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[fishladder.git] / vg / vg_m.h
1 // Copyright (C) 2021 Harry Godden (hgn) - All Rights Reserved
2
3 // Util
4 // ==================================================================================================================
5
6 #define VG_PIf 3.14159265358979323846264338327950288f
7 #define VG_TAUf 6.28318530717958647692528676655900576f
8
9 // Simple min/max replacements
10 static inline float vg_minf( float a, float b )
11 {
12 return a < b? a: b;
13 }
14
15 static inline float vg_maxf( float a, float b )
16 {
17 return a > b? a: b;
18 }
19
20 static inline float vg_clampf( float a, float min, float max )
21 {
22 return vg_minf( max, vg_maxf( a, min ) );
23 }
24
25 #define VG_MIN( A, B ) ((A)<(B)?(A):(B))
26 #define VG_MAX( A, B ) ((A)>(B)?(A):(B))
27
28 // Hopefully deprecate this!!
29 static inline int vg_min( int a, int b )
30 {
31 return a < b? a: b;
32 }
33
34 static inline int vg_max( int a, int b )
35 {
36 return a > b? a: b;
37 }
38
39 // Convert degrees to radians
40 static inline float vg_rad( float deg )
41 {
42 return deg * VG_PIf / 180.0f;
43 }
44
45 // Vector 2
46 // ==================================================================================================================
47
48 static inline void v2_copy( v2f a, v2f b )
49 {
50 b[0] = a[0]; b[1] = a[1];
51 }
52
53 static inline void v2i_copy( v2i a, v2i b )
54 {
55 b[0] = a[0]; b[1] = a[1];
56 }
57
58 static inline int v2i_eq( v2i a, v2i b )
59 {
60 return ((a[0] == b[0]) && (a[1] == b[1]));
61 }
62
63 static inline void v2i_add( v2i a, v2i b, v2i d )
64 {
65 d[0] = a[0]+b[0]; d[1] = a[1]+b[1];
66 }
67
68 static inline void v2i_sub( v2i a, v2i b, v2i d )
69 {
70 d[0] = a[0]-b[0]; d[1] = a[1]-b[1];
71 }
72
73 static inline void v2_minv( v2f a, v2f b, v2f dest )
74 {
75 dest[0] = vg_minf(a[0], b[0]);
76 dest[1] = vg_minf(a[1], b[1]);
77 }
78
79 static inline void v2_maxv( v2f a, v2f b, v2f dest )
80 {
81 dest[0] = vg_maxf(a[0], b[0]);
82 dest[1] = vg_maxf(a[1], b[1]);
83 }
84
85 static inline void v2_sub( v2f a, v2f b, v2f d )
86 {
87 d[0] = a[0]-b[0]; d[1] = a[1]-b[1];
88 }
89
90 static inline float v2_cross( v2f a, v2f b )
91 {
92 return a[0] * b[1] - a[1] * b[0];
93 }
94
95 static inline void v2_add( v2f a, v2f b, v2f d )
96 {
97 d[0] = a[0]+b[0]; d[1] = a[1]+b[1];
98 }
99
100 static inline void v2_muls( v2f a, float s, v2f d )
101 {
102 d[0] = a[0]*s; d[1] = a[1]*s;
103 }
104
105 static inline void v2_divs( v2f a, float s, v2f d )
106 {
107 d[0] = a[0]/s; d[1] = a[1]/s;
108 }
109
110
111 static inline void v2_mul( v2f a, v2f b, v2f d )
112 {
113 d[0] = a[0]*b[0];
114 d[1] = a[1]*b[1];
115 }
116
117 static inline void v2_div( v2f a, v2f b, v2f d )
118 {
119 d[0] = a[0]/b[0]; d[1] = a[1]/b[1];
120 }
121
122 static inline void v2_muladd( v2f a, v2f b, v2f s, v2f d )
123 {
124 d[0] = a[0]+b[0]*s[0];
125 d[1] = a[1]+b[1]*s[1];
126 }
127
128 static inline void v2_muladds( v2f a, v2f b, float s, v2f d )
129 {
130 d[0] = a[0]+b[0]*s;
131 d[1] = a[1]+b[1]*s;
132 }
133
134 static inline float v2_length2( v2f a )
135 {
136 return a[0]*a[0] + a[1]*a[1];
137 }
138
139 static inline float v2_length( v2f a )
140 {
141 return sqrtf( v2_length2( a ) );
142 }
143
144 static inline float v2_dist2( v2f a, v2f b )
145 {
146 v2f delta;
147 v2_sub( a, b, delta );
148 return v2_length2( delta );
149 }
150
151 static inline float v2_dist( v2f a, v2f b )
152 {
153 return sqrtf( v2_dist2( a, b ) );
154 }
155
156 static inline void v2_lerp( v2f a, v2f b, float t, v2f d )
157 {
158 d[0] = a[0] + t*(b[0]-a[0]);
159 d[1] = a[1] + t*(b[1]-a[1]);
160 }
161
162 // Vector 3
163 // ==================================================================================================================
164
165 static inline void v3_zero( v3f a )
166 {
167 a[0] = 0.f; a[1] = 0.f; a[2] = 0.f;
168 }
169
170 static inline void v3_copy( v3f a, v3f b )
171 {
172 b[0] = a[0]; b[1] = a[1]; b[2] = a[2];
173 }
174
175 static inline void v3_add( v3f a, v3f b, v3f d )
176 {
177 d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; d[2] = a[2]+b[2];
178 }
179
180 static inline void v3_sub( v3f a, v3f b, v3f d )
181 {
182 d[0] = a[0]-b[0]; d[1] = a[1]-b[1]; d[2] = a[2]-b[2];
183 }
184
185 static inline void v3_mul( v3f a, v3f b, v3f d )
186 {
187 d[0] = a[0]*b[0]; d[1] = a[1]*b[1]; d[2] = a[2]*b[2];
188 }
189
190 static inline void v3_div( v3f a, v3f b, v3f d )
191 {
192 d[0] = a[0]/b[0]; d[1] = a[1]/b[1]; d[2] = a[2]/b[2];
193 }
194
195 static inline void v3_muls( v3f a, float s, v3f d )
196 {
197 d[0] = a[0]*s; d[1] = a[1]*s; d[2] = a[2]*s;
198 }
199
200 static inline void v3_divs( v3f a, float s, v3f d )
201 {
202 d[0] = a[0]/s; d[1] = a[1]/s; d[2] = a[2]/s;
203 }
204
205 static inline void v3_muladds( v3f a, v3f b, float s, v3f d )
206 {
207 d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s; d[2] = a[2]+b[2]*s;
208 }
209
210 static inline float v3_dot( v3f a, v3f b )
211 {
212 return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
213 }
214
215 static inline void v3_cross( v3f a, v3f b, v3f d )
216 {
217 d[0] = a[1] * b[2] - a[2] * b[1];
218 d[1] = a[2] * b[0] - a[0] * b[2];
219 d[2] = a[0] * b[1] - a[1] * b[0];
220 }
221
222 static inline float v3_length2( v3f a )
223 {
224 return v3_dot( a, a );
225 }
226
227 static inline float v3_length( v3f a )
228 {
229 return sqrtf( v3_length2( a ) );
230 }
231
232 static inline float v3_dist2( v3f a, v3f b )
233 {
234 v3f delta;
235 v3_sub( a, b, delta );
236 return v3_length2( delta );
237 }
238
239 static inline float v3_dist( v3f a, v3f b )
240 {
241 return sqrtf( v3_dist2( a, b ) );
242 }
243
244 static inline void v3_normalize( v3f a )
245 {
246 v3_muls( a, 1.f / v3_length( a ), a );
247 }
248
249 static inline float vg_lerpf( float a, float b, float t )
250 {
251 return a + t*(b-a);
252 }
253
254 static inline void v3_lerp( v3f a, v3f b, float t, v3f d )
255 {
256 d[0] = a[0] + t*(b[0]-a[0]);
257 d[1] = a[1] + t*(b[1]-a[1]);
258 d[2] = a[2] + t*(b[2]-a[2]);
259 }
260
261 static inline void v3_minv( v3f a, v3f b, v3f dest )
262 {
263 dest[0] = vg_minf(a[0], b[0]);
264 dest[1] = vg_minf(a[1], b[1]);
265 dest[2] = vg_minf(a[2], b[2]);
266 }
267
268 static inline void v3_maxv( v3f a, v3f b, v3f dest )
269 {
270 dest[0] = vg_maxf(a[0], b[0]);
271 dest[1] = vg_maxf(a[1], b[1]);
272 dest[2] = vg_maxf(a[2], b[2]);
273 }
274
275 static inline float v3_minf( v3f a )
276 {
277 return vg_minf( vg_minf( a[0], a[1] ), a[2] );
278 }
279
280 static inline float v3_maxf( v3f a )
281 {
282 return vg_maxf( vg_maxf( a[0], a[1] ), a[2] );
283 }
284
285 static inline void v3_fill( v3f a, float v )
286 {
287 a[0] = v;
288 a[1] = v;
289 a[2] = v;
290 }
291
292 // Vector 4
293 // ==================================================================================================================
294
295 static inline void v4_copy( v4f a, v4f b )
296 {
297 b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; b[3] = a[3];
298 }
299
300 static inline void v4_zero( v4f a )
301 {
302 a[0] = 0.f; a[1] = 0.f; a[2] = 0.f; a[3] = 0.f;
303 }
304
305 // Matrix 2x2
306 // ===========================================================================================================
307
308 #define M2X2_INDENTIY {{1.0f, 0.0f, }, \
309 { 0.0f, 1.0f, }}
310
311 #define M2X2_ZERO {{0.0f, 0.0f, }, \
312 { 0.0f, 0.0f, }}
313
314 static inline void m2x2_copy( m2x2f a, m2x2f b )
315 {
316 v2_copy( a[0], b[0] );
317 v2_copy( a[1], b[1] );
318 }
319
320 static inline void m2x2_identity( m2x2f a )
321 {
322 m2x2f id = M2X2_INDENTIY;
323 m2x2_copy( id, a );
324 }
325
326 static inline void m2x2_create_rotation( m2x2f a, float theta )
327 {
328 float s, c;
329
330 s = sinf( theta );
331 c = cosf( theta );
332
333 a[0][0] = c;
334 a[0][1] = -s;
335 a[1][0] = s;
336 a[1][1] = c;
337 }
338
339 // Matrix 3x3
340 //======================================================================================================
341
342 #define M3X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
343 { 0.0f, 1.0f, 0.0f, },\
344 { 0.0f, 0.0f, 1.0f, }}
345
346 #define M3X3_ZERO {{0.0f, 0.0f, 0.0f, },\
347 { 0.0f, 0.0f, 0.0f, },\
348 { 0.0f, 0.0f, 0.0f, }}
349
350
351 static inline void m3x3_copy( m3x3f a, m3x3f b )
352 {
353 v3_copy( a[0], b[0] );
354 v3_copy( a[1], b[1] );
355 v3_copy( a[2], b[2] );
356 }
357
358 static inline void m3x3_identity( m3x3f a )
359 {
360 m3x3f id = M3X3_IDENTITY;
361 m3x3_copy( id, a );
362 }
363
364 static inline void m3x3_zero( m3x3f a )
365 {
366 m3x3f z = M3X3_ZERO;
367 m3x3_copy( z, a );
368 }
369
370 static inline void m3x3_inv( m3x3f src, m3x3f dest )
371 {
372 float a = src[0][0], b = src[0][1], c = src[0][2],
373 d = src[1][0], e = src[1][1], f = src[1][2],
374 g = src[2][0], h = src[2][1], i = src[2][2];
375
376 float det = 1.f /
377 (+a*(e*i-h*f)
378 -b*(d*i-f*g)
379 +c*(d*h-e*g));
380
381 dest[0][0] = (e*i-h*f)*det;
382 dest[0][1] = -(b*i-c*h)*det;
383 dest[0][2] = (b*f-c*e)*det;
384 dest[1][0] = -(d*i-f*g)*det;
385 dest[1][1] = (a*i-c*g)*det;
386 dest[1][2] = -(a*f-d*c)*det;
387 dest[2][0] = (d*h-g*e)*det;
388 dest[2][1] = -(a*h-g*b)*det;
389 dest[2][2] = (a*e-d*b)*det;
390 }
391
392 static inline void m3x3_transpose( m3x3f src, m3x3f dest )
393 {
394 float a = src[0][0], b = src[0][1], c = src[0][2],
395 d = src[1][0], e = src[1][1], f = src[1][2],
396 g = src[2][0], h = src[2][1], i = src[2][2];
397
398 dest[0][0] = a;
399 dest[0][1] = d;
400 dest[0][2] = g;
401 dest[1][0] = b;
402 dest[1][1] = e;
403 dest[1][2] = h;
404 dest[2][0] = c;
405 dest[2][1] = f;
406 dest[2][2] = i;
407 }
408
409 static inline void m3x3_mul( m3x3f a, m3x3f b, m3x3f d )
410 {
411 float a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
412 a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
413 a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
414
415 b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
416 b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
417 b20 = b[2][0], b21 = b[2][1], b22 = b[2][2];
418
419 d[0][0] = a00*b00 + a10*b01 + a20*b02;
420 d[0][1] = a01*b00 + a11*b01 + a21*b02;
421 d[0][2] = a02*b00 + a12*b01 + a22*b02;
422 d[1][0] = a00*b10 + a10*b11 + a20*b12;
423 d[1][1] = a01*b10 + a11*b11 + a21*b12;
424 d[1][2] = a02*b10 + a12*b11 + a22*b12;
425 d[2][0] = a00*b20 + a10*b21 + a20*b22;
426 d[2][1] = a01*b20 + a11*b21 + a21*b22;
427 d[2][2] = a02*b20 + a12*b21 + a22*b22;
428 }
429
430 static inline void m3x3_mulv( m3x3f m, v3f v, v3f d )
431 {
432 v3f res;
433
434 res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
435 res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
436 res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
437
438 v3_copy( res, d );
439 }
440
441 static inline void m3x3_projection( m3x3f dst, float const left, float const right, float const bottom, float const top )
442 {
443 float rl, tb;
444
445 m3x3_zero( dst );
446
447 rl = 1.0f / (right - left);
448 tb = 1.0f / (top - bottom);
449
450 dst[0][0] = 2.0f * rl;
451 dst[1][1] = 2.0f * tb;
452 dst[2][2] = 1.0f;
453 }
454
455 static inline void m3x3_translate( m3x3f m, v3f v )
456 {
457 m[2][0] = m[0][0] * v[0] + m[1][0] * v[1] + m[2][0];
458 m[2][1] = m[0][1] * v[0] + m[1][1] * v[1] + m[2][1];
459 m[2][2] = m[0][2] * v[0] + m[1][2] * v[1] + m[2][2];
460 }
461
462 static inline void m3x3_scale( m3x3f m, v3f v )
463 {
464 m[0][0] = m[0][0] * v[0];
465 m[0][1] = m[0][1] * v[0];
466 m[0][2] = m[0][2] * v[0];
467
468 m[1][0] = m[1][0] * v[1];
469 m[1][1] = m[1][1] * v[1];
470 m[1][2] = m[1][2] * v[1];
471 }
472
473 static inline void m3x3_rotate( m3x3f m, float angle )
474 {
475 float m00 = m[0][0], m10 = m[1][0],
476 m01 = m[0][1], m11 = m[1][1],
477 m02 = m[0][2], m12 = m[1][2];
478 float c, s;
479
480 s = sinf( angle );
481 c = cosf( angle );
482
483 m[0][0] = m00 * c + m10 * s;
484 m[0][1] = m01 * c + m11 * s;
485 m[0][2] = m02 * c + m12 * s;
486
487 m[1][0] = m00 * -s + m10 * c;
488 m[1][1] = m01 * -s + m11 * c;
489 m[1][2] = m02 * -s + m12 * c;
490 }
491
492 // Matrix 4x3
493 // ==================================================================================================================
494
495 #define M4X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
496 { 0.0f, 1.0f, 0.0f, },\
497 { 0.0f, 0.0f, 1.0f, },\
498 { 0.0f, 0.0f, 0.0f }}
499
500 static inline void m4x3_to_3x3( m4x3f a, m3x3f b )
501 {
502 v3_copy( a[0], b[0] );
503 v3_copy( a[1], b[1] );
504 v3_copy( a[2], b[2] );
505 }
506
507 static inline void m4x3_copy( m4x3f a, m4x3f b )
508 {
509 v3_copy( a[0], b[0] );
510 v3_copy( a[1], b[1] );
511 v3_copy( a[2], b[2] );
512 v3_copy( a[3], b[3] );
513 }
514
515 static inline void m4x3_identity( m4x3f a )
516 {
517 m4x3f id = M4X3_IDENTITY;
518 m4x3_copy( id, a );
519 }
520
521 static inline void m4x3_mul( m4x3f a, m4x3f b, m4x3f d )
522 {
523 float
524 a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
525 a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
526 a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
527 a30 = a[3][0], a31 = a[3][1], a32 = a[3][2],
528 b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
529 b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
530 b20 = b[2][0], b21 = b[2][1], b22 = b[2][2],
531 b30 = b[3][0], b31 = b[3][1], b32 = b[3][2];
532
533 d[0][0] = a00*b00 + a10*b01 + a20*b02;
534 d[0][1] = a01*b00 + a11*b01 + a21*b02;
535 d[0][2] = a02*b00 + a12*b01 + a22*b02;
536 d[1][0] = a00*b10 + a10*b11 + a20*b12;
537 d[1][1] = a01*b10 + a11*b11 + a21*b12;
538 d[1][2] = a02*b10 + a12*b11 + a22*b12;
539 d[2][0] = a00*b20 + a10*b21 + a20*b22;
540 d[2][1] = a01*b20 + a11*b21 + a21*b22;
541 d[2][2] = a02*b20 + a12*b21 + a22*b22;
542 d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30;
543 d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31;
544 d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32;
545 }
546
547 static inline void m4x3_mulv( m4x3f m, v3f v, v3f d )
548 {
549 v3f res;
550
551 res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0];
552 res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1];
553 res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2];
554
555 v3_copy( res, d );
556 }
557
558 // Affine transforms
559 // ====================================================================================================================
560
561 static inline void m4x3_translate( m4x3f m, v3f v )
562 {
563 v3_muladds( m[3], m[0], v[0], m[3] );
564 v3_muladds( m[3], m[1], v[1], m[3] );
565 v3_muladds( m[3], m[2], v[2], m[3] );
566 }
567
568 static inline void m4x3_scale( m4x3f m, float s )
569 {
570 v3_muls( m[0], s, m[0] );
571 v3_muls( m[1], s, m[1] );
572 v3_muls( m[2], s, m[2] );
573 }
574
575 static inline void m4x3_rotate_x( m4x3f m, float angle )
576 {
577 m4x3f t = M4X3_IDENTITY;
578 float c, s;
579
580 c = cosf( angle );
581 s = sinf( angle );
582
583 t[1][1] = c;
584 t[1][2] = s;
585 t[2][1] = -s;
586 t[2][2] = c;
587
588 m4x3_mul( m, t, m );
589 }
590
591 static inline void m4x3_rotate_y( m4x3f m, float angle )
592 {
593 m4x3f t = M4X3_IDENTITY;
594 float c, s;
595
596 c = cosf( angle );
597 s = sinf( angle );
598
599 t[0][0] = c;
600 t[0][2] = -s;
601 t[2][0] = s;
602 t[2][2] = c;
603
604 m4x3_mul( m, t, m );
605 }
606
607 static inline void m4x3_rotate_z( m4x3f m, float angle )
608 {
609 m4x3f t = M4X3_IDENTITY;
610 float c, s;
611
612 c = cosf( angle );
613 s = sinf( angle );
614
615 t[0][0] = c;
616 t[0][1] = s;
617 t[1][0] = -s;
618 t[1][1] = c;
619
620 m4x3_mul( m, t, m );
621 }
622
623 // Warning: These functions are unoptimized..
624 static inline void m4x3_expand_aabb_point( m4x3f m, boxf box, v3f point )
625 {
626 v3f v;
627 m4x3_mulv( m, point, v );
628
629 v3_minv( box[0], v, box[0] );
630 v3_maxv( box[1], v, box[1] );
631 }
632
633 static inline void box_concat( boxf a, boxf b )
634 {
635 v3_minv( a[0], b[0], a[0] );
636 v3_maxv( a[1], b[1], a[1] );
637 }
638
639 static inline void box_copy( boxf a, boxf b )
640 {
641 v3_copy( a[0], b[0] );
642 v3_copy( a[1], b[1] );
643 }
644
645 static inline void m4x3_transform_aabb( m4x3f m, boxf box )
646 {
647 v3f a; v3f b;
648
649 v3_copy( box[0], a );
650 v3_copy( box[1], b );
651 v3_fill( box[0], INFINITY );
652 v3_fill( box[1], -INFINITY );
653
654 m4x3_expand_aabb_point( m, box, a );
655 m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], a[2] } );
656 m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], a[2] } );
657 m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], a[2] } );
658 m4x3_expand_aabb_point( m, box, b );
659 m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], b[2] } );
660 m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], b[2] } );
661 m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], b[2] } );
662 }
663
664 // Planes (double precision)
665 // ==================================================================================================================
666
667 static inline void tri_to_plane( double a[3], double b[3], double c[3], double p[4] )
668 {
669 double edge0[3];
670 double edge1[3];
671 double l;
672
673 edge0[0] = b[0] - a[0];
674 edge0[1] = b[1] - a[1];
675 edge0[2] = b[2] - a[2];
676
677 edge1[0] = c[0] - a[0];
678 edge1[1] = c[1] - a[1];
679 edge1[2] = c[2] - a[2];
680
681 p[0] = edge0[1] * edge1[2] - edge0[2] * edge1[1];
682 p[1] = edge0[2] * edge1[0] - edge0[0] * edge1[2];
683 p[2] = edge0[0] * edge1[1] - edge0[1] * edge1[0];
684
685 l = sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2]);
686 p[3] = (p[0] * a[0] + p[1] * a[1] + p[2] * a[2]) / l;
687
688 p[0] = p[0] / l;
689 p[1] = p[1] / l;
690 p[2] = p[2] / l;
691 }
692
693 static inline int plane_intersect( double a[4], double b[4], double c[4], double p[4] )
694 {
695 double const epsilon = 1e-8f;
696
697 double x[3];
698 double d;
699
700 x[0] = a[1] * b[2] - a[2] * b[1];
701 x[1] = a[2] * b[0] - a[0] * b[2];
702 x[2] = a[0] * b[1] - a[1] * b[0];
703
704 d = x[0] * c[0] + x[1] * c[1] + x[2] * c[2];
705
706 if( d < epsilon && d > -epsilon ) return 0;
707
708 p[0] = (b[1] * c[2] - b[2] * c[1]) * -a[3];
709 p[1] = (b[2] * c[0] - b[0] * c[2]) * -a[3];
710 p[2] = (b[0] * c[1] - b[1] * c[0]) * -a[3];
711
712 p[0] += (c[1] * a[2] - c[2] * a[1]) * -b[3];
713 p[1] += (c[2] * a[0] - c[0] * a[2]) * -b[3];
714 p[2] += (c[0] * a[1] - c[1] * a[0]) * -b[3];
715
716 p[0] += (a[1] * b[2] - a[2] * b[1]) * -c[3];
717 p[1] += (a[2] * b[0] - a[0] * b[2]) * -c[3];
718 p[2] += (a[0] * b[1] - a[1] * b[0]) * -c[3];
719
720 p[0] = -p[0] / d;
721 p[1] = -p[1] / d;
722 p[2] = -p[2] / d;
723
724 return 1;
725 }
726
727 static inline double plane_polarity( double p[4], double a[3] )
728 {
729 return
730 (a[0] * p[0] + a[1] * p[1] + a[2] * p[2])
731 -(p[0]*p[3] * p[0] + p[1]*p[3] * p[1] + p[2]*p[3] * p[2])
732 ;
733 }
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