1// 3D Cube Rotation
2// http://www.speich.net/computer/moztesting/3d.htm
3// Created by Simon Speich
4
5var Q = new Array();
6var MTrans = new Array();  // transformation matrix
7var MQube = new Array();  // position information of qube
8var I = new Array();      // entity matrix
9var Origin = new Object();
10var Testing = new Object();
11var LoopTimer;
12
13var DisplArea = new Object();
14DisplArea.Width = 300;
15DisplArea.Height = 300;
16
17function DrawLine(From, To) {
18  var x1 = From.V[0];
19  var x2 = To.V[0];
20  var y1 = From.V[1];
21  var y2 = To.V[1];
22  var dx = Math.abs(x2 - x1);
23  var dy = Math.abs(y2 - y1);
24  var x = x1;
25  var y = y1;
26  var IncX1, IncY1;
27  var IncX2, IncY2;
28  var Den;
29  var Num;
30  var NumAdd;
31  var NumPix;
32
33  if (x2 >= x1) {  IncX1 = 1; IncX2 = 1;  }
34  else { IncX1 = -1; IncX2 = -1; }
35  if (y2 >= y1)  {  IncY1 = 1; IncY2 = 1; }
36  else { IncY1 = -1; IncY2 = -1; }
37  if (dx >= dy) {
38    IncX1 = 0;
39    IncY2 = 0;
40    Den = dx;
41    Num = dx / 2;
42    NumAdd = dy;
43    NumPix = dx;
44  }
45  else {
46    IncX2 = 0;
47    IncY1 = 0;
48    Den = dy;
49    Num = dy / 2;
50    NumAdd = dx;
51    NumPix = dy;
52  }
53
54  NumPix = Math.round(Q.LastPx + NumPix);
55
56  var i = Q.LastPx;
57  for (; i < NumPix; i++) {
58    Num += NumAdd;
59    if (Num >= Den) {
60      Num -= Den;
61      x += IncX1;
62      y += IncY1;
63    }
64    x += IncX2;
65    y += IncY2;
66  }
67  Q.LastPx = NumPix;
68}
69
70function CalcCross(V0, V1) {
71  var Cross = new Array();
72  Cross[0] = V0[1]*V1[2] - V0[2]*V1[1];
73  Cross[1] = V0[2]*V1[0] - V0[0]*V1[2];
74  Cross[2] = V0[0]*V1[1] - V0[1]*V1[0];
75  return Cross;
76}
77
78function CalcNormal(V0, V1, V2) {
79  var A = new Array();   var B = new Array();
80  for (var i = 0; i < 3; i++) {
81    A[i] = V0[i] - V1[i];
82    B[i] = V2[i] - V1[i];
83  }
84  A = CalcCross(A, B);
85  var Length = Math.sqrt(A[0]*A[0] + A[1]*A[1] + A[2]*A[2]);
86  for (var i = 0; i < 3; i++) A[i] = A[i] / Length;
87  A[3] = 1;
88  return A;
89}
90
91function CreateP(X,Y,Z) {
92  this.V = [X,Y,Z,1];
93}
94
95// multiplies two matrices
96function MMulti(M1, M2) {
97  var M = [[],[],[],[]];
98  var i = 0;
99  var j = 0;
100  for (; i < 4; i++) {
101    j = 0;
102    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];
103  }
104  return M;
105}
106
107//multiplies matrix with vector
108function VMulti(M, V) {
109  var Vect = new Array();
110  var i = 0;
111  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];
112  return Vect;
113}
114
115function VMulti2(M, V) {
116  var Vect = new Array();
117  var i = 0;
118  for (;i < 3; i++) Vect[i] = M[i][0] * V[0] + M[i][1] * V[1] + M[i][2] * V[2];
119  return Vect;
120}
121
122// add to matrices
123function MAdd(M1, M2) {
124  var M = [[],[],[],[]];
125  var i = 0;
126  var j = 0;
127  for (; i < 4; i++) {
128    j = 0;
129    for (; j < 4; j++) M[i][j] = M1[i][j] + M2[i][j];
130  }
131  return M;
132}
133
134function Translate(M, Dx, Dy, Dz) {
135  var T = [
136  [1,0,0,Dx],
137  [0,1,0,Dy],
138  [0,0,1,Dz],
139  [0,0,0,1]
140  ];
141  return MMulti(T, M);
142}
143
144function RotateX(M, Phi) {
145  var a = Phi;
146  a *= Math.PI / 180;
147  var Cos = Math.cos(a);
148  var Sin = Math.sin(a);
149  var R = [
150  [1,0,0,0],
151  [0,Cos,-Sin,0],
152  [0,Sin,Cos,0],
153  [0,0,0,1]
154  ];
155  return MMulti(R, M);
156}
157
158function RotateY(M, Phi) {
159  var a = Phi;
160  a *= Math.PI / 180;
161  var Cos = Math.cos(a);
162  var Sin = Math.sin(a);
163  var R = [
164  [Cos,0,Sin,0],
165  [0,1,0,0],
166  [-Sin,0,Cos,0],
167  [0,0,0,1]
168  ];
169  return MMulti(R, M);
170}
171
172function RotateZ(M, Phi) {
173  var a = Phi;
174  a *= Math.PI / 180;
175  var Cos = Math.cos(a);
176  var Sin = Math.sin(a);
177  var R = [
178  [Cos,-Sin,0,0],
179  [Sin,Cos,0,0],
180  [0,0,1,0],
181  [0,0,0,1]
182  ];
183  return MMulti(R, M);
184}
185
186function DrawQube() {
187  // calc current normals
188  var CurN = new Array();
189  var i = 5;
190  Q.LastPx = 0;
191  for (; i > -1; i--) CurN[i] = VMulti2(MQube, Q.Normal[i]);
192  if (CurN[0][2] < 0) {
193    if (!Q.Line[0]) { DrawLine(Q[0], Q[1]); Q.Line[0] = true; };
194    if (!Q.Line[1]) { DrawLine(Q[1], Q[2]); Q.Line[1] = true; };
195    if (!Q.Line[2]) { DrawLine(Q[2], Q[3]); Q.Line[2] = true; };
196    if (!Q.Line[3]) { DrawLine(Q[3], Q[0]); Q.Line[3] = true; };
197  }
198  if (CurN[1][2] < 0) {
199    if (!Q.Line[2]) { DrawLine(Q[3], Q[2]); Q.Line[2] = true; };
200    if (!Q.Line[9]) { DrawLine(Q[2], Q[6]); Q.Line[9] = true; };
201    if (!Q.Line[6]) { DrawLine(Q[6], Q[7]); Q.Line[6] = true; };
202    if (!Q.Line[10]) { DrawLine(Q[7], Q[3]); Q.Line[10] = true; };
203  }
204  if (CurN[2][2] < 0) {
205    if (!Q.Line[4]) { DrawLine(Q[4], Q[5]); Q.Line[4] = true; };
206    if (!Q.Line[5]) { DrawLine(Q[5], Q[6]); Q.Line[5] = true; };
207    if (!Q.Line[6]) { DrawLine(Q[6], Q[7]); Q.Line[6] = true; };
208    if (!Q.Line[7]) { DrawLine(Q[7], Q[4]); Q.Line[7] = true; };
209  }
210  if (CurN[3][2] < 0) {
211    if (!Q.Line[4]) { DrawLine(Q[4], Q[5]); Q.Line[4] = true; };
212    if (!Q.Line[8]) { DrawLine(Q[5], Q[1]); Q.Line[8] = true; };
213    if (!Q.Line[0]) { DrawLine(Q[1], Q[0]); Q.Line[0] = true; };
214    if (!Q.Line[11]) { DrawLine(Q[0], Q[4]); Q.Line[11] = true; };
215  }
216  if (CurN[4][2] < 0) {
217    if (!Q.Line[11]) { DrawLine(Q[4], Q[0]); Q.Line[11] = true; };
218    if (!Q.Line[3]) { DrawLine(Q[0], Q[3]); Q.Line[3] = true; };
219    if (!Q.Line[10]) { DrawLine(Q[3], Q[7]); Q.Line[10] = true; };
220    if (!Q.Line[7]) { DrawLine(Q[7], Q[4]); Q.Line[7] = true; };
221  }
222  if (CurN[5][2] < 0) {
223    if (!Q.Line[8]) { DrawLine(Q[1], Q[5]); Q.Line[8] = true; };
224    if (!Q.Line[5]) { DrawLine(Q[5], Q[6]); Q.Line[5] = true; };
225    if (!Q.Line[9]) { DrawLine(Q[6], Q[2]); Q.Line[9] = true; };
226    if (!Q.Line[1]) { DrawLine(Q[2], Q[1]); Q.Line[1] = true; };
227  }
228  Q.Line = [false,false,false,false,false,false,false,false,false,false,false,false];
229  Q.LastPx = 0;
230}
231
232function Loop() {
233  if (Testing.LoopCount > Testing.LoopMax) return;
234  var TestingStr = String(Testing.LoopCount);
235  while (TestingStr.length < 3) TestingStr = "0" + TestingStr;
236  MTrans = Translate(I, -Q[8].V[0], -Q[8].V[1], -Q[8].V[2]);
237  MTrans = RotateX(MTrans, 1);
238  MTrans = RotateY(MTrans, 3);
239  MTrans = RotateZ(MTrans, 5);
240  MTrans = Translate(MTrans, Q[8].V[0], Q[8].V[1], Q[8].V[2]);
241  MQube = MMulti(MTrans, MQube);
242  var i = 8;
243  for (; i > -1; i--) {
244    Q[i].V = VMulti(MTrans, Q[i].V);
245  }
246  DrawQube();
247  Testing.LoopCount++;
248  Loop();
249}
250
251function Init(CubeSize) {
252  // init/reset vars
253  Origin.V = [150,150,20,1];
254  Testing.LoopCount = 0;
255  Testing.LoopMax = 50;
256  Testing.TimeMax = 0;
257  Testing.TimeAvg = 0;
258  Testing.TimeMin = 0;
259  Testing.TimeTemp = 0;
260  Testing.TimeTotal = 0;
261  Testing.Init = false;
262
263  // transformation matrix
264  MTrans = [
265  [1,0,0,0],
266  [0,1,0,0],
267  [0,0,1,0],
268  [0,0,0,1]
269  ];
270
271  // position information of qube
272  MQube = [
273  [1,0,0,0],
274  [0,1,0,0],
275  [0,0,1,0],
276  [0,0,0,1]
277  ];
278
279  // entity matrix
280  I = [
281  [1,0,0,0],
282  [0,1,0,0],
283  [0,0,1,0],
284  [0,0,0,1]
285  ];
286
287  // create qube
288  Q[0] = new CreateP(-CubeSize,-CubeSize, CubeSize);
289  Q[1] = new CreateP(-CubeSize, CubeSize, CubeSize);
290  Q[2] = new CreateP( CubeSize, CubeSize, CubeSize);
291  Q[3] = new CreateP( CubeSize,-CubeSize, CubeSize);
292  Q[4] = new CreateP(-CubeSize,-CubeSize,-CubeSize);
293  Q[5] = new CreateP(-CubeSize, CubeSize,-CubeSize);
294  Q[6] = new CreateP( CubeSize, CubeSize,-CubeSize);
295  Q[7] = new CreateP( CubeSize,-CubeSize,-CubeSize);
296
297  // center of gravity
298  Q[8] = new CreateP(0, 0, 0);
299
300  // anti-clockwise edge check
301  Q.Edge = [[0,1,2],[3,2,6],[7,6,5],[4,5,1],[4,0,3],[1,5,6]];
302
303  // calculate squad normals
304  Q.Normal = new Array();
305  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);
306
307  // line drawn ?
308  Q.Line = [false,false,false,false,false,false,false,false,false,false,false,false];
309
310  // create line pixels
311  Q.NumPx = 9 * 2 * CubeSize;
312  for (var i = 0; i < Q.NumPx; i++) CreateP(0,0,0);
313
314  MTrans = Translate(MTrans, Origin.V[0], Origin.V[1], Origin.V[2]);
315  MQube = MMulti(MTrans, MQube);
316
317  var i = 0;
318  for (; i < 9; i++) {
319    Q[i].V = VMulti(MTrans, Q[i].V);
320  }
321  DrawQube();
322  Testing.Init = true;
323  Loop();
324}
325
326for ( var i = 20; i <= 160; i *= 2 ) {
327  Init(i);
328}
329
330Q = null;
331MTrans = null;
332MQube = null;
333I = null;
334Origin = null;
335Testing = null;
336LoopTime = null;
337DisplArea = null;
338