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