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