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 static inline void v2_lerp( v2f a, v2f b, float t, v2f d )
 149 {
 150         d[0] = a[0] + t*(b[0]-a[0]);
 151         d[1] = a[1] + t*(b[1]-a[1]);
 152 }
 153
 154 // Vector 3
 155 // ==================================================================================================================
 156
 157 static inline void v3_zero( v3f a )
 158 {
 159         a[0] = 0.f; a[1] = 0.f; a[2] = 0.f;
 160 }
 161
 162 static inline void v3_copy( v3f a, v3f b )
 163 {
 164         b[0] = a[0]; b[1] = a[1]; b[2] = a[2];
 165 }
 166
 167 static inline void v3_add( v3f a, v3f b, v3f d )
 168 {
 169         d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; d[2] = a[2]+b[2];
 170 }
 171
 172 static inline void v3_sub( v3f a, v3f b, v3f d )
 173 {
 174         d[0] = a[0]-b[0]; d[1] = a[1]-b[1]; d[2] = a[2]-b[2];
 175 }
 176
 177 static inline void v3_mul( v3f a, v3f b, v3f d )
 178 {
 179         d[0] = a[0]*b[0]; d[1] = a[1]*b[1]; d[2] = a[2]*b[2];
 180 }
 181
 182 static inline void v3_div( v3f a, v3f b, v3f d )
 183 {
 184         d[0] = a[0]/b[0]; d[1] = a[1]/b[1];     d[2] = a[2]/b[2];
 185 }
 186
 187 static inline void v3_muls( v3f a, float s, v3f d )
 188 {
 189         d[0] = a[0]*s; d[1] = a[1]*s; d[2] = a[2]*s;
 190 }
 191
 192 static inline void v3_divs( v3f a, float s, v3f d )
 193 {
 194         d[0] = a[0]/s; d[1] = a[1]/s; d[2] = a[2]/s;
 195 }
 196
 197 static inline void v3_muladds( v3f a, v3f b, float s, v3f d )
 198 {
 199         d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s; d[2] = a[2]+b[2]*s;
 200 }
 201
 202 static inline float v3_dot( v3f a, v3f b )
 203 {
 204         return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
 205 }
 206
 207 static inline void v3_cross( v3f a, v3f b, v3f d )
 208 {
 209   d[0] = a[1] * b[2] - a[2] * b[1];
 210   d[1] = a[2] * b[0] - a[0] * b[2];
 211   d[2] = a[0] * b[1] - a[1] * b[0];
 212 }
 213
 214 static inline float v3_length2( v3f a )
 215 {
 216         return v3_dot( a, a );
 217 }
 218
 219 static inline float v3_length( v3f a )
 220 {
 221         return sqrtf( v3_length2( a ) );
 222 }
 223
 224 static inline float v3_dist2( v3f a, v3f b )
 225 {
 226         v3f delta;
 227         v3_sub( a, b, delta );
 228         return v3_length2( delta );
 229 }
 230
 231 static inline float v3_dist( v3f a, v3f b )
 232 {
 233         return sqrtf( v3_dist2( a, b ) );
 234 }
 235
 236 static inline void v3_normalize( v3f a )
 237 {
 238         v3_muls( a, 1.f / v3_length( a ), a );
 239 }
 240
 241 static inline float vg_lerpf( float a, float b, float t )
 242 {
 243         return a + t*(b-a);
 244 }
 245
 246 static inline void v3_lerp( v3f a, v3f b, float t, v3f d )
 247 {
 248         d[0] = a[0] + t*(b[0]-a[0]);
 249         d[1] = a[1] + t*(b[1]-a[1]);
 250         d[2] = a[2] + t*(b[2]-a[2]);
 251 }
 252
 253 static inline void v3_minv( v3f a, v3f b, v3f dest )
 254 {
 255         dest[0] = vg_minf(a[0], b[0]);
 256         dest[1] = vg_minf(a[1], b[1]);
 257         dest[2] = vg_minf(a[2], b[2]);
 258 }
 259
 260 static inline void v3_maxv( v3f a, v3f b, v3f dest )
 261 {
 262         dest[0] = vg_maxf(a[0], b[0]);
 263         dest[1] = vg_maxf(a[1], b[1]);
 264         dest[2] = vg_maxf(a[2], b[2]);
 265 }
 266
 267 static inline float v3_minf( v3f a )
 268 {
 269         return vg_minf( vg_minf( a[0], a[1] ), a[2] );
 270 }
 271
 272 static inline float v3_maxf( v3f a )
 273 {
 274         return vg_maxf( vg_maxf( a[0], a[1] ), a[2] );
 275 }
 276
 277 static inline void v3_fill( v3f a, float v )
 278 {
 279         a[0] = v;
 280         a[1] = v;
 281         a[2] = v;
 282 }
 283
 284 // Vector 4
 285 // ==================================================================================================================
 286
 287 static inline void v4_copy( v4f a, v4f b )
 288 {
 289         b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; b[3] = a[3];
 290 }
 291
 292 static inline void v4_zero( v4f a )
 293 {
 294         a[0] = 0.f; a[1] = 0.f; a[2] = 0.f; a[3] = 0.f;
 295 }
 296
 297 // Matrix 2x2
 298 // ===========================================================================================================
 299
 300 #define M2X2_INDENTIY   {{1.0f, 0.0f, }, \
 301                                                                 { 0.0f, 1.0f, }}
 302
 303 #define M2X2_ZERO                       {{0.0f, 0.0f, }, \
 304                                                                 { 0.0f, 0.0f, }}
 305
 306 static inline void m2x2_copy( m2x2f a, m2x2f b )
 307 {
 308         v2_copy( a[0], b[0] );
 309         v2_copy( a[1], b[1] );
 310 }
 311
 312 static inline void m2x2_identity( m2x2f a )
 313 {
 314         m2x2f id = M2X2_INDENTIY;
 315         m2x2_copy( id, a );
 316 }
 317
 318 static inline void m2x2_create_rotation( m2x2f a, float theta )
 319 {
 320         float s, c;
 321
 322         s = sinf( theta );
 323         c = cosf( theta );
 324
 325         a[0][0] =  c;
 326         a[0][1] = -s;
 327         a[1][0] =  s;
 328         a[1][1] =  c;
 329 }
 330
 331 // Matrix 3x3
 332 //======================================================================================================
 333
 334 #define M3X3_IDENTITY   {{1.0f, 0.0f, 0.0f, },\
 335                                                                 { 0.0f, 1.0f, 0.0f, },\
 336                                                                 { 0.0f, 0.0f, 1.0f, }}
 337
 338 #define M3X3_ZERO                       {{0.0f, 0.0f, 0.0f, },\
 339                                                                 { 0.0f, 0.0f, 0.0f, },\
 340                                                                 { 0.0f, 0.0f, 0.0f, }}
 341
 342
 343 static inline void m3x3_copy( m3x3f a, m3x3f b )
 344 {
 345         v3_copy( a[0], b[0] );
 346         v3_copy( a[1], b[1] );
 347         v3_copy( a[2], b[2] );
 348 }
 349
 350 static inline void m3x3_identity( m3x3f a )
 351 {
 352         m3x3f id = M3X3_IDENTITY;
 353         m3x3_copy( id, a );
 354 }
 355
 356 static inline void m3x3_zero( m3x3f a )
 357 {
 358         m3x3f z = M3X3_ZERO;
 359         m3x3_copy( z, a );
 360 }
 361
 362 static inline void m3x3_inv( m3x3f src, m3x3f dest )
 363 {
 364         float a = src[0][0], b = src[0][1], c = src[0][2],
 365                         d = src[1][0], e = src[1][1], f = src[1][2],
 366                         g = src[2][0], h = src[2][1], i = src[2][2];
 367
 368         float det =    1.f /
 369                                         (+a*(e*i-h*f)
 370                 -b*(d*i-f*g)
 371                 +c*(d*h-e*g));
 372
 373         dest[0][0] =  (e*i-h*f)*det;
 374         dest[0][1] = -(b*i-c*h)*det;
 375         dest[0][2] =  (b*f-c*e)*det;
 376         dest[1][0] = -(d*i-f*g)*det;
 377         dest[1][1] =  (a*i-c*g)*det;
 378         dest[1][2] = -(a*f-d*c)*det;
 379         dest[2][0] =  (d*h-g*e)*det;
 380         dest[2][1] = -(a*h-g*b)*det;
 381         dest[2][2] =  (a*e-d*b)*det;
 382 }
 383
 384 static inline void m3x3_transpose( m3x3f src, m3x3f dest )
 385 {
 386         float a = src[0][0], b = src[0][1], c = src[0][2],
 387                         d = src[1][0], e = src[1][1], f = src[1][2],
 388                         g = src[2][0], h = src[2][1], i = src[2][2];
 389
 390         dest[0][0] = a;
 391         dest[0][1] = d;
 392         dest[0][2] = g;
 393         dest[1][0] = b;
 394         dest[1][1] = e;
 395         dest[1][2] = h;
 396         dest[2][0] = c;
 397         dest[2][1] = f;
 398         dest[2][2] = i;
 399 }
 400
 401 static inline void m3x3_mul( m3x3f a, m3x3f b, m3x3f d )
 402 {
 403         float a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
 404                         a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
 405                         a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
 406
 407                         b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
 408                         b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
 409                         b20 = b[2][0], b21 = b[2][1], b22 = b[2][2];
 410
 411         d[0][0] = a00*b00 + a10*b01 + a20*b02;
 412         d[0][1] = a01*b00 + a11*b01 + a21*b02;
 413         d[0][2] = a02*b00 + a12*b01 + a22*b02;
 414         d[1][0] = a00*b10 + a10*b11 + a20*b12;
 415         d[1][1] = a01*b10 + a11*b11 + a21*b12;
 416         d[1][2] = a02*b10 + a12*b11 + a22*b12;
 417         d[2][0] = a00*b20 + a10*b21 + a20*b22;
 418         d[2][1] = a01*b20 + a11*b21 + a21*b22;
 419         d[2][2] = a02*b20 + a12*b21 + a22*b22;
 420 }
 421
 422 static inline void m3x3_mulv( m3x3f m, v3f v, v3f d )
 423 {
 424         v3f res;
 425
 426         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
 427         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
 428         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
 429
 430         v3_copy( res, d );
 431 }
 432
 433 static inline void m3x3_projection( m3x3f dst, float const left, float const right, float const bottom, float const top )
 434 {
 435         float rl, tb;
 436
 437         m3x3_zero( dst );
 438
 439         rl = 1.0f / (right - left);
 440         tb = 1.0f / (top   - bottom);
 441
 442         dst[0][0] = 2.0f * rl;
 443         dst[1][1] = 2.0f * tb;
 444         dst[2][2] = 1.0f;
 445 }
 446
 447 static inline void m3x3_translate( m3x3f m, v3f v )
 448 {
 449         m[2][0] = m[0][0] * v[0] + m[1][0] * v[1] + m[2][0];
 450         m[2][1] = m[0][1] * v[0] + m[1][1] * v[1] + m[2][1];
 451         m[2][2] = m[0][2] * v[0] + m[1][2] * v[1] + m[2][2];
 452 }
 453
 454 static inline void m3x3_scale( m3x3f m, v3f v )
 455 {
 456         m[0][0] = m[0][0] * v[0];
 457         m[0][1] = m[0][1] * v[0];
 458         m[0][2] = m[0][2] * v[0];
 459
 460         m[1][0] = m[1][0] * v[1];
 461         m[1][1] = m[1][1] * v[1];
 462         m[1][2] = m[1][2] * v[1];
 463 }
 464
 465 static inline void m3x3_rotate( m3x3f m, float angle )
 466 {
 467         float m00 = m[0][0], m10 = m[1][0],
 468                         m01 = m[0][1], m11 = m[1][1],
 469                         m02 = m[0][2], m12 = m[1][2];
 470         float c, s;
 471
 472         s = sinf( angle );
 473         c = cosf( angle );
 474
 475         m[0][0] = m00 * c + m10 * s;
 476         m[0][1] = m01 * c + m11 * s;
 477         m[0][2] = m02 * c + m12 * s;
 478
 479         m[1][0] = m00 * -s + m10 * c;
 480         m[1][1] = m01 * -s + m11 * c;
 481         m[1][2] = m02 * -s + m12 * c;
 482 }
 483
 484 // Matrix 4x3
 485 // ==================================================================================================================
 486
 487 #define M4X3_IDENTITY   {{1.0f, 0.0f, 0.0f, },\
 488                                                                 { 0.0f, 1.0f, 0.0f, },\
 489                                                                 { 0.0f, 0.0f, 1.0f, },\
 490                                                                 { 0.0f, 0.0f, 0.0f }}
 491
 492 static inline void m4x3_to_3x3( m4x3f a, m3x3f b )
 493 {
 494         v3_copy( a[0], b[0] );
 495         v3_copy( a[1], b[1] );
 496         v3_copy( a[2], b[2] );
 497 }
 498
 499 static inline void m4x3_copy( m4x3f a, m4x3f b )
 500 {
 501         v3_copy( a[0], b[0] );
 502         v3_copy( a[1], b[1] );
 503         v3_copy( a[2], b[2] );
 504         v3_copy( a[3], b[3] );
 505 }
 506
 507 static inline void m4x3_identity( m4x3f a )
 508 {
 509         m4x3f id = M4X3_IDENTITY;
 510         m4x3_copy( id, a );
 511 }
 512
 513 static inline void m4x3_mul( m4x3f a, m4x3f b, m4x3f d )
 514 {
 515         float
 516         a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
 517         a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
 518         a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
 519         a30 = a[3][0], a31 = a[3][1], a32 = a[3][2],
 520         b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
 521         b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
 522         b20 = b[2][0], b21 = b[2][1], b22 = b[2][2],
 523         b30 = b[3][0], b31 = b[3][1], b32 = b[3][2];
 524
 525         d[0][0] = a00*b00 + a10*b01 + a20*b02;
 526         d[0][1] = a01*b00 + a11*b01 + a21*b02;
 527         d[0][2] = a02*b00 + a12*b01 + a22*b02;
 528         d[1][0] = a00*b10 + a10*b11 + a20*b12;
 529         d[1][1] = a01*b10 + a11*b11 + a21*b12;
 530         d[1][2] = a02*b10 + a12*b11 + a22*b12;
 531         d[2][0] = a00*b20 + a10*b21 + a20*b22;
 532         d[2][1] = a01*b20 + a11*b21 + a21*b22;
 533         d[2][2] = a02*b20 + a12*b21 + a22*b22;
 534         d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30;
 535         d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31;
 536         d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32;
 537 }
 538
 539 static inline void m4x3_mulv( m4x3f m, v3f v, v3f d )
 540 {
 541         v3f res;
 542
 543         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0];
 544         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1];
 545         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2];
 546
 547         v3_copy( res, d );
 548 }
 549
 550 // Affine transforms
 551 // ====================================================================================================================
 552
 553 static inline void m4x3_translate( m4x3f m, v3f v )
 554 {
 555         v3_muladds( m[3], m[0], v[0], m[3] );
 556         v3_muladds( m[3], m[1], v[1], m[3] );
 557         v3_muladds( m[3], m[2], v[2], m[3] );
 558 }
 559
 560 static inline void m4x3_scale( m4x3f m, float s )
 561 {
 562         v3_muls( m[0], s, m[0] );
 563         v3_muls( m[1], s, m[1] );
 564         v3_muls( m[2], s, m[2] );
 565 }
 566
 567 static inline void m4x3_rotate_x( 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[1][1] =  c;
 576         t[1][2] =  s;
 577         t[2][1] = -s;
 578         t[2][2] =  c;
 579
 580         m4x3_mul( m, t, m );
 581 }
 582
 583 static inline void m4x3_rotate_y( 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][2] = -s;
 593         t[2][0] =  s;
 594         t[2][2] =  c;
 595
 596         m4x3_mul( m, t, m );
 597 }
 598
 599 static inline void m4x3_rotate_z( m4x3f m, float angle )
 600 {
 601         m4x3f t = M4X3_IDENTITY;
 602         float c, s;
 603
 604         c = cosf( angle );
 605         s = sinf( angle );
 606
 607         t[0][0] =  c;
 608         t[0][1] =  s;
 609         t[1][0] = -s;
 610         t[1][1] =  c;
 611
 612         m4x3_mul( m, t, m );
 613 }
 614
 615 // Warning: These functions are unoptimized..
 616 static inline void m4x3_expand_aabb_point( m4x3f m, boxf box, v3f point )
 617 {
 618         v3f v;
 619         m4x3_mulv( m, point, v );
 620
 621         v3_minv( box[0], v, box[0] );
 622         v3_maxv( box[1], v, box[1] );
 623 }
 624
 625 static inline void box_concat( boxf a, boxf b )
 626 {
 627         v3_minv( a[0], b[0], a[0] );
 628         v3_maxv( a[1], b[1], a[1] );
 629 }
 630
 631 static inline void box_copy( boxf a, boxf b )
 632 {
 633         v3_copy( a[0], b[0] );
 634         v3_copy( a[1], b[1] );
 635 }
 636
 637 static inline void m4x3_transform_aabb( m4x3f m, boxf box )
 638 {
 639         v3f a; v3f b;
 640
 641         v3_copy( box[0], a );
 642         v3_copy( box[1], b );
 643         v3_fill( box[0],  INFINITY );
 644         v3_fill( box[1], -INFINITY );
 645
 646         m4x3_expand_aabb_point( m, box, a );
 647         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], a[2] } );
 648         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], a[2] } );
 649         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], a[2] } );
 650         m4x3_expand_aabb_point( m, box, b );
 651         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], b[2] } );
 652         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], b[2] } );
 653         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], b[2] } );
 654 }
 655
 656 // Planes (double precision)
 657 // ==================================================================================================================
 658
 659 static inline void tri_to_plane( double a[3], double b[3], double c[3], double p[4] )
 660 {
 661         double edge0[3];
 662         double edge1[3];
 663         double l;
 664
 665         edge0[0] = b[0] - a[0];
 666         edge0[1] = b[1] - a[1];
 667         edge0[2] = b[2] - a[2];
 668
 669         edge1[0] = c[0] - a[0];
 670         edge1[1] = c[1] - a[1];
 671         edge1[2] = c[2] - a[2];
 672
 673         p[0] = edge0[1] * edge1[2] - edge0[2] * edge1[1];
 674         p[1] = edge0[2] * edge1[0] - edge0[0] * edge1[2];
 675         p[2] = edge0[0] * edge1[1] - edge0[1] * edge1[0];
 676
 677         l = sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2]);
 678         p[3] = (p[0] * a[0] + p[1] * a[1] + p[2] * a[2]) / l;
 679
 680         p[0] = p[0] / l;
 681         p[1] = p[1] / l;
 682         p[2] = p[2] / l;
 683 }
 684
 685 static inline int plane_intersect( double a[4], double b[4], double c[4], double p[4] )
 686 {
 687         double const epsilon = 1e-8f;
 688
 689         double x[3];
 690         double d;
 691
 692         x[0] = a[1] * b[2] - a[2] * b[1];
 693         x[1] = a[2] * b[0] - a[0] * b[2];
 694         x[2] = a[0] * b[1] - a[1] * b[0];
 695
 696         d = x[0] * c[0] + x[1] * c[1] + x[2] * c[2];
 697
 698         if( d < epsilon && d > -epsilon ) return 0;
 699
 700         p[0] = (b[1] * c[2] - b[2] * c[1]) * -a[3];
 701         p[1] = (b[2] * c[0] - b[0] * c[2]) * -a[3];
 702         p[2] = (b[0] * c[1] - b[1] * c[0]) * -a[3];
 703
 704         p[0] += (c[1] * a[2] - c[2] * a[1]) * -b[3];
 705         p[1] += (c[2] * a[0] - c[0] * a[2]) * -b[3];
 706         p[2] += (c[0] * a[1] - c[1] * a[0]) * -b[3];
 707
 708         p[0] += (a[1] * b[2] - a[2] * b[1]) * -c[3];
 709         p[1] += (a[2] * b[0] - a[0] * b[2]) * -c[3];
 710         p[2] += (a[0] * b[1] - a[1] * b[0]) * -c[3];
 711
 712         p[0] = -p[0] / d;
 713         p[1] = -p[1] / d;
 714         p[2] = -p[2] / d;
 715
 716         return 1;
 717 }
 718
 719 static inline double plane_polarity( double p[4], double a[3] )
 720 {
 721         return
 722         (a[0] * p[0] + a[1] * p[1] + a[2] * p[2])
 723         -(p[0]*p[3] * p[0] + p[1]*p[3] * p[1] + p[2]*p[3] * p[2])
 724         ;
 725 }