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mc 1.9
[vg.git] / src / vg / vg_m.h
1 /* Copyright (C) 2021 Harry Godden (hgn) - All Rights Reserved */
2
3 #define VG_PIf 3.14159265358979323846264338327950288f
4 #define VG_TAUf 6.28318530717958647692528676655900576f
5
6 static inline float vg_minf( float a, float b )
7 {
8 return a < b? a: b;
9 }
10
11 static inline float vg_maxf( float a, float b )
12 {
13 return a > b? a: b;
14 }
15
16 static inline float vg_clampf( float a, float min, float max )
17 {
18 return vg_minf( max, vg_maxf( a, min ) );
19 }
20
21 #define VG_MIN( A, B ) ((A)<(B)?(A):(B))
22 #define VG_MAX( A, B ) ((A)>(B)?(A):(B))
23
24 static inline int vg_min( int a, int b )
25 {
26 return a < b? a: b;
27 }
28
29 static inline int vg_max( int a, int b )
30 {
31 return a > b? a: b;
32 }
33
34 static inline float vg_rad( float deg )
35 {
36 return deg * VG_PIf / 180.0f;
37 }
38
39 /*
40 * Vector 3
41 */
42 static inline void v2_copy( v2f a, v2f b )
43 {
44 b[0] = a[0]; b[1] = a[1];
45 }
46
47 static inline void v2i_copy( v2i a, v2i b )
48 {
49 b[0] = a[0]; b[1] = a[1];
50 }
51
52 static inline int v2i_eq( v2i a, v2i b )
53 {
54 return ((a[0] == b[0]) && (a[1] == b[1]));
55 }
56
57 static inline void v2i_add( v2i a, v2i b, v2i d )
58 {
59 d[0] = a[0]+b[0]; d[1] = a[1]+b[1];
60 }
61
62 static inline void v2i_sub( v2i a, v2i b, v2i d )
63 {
64 d[0] = a[0]-b[0]; d[1] = a[1]-b[1];
65 }
66
67 static inline void v2_minv( v2f a, v2f b, v2f dest )
68 {
69 dest[0] = vg_minf(a[0], b[0]);
70 dest[1] = vg_minf(a[1], b[1]);
71 }
72
73 static inline void v2_maxv( v2f a, v2f b, v2f dest )
74 {
75 dest[0] = vg_maxf(a[0], b[0]);
76 dest[1] = vg_maxf(a[1], b[1]);
77 }
78
79 static inline void v2_sub( v2f a, v2f b, v2f d )
80 {
81 d[0] = a[0]-b[0]; d[1] = a[1]-b[1];
82 }
83
84 static inline float v2_cross( v2f a, v2f b )
85 {
86 return a[0] * b[1] - a[1] * b[0];
87 }
88
89 static inline void v2_add( v2f a, v2f b, v2f d )
90 {
91 d[0] = a[0]+b[0]; d[1] = a[1]+b[1];
92 }
93
94 static inline void v2_muls( v2f a, float s, v2f d )
95 {
96 d[0] = a[0]*s; d[1] = a[1]*s;
97 }
98
99 static inline void v2_divs( v2f a, float s, v2f d )
100 {
101 d[0] = a[0]/s; d[1] = a[1]/s;
102 }
103
104 static inline void v2_mul( v2f a, v2f b, v2f d )
105 {
106 d[0] = a[0]*b[0];
107 d[1] = a[1]*b[1];
108 }
109
110 static inline void v2_div( v2f a, v2f b, v2f d )
111 {
112 d[0] = a[0]/b[0]; d[1] = a[1]/b[1];
113 }
114
115 static inline void v2_muladd( v2f a, v2f b, v2f s, v2f d )
116 {
117 d[0] = a[0]+b[0]*s[0];
118 d[1] = a[1]+b[1]*s[1];
119 }
120
121 static inline void v2_muladds( v2f a, v2f b, float s, v2f d )
122 {
123 d[0] = a[0]+b[0]*s;
124 d[1] = a[1]+b[1]*s;
125 }
126
127 static inline float v2_length2( v2f a )
128 {
129 return a[0]*a[0] + a[1]*a[1];
130 }
131
132 static inline float v2_length( v2f a )
133 {
134 return sqrtf( v2_length2( a ) );
135 }
136
137 static inline float v2_dist2( v2f a, v2f b )
138 {
139 v2f delta;
140 v2_sub( a, b, delta );
141 return v2_length2( delta );
142 }
143
144 static inline float v2_dist( v2f a, v2f b )
145 {
146 return sqrtf( v2_dist2( a, b ) );
147 }
148
149 static inline void v2_lerp( v2f a, v2f b, float t, v2f d )
150 {
151 d[0] = a[0] + t*(b[0]-a[0]);
152 d[1] = a[1] + t*(b[1]-a[1]);
153 }
154
155 /*
156 * Vector 3
157 */
158 static inline void v3_zero( v3f a )
159 {
160 a[0] = 0.f; a[1] = 0.f; a[2] = 0.f;
161 }
162
163 static inline void v3_copy( v3f a, v3f b )
164 {
165 b[0] = a[0]; b[1] = a[1]; b[2] = a[2];
166 }
167
168 static inline void v3_add( v3f a, v3f b, v3f d )
169 {
170 d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; d[2] = a[2]+b[2];
171 }
172
173 static inline void v3_sub( v3f a, v3f b, v3f d )
174 {
175 d[0] = a[0]-b[0]; d[1] = a[1]-b[1]; d[2] = a[2]-b[2];
176 }
177
178 static inline void v3_mul( v3f a, v3f b, v3f d )
179 {
180 d[0] = a[0]*b[0]; d[1] = a[1]*b[1]; d[2] = a[2]*b[2];
181 }
182
183 static inline void v3_div( v3f a, v3f b, v3f d )
184 {
185 d[0] = a[0]/b[0]; d[1] = a[1]/b[1]; d[2] = a[2]/b[2];
186 }
187
188 static inline void v3_muls( v3f a, float s, v3f d )
189 {
190 d[0] = a[0]*s; d[1] = a[1]*s; d[2] = a[2]*s;
191 }
192
193 static inline void v3_divs( v3f a, float s, v3f d )
194 {
195 d[0] = a[0]/s; d[1] = a[1]/s; d[2] = a[2]/s;
196 }
197
198 static inline void v3_muladds( v3f a, v3f b, float s, v3f d )
199 {
200 d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s; d[2] = a[2]+b[2]*s;
201 }
202
203 static inline float v3_dot( v3f a, v3f b )
204 {
205 return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
206 }
207
208 static inline void v3_cross( v3f a, v3f b, v3f d )
209 {
210 d[0] = a[1] * b[2] - a[2] * b[1];
211 d[1] = a[2] * b[0] - a[0] * b[2];
212 d[2] = a[0] * b[1] - a[1] * b[0];
213 }
214
215 static inline float v3_length2( v3f a )
216 {
217 return v3_dot( a, a );
218 }
219
220 static inline float v3_length( v3f a )
221 {
222 return sqrtf( v3_length2( a ) );
223 }
224
225 static inline float v3_dist2( v3f a, v3f b )
226 {
227 v3f delta;
228 v3_sub( a, b, delta );
229 return v3_length2( delta );
230 }
231
232 static inline float v3_dist( v3f a, v3f b )
233 {
234 return sqrtf( v3_dist2( a, b ) );
235 }
236
237 static inline void v3_normalize( v3f a )
238 {
239 v3_muls( a, 1.f / v3_length( a ), a );
240 }
241
242 static inline float vg_lerpf( float a, float b, float t )
243 {
244 return a + t*(b-a);
245 }
246
247 static inline void v3_lerp( v3f a, v3f b, float t, v3f d )
248 {
249 d[0] = a[0] + t*(b[0]-a[0]);
250 d[1] = a[1] + t*(b[1]-a[1]);
251 d[2] = a[2] + t*(b[2]-a[2]);
252 }
253
254 static inline void v3_minv( v3f a, v3f b, v3f dest )
255 {
256 dest[0] = vg_minf(a[0], b[0]);
257 dest[1] = vg_minf(a[1], b[1]);
258 dest[2] = vg_minf(a[2], b[2]);
259 }
260
261 static inline void v3_maxv( v3f a, v3f b, v3f dest )
262 {
263 dest[0] = vg_maxf(a[0], b[0]);
264 dest[1] = vg_maxf(a[1], b[1]);
265 dest[2] = vg_maxf(a[2], b[2]);
266 }
267
268 static inline float v3_minf( v3f a )
269 {
270 return vg_minf( vg_minf( a[0], a[1] ), a[2] );
271 }
272
273 static inline float v3_maxf( v3f a )
274 {
275 return vg_maxf( vg_maxf( a[0], a[1] ), a[2] );
276 }
277
278 static inline void v3_fill( v3f a, float v )
279 {
280 a[0] = v;
281 a[1] = v;
282 a[2] = v;
283 }
284
285 /*
286 * Vector 4
287 */
288 static inline void v4_copy( v4f a, v4f b )
289 {
290 b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; b[3] = a[3];
291 }
292
293 static inline void v4_zero( v4f a )
294 {
295 a[0] = 0.f; a[1] = 0.f; a[2] = 0.f; a[3] = 0.f;
296 }
297
298 /*
299 * Matrix 2x2
300 */
301
302 #define M2X2_INDENTIY {{1.0f, 0.0f, }, \
303 { 0.0f, 1.0f, }}
304
305 #define M2X2_ZERO {{0.0f, 0.0f, }, \
306 { 0.0f, 0.0f, }}
307
308 static inline void m2x2_copy( m2x2f a, m2x2f b )
309 {
310 v2_copy( a[0], b[0] );
311 v2_copy( a[1], b[1] );
312 }
313
314 static inline void m2x2_identity( m2x2f a )
315 {
316 m2x2f id = M2X2_INDENTIY;
317 m2x2_copy( id, a );
318 }
319
320 static inline void m2x2_create_rotation( m2x2f a, float theta )
321 {
322 float s, c;
323
324 s = sinf( theta );
325 c = cosf( theta );
326
327 a[0][0] = c;
328 a[0][1] = -s;
329 a[1][0] = s;
330 a[1][1] = c;
331 }
332
333 /*
334 * Matrix 3x3
335 */
336
337 #define M3X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
338 { 0.0f, 1.0f, 0.0f, },\
339 { 0.0f, 0.0f, 1.0f, }}
340
341 #define M3X3_ZERO {{0.0f, 0.0f, 0.0f, },\
342 { 0.0f, 0.0f, 0.0f, },\
343 { 0.0f, 0.0f, 0.0f, }}
344
345
346 static inline void m3x3_copy( m3x3f a, m3x3f b )
347 {
348 v3_copy( a[0], b[0] );
349 v3_copy( a[1], b[1] );
350 v3_copy( a[2], b[2] );
351 }
352
353 static inline void m3x3_identity( m3x3f a )
354 {
355 m3x3f id = M3X3_IDENTITY;
356 m3x3_copy( id, a );
357 }
358
359 static inline void m3x3_zero( m3x3f a )
360 {
361 m3x3f z = M3X3_ZERO;
362 m3x3_copy( z, a );
363 }
364
365 static inline void m3x3_inv( m3x3f src, m3x3f dest )
366 {
367 float a = src[0][0], b = src[0][1], c = src[0][2],
368 d = src[1][0], e = src[1][1], f = src[1][2],
369 g = src[2][0], h = src[2][1], i = src[2][2];
370
371 float det = 1.f /
372 (+a*(e*i-h*f)
373 -b*(d*i-f*g)
374 +c*(d*h-e*g));
375
376 dest[0][0] = (e*i-h*f)*det;
377 dest[0][1] = -(b*i-c*h)*det;
378 dest[0][2] = (b*f-c*e)*det;
379 dest[1][0] = -(d*i-f*g)*det;
380 dest[1][1] = (a*i-c*g)*det;
381 dest[1][2] = -(a*f-d*c)*det;
382 dest[2][0] = (d*h-g*e)*det;
383 dest[2][1] = -(a*h-g*b)*det;
384 dest[2][2] = (a*e-d*b)*det;
385 }
386
387 static inline void m3x3_transpose( m3x3f src, m3x3f dest )
388 {
389 float a = src[0][0], b = src[0][1], c = src[0][2],
390 d = src[1][0], e = src[1][1], f = src[1][2],
391 g = src[2][0], h = src[2][1], i = src[2][2];
392
393 dest[0][0] = a;
394 dest[0][1] = d;
395 dest[0][2] = g;
396 dest[1][0] = b;
397 dest[1][1] = e;
398 dest[1][2] = h;
399 dest[2][0] = c;
400 dest[2][1] = f;
401 dest[2][2] = i;
402 }
403
404 static inline void m3x3_mul( m3x3f a, m3x3f b, m3x3f d )
405 {
406 float a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
407 a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
408 a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
409
410 b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
411 b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
412 b20 = b[2][0], b21 = b[2][1], b22 = b[2][2];
413
414 d[0][0] = a00*b00 + a10*b01 + a20*b02;
415 d[0][1] = a01*b00 + a11*b01 + a21*b02;
416 d[0][2] = a02*b00 + a12*b01 + a22*b02;
417 d[1][0] = a00*b10 + a10*b11 + a20*b12;
418 d[1][1] = a01*b10 + a11*b11 + a21*b12;
419 d[1][2] = a02*b10 + a12*b11 + a22*b12;
420 d[2][0] = a00*b20 + a10*b21 + a20*b22;
421 d[2][1] = a01*b20 + a11*b21 + a21*b22;
422 d[2][2] = a02*b20 + a12*b21 + a22*b22;
423 }
424
425 static inline void m3x3_mulv( m3x3f m, v3f v, v3f d )
426 {
427 v3f res;
428
429 res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
430 res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
431 res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
432
433 v3_copy( res, d );
434 }
435
436 static inline void m3x3_projection( m3x3f dst,
437 float const left, float const right, float const bottom, float const top )
438 {
439 float rl, tb;
440
441 m3x3_zero( dst );
442
443 rl = 1.0f / (right - left);
444 tb = 1.0f / (top - bottom);
445
446 dst[0][0] = 2.0f * rl;
447 dst[1][1] = 2.0f * tb;
448 dst[2][2] = 1.0f;
449 }
450
451 static inline void m3x3_translate( m3x3f m, v3f v )
452 {
453 m[2][0] = m[0][0] * v[0] + m[1][0] * v[1] + m[2][0];
454 m[2][1] = m[0][1] * v[0] + m[1][1] * v[1] + m[2][1];
455 m[2][2] = m[0][2] * v[0] + m[1][2] * v[1] + m[2][2];
456 }
457
458 static inline void m3x3_scale( m3x3f m, v3f v )
459 {
460 m[0][0] = m[0][0] * v[0];
461 m[0][1] = m[0][1] * v[0];
462 m[0][2] = m[0][2] * v[0];
463
464 m[1][0] = m[1][0] * v[1];
465 m[1][1] = m[1][1] * v[1];
466 m[1][2] = m[1][2] * v[1];
467 }
468
469 static inline void m3x3_rotate( m3x3f m, float angle )
470 {
471 float m00 = m[0][0], m10 = m[1][0],
472 m01 = m[0][1], m11 = m[1][1],
473 m02 = m[0][2], m12 = m[1][2];
474 float c, s;
475
476 s = sinf( angle );
477 c = cosf( angle );
478
479 m[0][0] = m00 * c + m10 * s;
480 m[0][1] = m01 * c + m11 * s;
481 m[0][2] = m02 * c + m12 * s;
482
483 m[1][0] = m00 * -s + m10 * c;
484 m[1][1] = m01 * -s + m11 * c;
485 m[1][2] = m02 * -s + m12 * c;
486 }
487
488 /*
489 * Matrix 4x3
490 */
491
492 #define M4X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
493 { 0.0f, 1.0f, 0.0f, },\
494 { 0.0f, 0.0f, 1.0f, },\
495 { 0.0f, 0.0f, 0.0f }}
496
497 static inline void m4x3_to_3x3( m4x3f a, m3x3f b )
498 {
499 v3_copy( a[0], b[0] );
500 v3_copy( a[1], b[1] );
501 v3_copy( a[2], b[2] );
502 }
503
504 static inline void m4x3_copy( m4x3f a, m4x3f b )
505 {
506 v3_copy( a[0], b[0] );
507 v3_copy( a[1], b[1] );
508 v3_copy( a[2], b[2] );
509 v3_copy( a[3], b[3] );
510 }
511
512 static inline void m4x3_identity( m4x3f a )
513 {
514 m4x3f id = M4X3_IDENTITY;
515 m4x3_copy( id, a );
516 }
517
518 static inline void m4x3_mul( m4x3f a, m4x3f b, m4x3f d )
519 {
520 float
521 a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
522 a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
523 a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
524 a30 = a[3][0], a31 = a[3][1], a32 = a[3][2],
525 b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
526 b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
527 b20 = b[2][0], b21 = b[2][1], b22 = b[2][2],
528 b30 = b[3][0], b31 = b[3][1], b32 = b[3][2];
529
530 d[0][0] = a00*b00 + a10*b01 + a20*b02;
531 d[0][1] = a01*b00 + a11*b01 + a21*b02;
532 d[0][2] = a02*b00 + a12*b01 + a22*b02;
533 d[1][0] = a00*b10 + a10*b11 + a20*b12;
534 d[1][1] = a01*b10 + a11*b11 + a21*b12;
535 d[1][2] = a02*b10 + a12*b11 + a22*b12;
536 d[2][0] = a00*b20 + a10*b21 + a20*b22;
537 d[2][1] = a01*b20 + a11*b21 + a21*b22;
538 d[2][2] = a02*b20 + a12*b21 + a22*b22;
539 d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30;
540 d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31;
541 d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32;
542 }
543
544 static inline void m4x3_mulv( m4x3f m, v3f v, v3f d )
545 {
546 v3f res;
547
548 res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0];
549 res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1];
550 res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2];
551
552 v3_copy( res, d );
553 }
554
555 /*
556 * Affine transforms
557 */
558
559 static inline void m4x3_translate( m4x3f m, v3f v )
560 {
561 v3_muladds( m[3], m[0], v[0], m[3] );
562 v3_muladds( m[3], m[1], v[1], m[3] );
563 v3_muladds( m[3], m[2], v[2], m[3] );
564 }
565
566 static inline void m4x3_scale( m4x3f m, float s )
567 {
568 v3_muls( m[0], s, m[0] );
569 v3_muls( m[1], s, m[1] );
570 v3_muls( m[2], s, m[2] );
571 }
572
573 static inline void m4x3_rotate_x( m4x3f m, float angle )
574 {
575 m4x3f t = M4X3_IDENTITY;
576 float c, s;
577
578 c = cosf( angle );
579 s = sinf( angle );
580
581 t[1][1] = c;
582 t[1][2] = s;
583 t[2][1] = -s;
584 t[2][2] = c;
585
586 m4x3_mul( m, t, m );
587 }
588
589 static inline void m4x3_rotate_y( m4x3f m, float angle )
590 {
591 m4x3f t = M4X3_IDENTITY;
592 float c, s;
593
594 c = cosf( angle );
595 s = sinf( angle );
596
597 t[0][0] = c;
598 t[0][2] = -s;
599 t[2][0] = s;
600 t[2][2] = c;
601
602 m4x3_mul( m, t, m );
603 }
604
605 static inline void m4x3_rotate_z( m4x3f m, float angle )
606 {
607 m4x3f t = M4X3_IDENTITY;
608 float c, s;
609
610 c = cosf( angle );
611 s = sinf( angle );
612
613 t[0][0] = c;
614 t[0][1] = s;
615 t[1][0] = -s;
616 t[1][1] = c;
617
618 m4x3_mul( m, t, m );
619 }
620
621 static inline void m4x3_expand_aabb_point( m4x3f m, boxf box, v3f point )
622 {
623 v3f v;
624 m4x3_mulv( m, point, v );
625
626 v3_minv( box[0], v, box[0] );
627 v3_maxv( box[1], v, box[1] );
628 }
629
630 static inline void box_concat( boxf a, boxf b )
631 {
632 v3_minv( a[0], b[0], a[0] );
633 v3_maxv( a[1], b[1], a[1] );
634 }
635
636 static inline void box_copy( boxf a, boxf b )
637 {
638 v3_copy( a[0], b[0] );
639 v3_copy( a[1], b[1] );
640 }
641
642 static inline void m4x3_transform_aabb( m4x3f m, boxf box )
643 {
644 v3f a; v3f b;
645
646 v3_copy( box[0], a );
647 v3_copy( box[1], b );
648 v3_fill( box[0], INFINITY );
649 v3_fill( box[1], -INFINITY );
650
651 m4x3_expand_aabb_point( m, box, a );
652 m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], a[2] } );
653 m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], a[2] } );
654 m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], a[2] } );
655 m4x3_expand_aabb_point( m, box, b );
656 m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], b[2] } );
657 m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], b[2] } );
658 m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], b[2] } );
659 }
660
661 /*
662 * Planes (double precision)
663 */
664 static inline void tri_to_plane( double a[3], double b[3],
665 double c[3], double p[4] )
666 {
667 double edge0[3];
668 double edge1[3];
669 double l;
670
671 edge0[0] = b[0] - a[0];
672 edge0[1] = b[1] - a[1];
673 edge0[2] = b[2] - a[2];
674
675 edge1[0] = c[0] - a[0];
676 edge1[1] = c[1] - a[1];
677 edge1[2] = c[2] - a[2];
678
679 p[0] = edge0[1] * edge1[2] - edge0[2] * edge1[1];
680 p[1] = edge0[2] * edge1[0] - edge0[0] * edge1[2];
681 p[2] = edge0[0] * edge1[1] - edge0[1] * edge1[0];
682
683 l = sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2]);
684 p[3] = (p[0] * a[0] + p[1] * a[1] + p[2] * a[2]) / l;
685
686 p[0] = p[0] / l;
687 p[1] = p[1] / l;
688 p[2] = p[2] / l;
689 }
690
691 static inline int plane_intersect( double a[4], double b[4],
692 double c[4], double p[4] )
693 {
694 double const epsilon = 1e-8f;
695
696 double x[3];
697 double d;
698
699 x[0] = a[1] * b[2] - a[2] * b[1];
700 x[1] = a[2] * b[0] - a[0] * b[2];
701 x[2] = a[0] * b[1] - a[1] * b[0];
702
703 d = x[0] * c[0] + x[1] * c[1] + x[2] * c[2];
704
705 if( d < epsilon && d > -epsilon ) return 0;
706
707 p[0] = (b[1] * c[2] - b[2] * c[1]) * -a[3];
708 p[1] = (b[2] * c[0] - b[0] * c[2]) * -a[3];
709 p[2] = (b[0] * c[1] - b[1] * c[0]) * -a[3];
710
711 p[0] += (c[1] * a[2] - c[2] * a[1]) * -b[3];
712 p[1] += (c[2] * a[0] - c[0] * a[2]) * -b[3];
713 p[2] += (c[0] * a[1] - c[1] * a[0]) * -b[3];
714
715 p[0] += (a[1] * b[2] - a[2] * b[1]) * -c[3];
716 p[1] += (a[2] * b[0] - a[0] * b[2]) * -c[3];
717 p[2] += (a[0] * b[1] - a[1] * b[0]) * -c[3];
718
719 p[0] = -p[0] / d;
720 p[1] = -p[1] / d;
721 p[2] = -p[2] / d;
722
723 return 1;
724 }
725
726 static inline double plane_polarity( double p[4], double a[3] )
727 {
728 return
729 (a[0] * p[0] + a[1] * p[1] + a[2] * p[2])
730 -(p[0]*p[3] * p[0] + p[1]*p[3] * p[1] + p[2]*p[3] * p[2])
731 ;
732 }
Voyager Game Engine