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