = 0;
michael@0:   Testing.TimeTemp = 0;
michael@0:   Testing.TimeTotal = 0;
michael@0:   Testing.Init = false;
michael@0: 
michael@0:   // transformation matrix
michael@0:   MTrans = [
michael@0:   [1,0,0,0],
michael@0:   [0,1,0,0],
michael@0:   [0,0,1,0],
michael@0:   [0,0,0,1]
michael@0:   ];
michael@0:   
michael@0:   // position information of qube
michael@0:   MQube = [
michael@0:   [1,0,0,0],
michael@0:   [0,1,0,0],
michael@0:   [0,0,1,0],
michael@0:   [0,0,0,1]
michael@0:   ];
michael@0:   
michael@0:   // entity matrix
michael@0:   I = [
michael@0:   [1,0,0,0],
michael@0:   [0,1,0,0],
michael@0:   [0,0,1,0],
michael@0:   [0,0,0,1]
michael@0:   ];
michael@0:   
michael@0:   // create qube
michael@0:   Q[0] = new CreateP(-CubeSize,-CubeSize, CubeSize);
michael@0:   Q[1] = new CreateP(-CubeSize, CubeSize, CubeSize);
michael@0:   Q[2] = new CreateP( CubeSize, CubeSize, CubeSize);
michael@0:   Q[3] = new CreateP( CubeSize,-CubeSize, CubeSize);
michael@0:   Q[4] = new CreateP(-CubeSize,-CubeSize,-CubeSize);
michael@0:   Q[5] = new CreateP(-CubeSize, CubeSize,-CubeSize);
michael@0:   Q[6] = new CreateP( CubeSize, CubeSize,-CubeSize);
michael@0:   Q[7] = new CreateP( CubeSize,-CubeSize,-CubeSize);
michael@0:   
michael@0:   // center of gravity
michael@0:   Q[8] = new CreateP(0, 0, 0);
michael@0:   
michael@0:   // anti-clockwise edge check
michael@0:   Q.Edge = [[0,1,2],[3,2,6],[7,6,5],[4,5,1],[4,0,3],[1,5,6]];
michael@0:   
michael@0:   // calculate squad normals
michael@0:   Q.Normal = new Array();
michael@0:   for (var i = 0; i < Q.Edge.length; i++) Q.Normal[i] = CalcNormal(Q[Q.Edge[i][0]].V, Q[Q.Edge[i][1]].V, Q[Q.Edge[i][2]].V);
michael@0:   
michael@0:   // line drawn ?
michael@0:   Q.Line = [false,false,false,false,false,false,false,false,false,false,false,false];
michael@0:   
michael@0:   // create line pixels
michael@0:   Q.NumPx = 9 * 2 * CubeSize;
michael@0:   for (var i = 0; i < Q.NumPx; i++) CreateP(0,0,0);
michael@0:   
michael@0:   MTrans = Translate(MTrans, Origin.V[0], Origin.V[1], Origin.V[2]);
michael@0:   MQube = MMulti(MTrans, MQube);
michael@0: 
michael@0:   var i = 0;
michael@0:   for (; i < 9; i++) {
michael@0:     Q[i].V = VMulti(MTrans, Q[i].V);
michael@0:   }
michael@0:   DrawQube();
michael@0:   Testing.Init = true;
michael@0:   Loop();
michael@0: }
michael@0: 
michael@0: for ( var i = 20; i <= 160; i *= 2 ) {
michael@0:   Init(i);
michael@0: }
michael@0: 
michael@0: var actual = '';
michael@0: for (var i = 0; i < Q.length; ++i) {
michael@0:   actual += Q[i].V + ';';
michael@0: }
michael@0: var expected = "-116.618229186398,212.51135212951073,62.5094191967962,1;127.83701023614447,417.11611179082263,90.41153816299942,1;293.9570894432935,196.58093046570656,252.17789153139591,1;49.501850020750915,-8.02382919560505,224.275772565193,1;6.042910556709444,103.41906953429206,-212.1778915313964,1;250.49814997925202,308.02382919560387,-184.27577256519325,1;416.61822918640064,87.48864787048812,-22.509419196796493,1;172.1629897638581,-117.1161117908236,-50.41153816299975,1;150.0000000000007,149.99999999999952,20,1;";
michael@0: assertEq(actual, expected);
michael@0: 
michael@0: Q = null;
michael@0: MTrans = null;
michael@0: MQube = null;
michael@0: I = null;
michael@0: Origin = null;
michael@0: Testing = null;
michael@0: LoopTime = null;
michael@0: DisplArea = null;
michael@0: