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