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