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