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 v2_minv( v2f a, v2f b, v2f dest )
  54 {
  55         dest[0] = vg_minf(a[0], b[0]);
  56         dest[1] = vg_minf(a[1], b[1]);
  57 }
  58
  59 static inline void v2_maxv( v2f a, v2f b, v2f dest )
  60 {
  61         dest[0] = vg_maxf(a[0], b[0]);
  62         dest[1] = vg_maxf(a[1], b[1]);
  63 }
  64
  65 static inline void v2_sub( v2f a, v2f b, v2f d )
  66 {
  67         d[0] = a[0]-b[0]; d[1] = a[1]-b[1];
  68 }
  69
  70 static inline float v2_cross( v2f a, v2f b )
  71 {
  72         return a[0] * b[1] - a[1] * b[0];
  73 }
  74
  75 static inline void v2_add( 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 void v2_muls( v2f a, float s, v2f d )
  81 {
  82         d[0] = a[0]*s; d[1] = a[1]*s;
  83 }
  84
  85 static inline void v2_divs( v2f a, float s, v2f d )
  86 {
  87         d[0] = a[0]/s; d[1] = a[1]/s;
  88 }
  89
  90
  91 static inline void v2_mul( v2f a, v2f b, v2f d )
  92 {
  93         d[0] = a[0]*b[0]; d[1] = a[1]*b[1];
  94 }
  95
  96 static inline void v2_div( v2f a, v2f b, v2f d )
  97 {
  98         d[0] = a[0]/b[0]; d[1] = a[1]/b[1];
  99 }
 100
 101 static inline void v2_muladds( v2f a, v2f b, float s, v2f d )
 102 {
 103         d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s;
 104 }
 105
 106 static inline float v2_length2( v2f a )
 107 {
 108         return a[0]*a[0] + a[1]*a[1];
 109 }
 110
 111 static inline float v2_length( v2f a )
 112 {
 113         return sqrtf( v2_length2( a ) );
 114 }
 115
 116 static inline float v2_dist2( v2f a, v2f b )
 117 {
 118         v2f delta;
 119         v2_sub( a, b, delta );
 120         return v2_length2( delta );
 121 }
 122
 123 static inline float v2_dist( v2f a, v2f b )
 124 {
 125         return sqrtf( v2_dist2( a, b ) );
 126 }
 127
 128 // Vector 3
 129 // ==================================================================================================================
 130
 131 static inline void v3_zero( v3f a )
 132 {
 133         a[0] = 0.f; a[1] = 0.f; a[2] = 0.f;
 134 }
 135
 136 static inline void v3_copy( v3f a, v3f b )
 137 {
 138         b[0] = a[0]; b[1] = a[1]; b[2] = a[2];
 139 }
 140
 141 static inline void v3_add( v3f a, v3f b, v3f d )
 142 {
 143         d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; d[2] = a[2]+b[2];
 144 }
 145
 146 static inline void v3_sub( v3f a, v3f b, v3f d )
 147 {
 148         d[0] = a[0]-b[0]; d[1] = a[1]-b[1]; d[2] = a[2]-b[2];
 149 }
 150
 151 static inline void v3_mul( 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_div( 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_muls( v3f a, float s, v3f d )
 162 {
 163         d[0] = a[0]*s; d[1] = a[1]*s; d[2] = a[2]*s;
 164 }
 165
 166 static inline void v3_divs( v3f a, float s, v3f d )
 167 {
 168         d[0] = a[0]/s; d[1] = a[1]/s; d[2] = a[2]/s;
 169 }
 170
 171 static inline void v3_muladds( v3f a, v3f b, float s, v3f d )
 172 {
 173         d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s; d[2] = a[2]+b[2]*s;
 174 }
 175
 176 static inline float v3_dot( v3f a, v3f b )
 177 {
 178         return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
 179 }
 180
 181 static inline void v3_cross( v3f a, v3f b, v3f d )
 182 {
 183   d[0] = a[1] * b[2] - a[2] * b[1];
 184   d[1] = a[2] * b[0] - a[0] * b[2];
 185   d[2] = a[0] * b[1] - a[1] * b[0];
 186 }
 187
 188 static inline float v3_length2( v3f a )
 189 {
 190         return v3_dot( a, a );
 191 }
 192
 193 static inline float v3_length( v3f a )
 194 {
 195         return sqrtf( v3_length2( a ) );
 196 }
 197
 198 static inline float v3_dist2( v3f a, v3f b )
 199 {
 200         v3f delta;
 201         v3_sub( a, b, delta );
 202         return v3_length2( delta );
 203 }
 204
 205 static inline float v3_dist( v3f a, v3f b )
 206 {
 207         return sqrtf( v3_dist2( a, b ) );
 208 }
 209
 210 static inline void v3_normalize( v3f a )
 211 {
 212         v3_muls( a, 1.f / v3_length( a ), a );
 213 }
 214
 215 static inline float csr_lerpf( float a, float b, float t )
 216 {
 217         return a + t*(b-a);
 218 }
 219
 220 static inline void v3_lerp( v3f a, v3f b, float t, v3f d )
 221 {
 222         d[0] = a[0] + t*(b[0]-a[0]);
 223         d[1] = a[1] + t*(b[1]-a[1]);
 224         d[2] = a[2] + t*(b[2]-a[2]);
 225 }
 226
 227 static inline void v3_minv( v3f a, v3f b, v3f dest )
 228 {
 229         dest[0] = vg_minf(a[0], b[0]);
 230         dest[1] = vg_minf(a[1], b[1]);
 231         dest[2] = vg_minf(a[2], b[2]);
 232 }
 233
 234 static inline void v3_maxv( v3f a, v3f b, v3f dest )
 235 {
 236         dest[0] = vg_maxf(a[0], b[0]);
 237         dest[1] = vg_maxf(a[1], b[1]);
 238         dest[2] = vg_maxf(a[2], b[2]);
 239 }
 240
 241 static inline float v3_minf( v3f a )
 242 {
 243         return vg_minf( vg_minf( a[0], a[1] ), a[2] );
 244 }
 245
 246 static inline float v3_maxf( v3f a )
 247 {
 248         return vg_maxf( vg_maxf( a[0], a[1] ), a[2] );
 249 }
 250
 251 static inline void v3_fill( v3f a, float v )
 252 {
 253         a[0] = v;
 254         a[1] = v;
 255         a[2] = v;
 256 }
 257
 258 // Vector 4
 259 // ==================================================================================================================
 260
 261 static inline void v4_copy( v4f a, v4f b )
 262 {
 263         b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; b[3] = a[3];
 264 }
 265
 266 static inline void v4_zero( v4f a )
 267 {
 268         a[0] = 0.f; a[1] = 0.f; a[2] = 0.f; a[3] = 0.f;
 269 }
 270
 271 // Matrix 2x2
 272 // ===========================================================================================================
 273
 274 #define M2X2_INDENTIY   {{1.0f, 0.0f, }, \
 275                                                                 { 0.0f, 1.0f, }}
 276
 277 #define M2X2_ZERO                       {{0.0f, 0.0f, }, \
 278                                                                 { 0.0f, 0.0f, }}
 279
 280 static inline void m2x2_copy( m2x2f a, m2x2f b )
 281 {
 282         v2_copy( a[0], b[0] );
 283         v2_copy( a[1], b[1] );
 284 }
 285
 286 static inline void m2x2_identity( m2x2f a )
 287 {
 288         m2x2f id = M2X2_INDENTIY;
 289         m2x2_copy( id, a );
 290 }
 291
 292 static inline void m2x2_create_rotation( m2x2f a, float theta )
 293 {
 294         float s, c;
 295
 296         s = sinf( theta );
 297         c = cosf( theta );
 298
 299         a[0][0] =  c;
 300         a[0][1] = -s;
 301         a[1][0] =  s;
 302         a[1][1] =  c;
 303 }
 304
 305 // Matrix 3x3
 306 //======================================================================================================
 307
 308 #define M3X3_IDENTITY   {{1.0f, 0.0f, 0.0f, },\
 309                                                                 { 0.0f, 1.0f, 0.0f, },\
 310                                                                 { 0.0f, 0.0f, 1.0f, }}
 311
 312 #define M3X3_ZERO                       {{0.0f, 0.0f, 0.0f, },\
 313                                                                 { 0.0f, 0.0f, 0.0f, },\
 314                                                                 { 0.0f, 0.0f, 0.0f, }}
 315
 316
 317 static inline void m3x3_copy( m3x3f a, m3x3f b )
 318 {
 319         v3_copy( a[0], b[0] );
 320         v3_copy( a[1], b[1] );
 321         v3_copy( a[2], b[2] );
 322 }
 323
 324 static inline void m3x3_identity( m3x3f a )
 325 {
 326         m3x3f id = M3X3_IDENTITY;
 327         m3x3_copy( id, a );
 328 }
 329
 330 static inline void m3x3_zero( m3x3f a )
 331 {
 332         m3x3f z = M3X3_ZERO;
 333         m3x3_copy( z, a );
 334 }
 335
 336 static inline void m3x3_inv( m3x3f src, m3x3f dest )
 337 {
 338         float a = src[0][0], b = src[0][1], c = src[0][2],
 339                         d = src[1][0], e = src[1][1], f = src[1][2],
 340                         g = src[2][0], h = src[2][1], i = src[2][2];
 341
 342         float det =    1.f /
 343                                         (+a*(e*i-h*f)
 344                 -b*(d*i-f*g)
 345                 +c*(d*h-e*g));
 346
 347         dest[0][0] =  (e*i-h*f)*det;
 348         dest[0][1] = -(b*i-c*h)*det;
 349         dest[0][2] =  (b*f-c*e)*det;
 350         dest[1][0] = -(d*i-f*g)*det;
 351         dest[1][1] =  (a*i-c*g)*det;
 352         dest[1][2] = -(a*f-d*c)*det;
 353         dest[2][0] =  (d*h-g*e)*det;
 354         dest[2][1] = -(a*h-g*b)*det;
 355         dest[2][2] =  (a*e-d*b)*det;
 356 }
 357
 358 static inline void m3x3_transpose( m3x3f src, m3x3f dest )
 359 {
 360         float a = src[0][0], b = src[0][1], c = src[0][2],
 361                         d = src[1][0], e = src[1][1], f = src[1][2],
 362                         g = src[2][0], h = src[2][1], i = src[2][2];
 363
 364         dest[0][0] = a;
 365         dest[0][1] = d;
 366         dest[0][2] = g;
 367         dest[1][0] = b;
 368         dest[1][1] = e;
 369         dest[1][2] = h;
 370         dest[2][0] = c;
 371         dest[2][1] = f;
 372         dest[2][2] = i;
 373 }
 374
 375 static inline void m3x3_mul( m3x3f a, m3x3f b, m3x3f d )
 376 {
 377         float a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
 378                         a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
 379                         a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
 380
 381                         b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
 382                         b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
 383                         b20 = b[2][0], b21 = b[2][1], b22 = b[2][2];
 384
 385         d[0][0] = a00*b00 + a10*b01 + a20*b02;
 386         d[0][1] = a01*b00 + a11*b01 + a21*b02;
 387         d[0][2] = a02*b00 + a12*b01 + a22*b02;
 388         d[1][0] = a00*b10 + a10*b11 + a20*b12;
 389         d[1][1] = a01*b10 + a11*b11 + a21*b12;
 390         d[1][2] = a02*b10 + a12*b11 + a22*b12;
 391         d[2][0] = a00*b20 + a10*b21 + a20*b22;
 392         d[2][1] = a01*b20 + a11*b21 + a21*b22;
 393         d[2][2] = a02*b20 + a12*b21 + a22*b22;
 394 }
 395
 396 static inline void m3x3_mulv( m3x3f m, v3f v, v3f d )
 397 {
 398         v3f res;
 399
 400         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
 401         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
 402         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
 403
 404         v3_copy( res, d );
 405 }
 406
 407 static inline void m3x3_projection( m3x3f dst, float const left, float const right, float const bottom, float const top )
 408 {
 409         float rl, tb;
 410
 411         m3x3_zero( dst );
 412
 413         rl = 1.0f / (right - left);
 414         tb = 1.0f / (top   - bottom);
 415
 416         dst[0][0] = 2.0f * rl;
 417         dst[1][1] = 2.0f * tb;
 418         dst[2][2] = 1.0f;
 419 }
 420
 421 static inline void m3x3_translate( m3x3f m, v3f v )
 422 {
 423         m[2][0] = m[0][0] * v[0] + m[1][0] * v[1] + m[2][0];
 424         m[2][1] = m[0][1] * v[0] + m[1][1] * v[1] + m[2][1];
 425         m[2][2] = m[0][2] * v[0] + m[1][2] * v[1] + m[2][2];
 426 }
 427
 428 static inline void m3x3_scale( m3x3f m, v3f v )
 429 {
 430         m[0][0] = m[0][0] * v[0];
 431         m[0][1] = m[0][1] * v[0];
 432         m[0][2] = m[0][2] * v[0];
 433
 434         m[1][0] = m[1][0] * v[1];
 435         m[1][1] = m[1][1] * v[1];
 436         m[1][2] = m[1][2] * v[1];
 437 }
 438
 439 static inline void m3x3_rotate( m3x3f m, float angle )
 440 {
 441         float m00 = m[0][0], m10 = m[1][0],
 442                         m01 = m[0][1], m11 = m[1][1],
 443                         m02 = m[0][2], m12 = m[1][2];
 444         float c, s;
 445
 446         s = sinf( angle );
 447         c = cosf( angle );
 448
 449         m[0][0] = m00 * c + m10 * s;
 450         m[0][1] = m01 * c + m11 * s;
 451         m[0][2] = m02 * c + m12 * s;
 452
 453         m[1][0] = m00 * -s + m10 * c;
 454         m[1][1] = m01 * -s + m11 * c;
 455         m[1][2] = m02 * -s + m12 * c;
 456 }
 457
 458 // Matrix 4x3
 459 // ==================================================================================================================
 460
 461 #define M4X3_IDENTITY   {{1.0f, 0.0f, 0.0f, },\
 462                                                                 { 0.0f, 1.0f, 0.0f, },\
 463                                                                 { 0.0f, 0.0f, 1.0f, },\
 464                                                                 { 0.0f, 0.0f, 0.0f }}
 465
 466 static inline void m4x3_to_3x3( m4x3f a, m3x3f b )
 467 {
 468         v3_copy( a[0], b[0] );
 469         v3_copy( a[1], b[1] );
 470         v3_copy( a[2], b[2] );
 471 }
 472
 473 static inline void m4x3_copy( m4x3f a, m4x3f b )
 474 {
 475         v3_copy( a[0], b[0] );
 476         v3_copy( a[1], b[1] );
 477         v3_copy( a[2], b[2] );
 478         v3_copy( a[3], b[3] );
 479 }
 480
 481 static inline void m4x3_identity( m4x3f a )
 482 {
 483         m4x3f id = M4X3_IDENTITY;
 484         m4x3_copy( id, a );
 485 }
 486
 487 static inline void m4x3_mul( m4x3f a, m4x3f b, m4x3f d )
 488 {
 489         float
 490         a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
 491         a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
 492         a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
 493         a30 = a[3][0], a31 = a[3][1], a32 = a[3][2],
 494         b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
 495         b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
 496         b20 = b[2][0], b21 = b[2][1], b22 = b[2][2],
 497         b30 = b[3][0], b31 = b[3][1], b32 = b[3][2];
 498
 499         d[0][0] = a00*b00 + a10*b01 + a20*b02;
 500         d[0][1] = a01*b00 + a11*b01 + a21*b02;
 501         d[0][2] = a02*b00 + a12*b01 + a22*b02;
 502         d[1][0] = a00*b10 + a10*b11 + a20*b12;
 503         d[1][1] = a01*b10 + a11*b11 + a21*b12;
 504         d[1][2] = a02*b10 + a12*b11 + a22*b12;
 505         d[2][0] = a00*b20 + a10*b21 + a20*b22;
 506         d[2][1] = a01*b20 + a11*b21 + a21*b22;
 507         d[2][2] = a02*b20 + a12*b21 + a22*b22;
 508         d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30;
 509         d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31;
 510         d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32;
 511 }
 512
 513 static inline void m4x3_mulv( m4x3f m, v3f v, v3f d )
 514 {
 515         v3f res;
 516
 517         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0];
 518         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1];
 519         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2];
 520
 521         v3_copy( res, d );
 522 }
 523
 524 // Affine transforms
 525 // ====================================================================================================================
 526
 527 static inline void m4x3_translate( m4x3f m, v3f v )
 528 {
 529         v3_muladds( m[3], m[0], v[0], m[3] );
 530         v3_muladds( m[3], m[1], v[1], m[3] );
 531         v3_muladds( m[3], m[2], v[2], m[3] );
 532 }
 533
 534 static inline void m4x3_scale( m4x3f m, float s )
 535 {
 536         v3_muls( m[0], s, m[0] );
 537         v3_muls( m[1], s, m[1] );
 538         v3_muls( m[2], s, m[2] );
 539 }
 540
 541 static inline void m4x3_rotate_x( m4x3f m, float angle )
 542 {
 543         m4x3f t = M4X3_IDENTITY;
 544         float c, s;
 545
 546         c = cosf( angle );
 547         s = sinf( angle );
 548
 549         t[1][1] =  c;
 550         t[1][2] =  s;
 551         t[2][1] = -s;
 552         t[2][2] =  c;
 553
 554         m4x3_mul( m, t, m );
 555 }
 556
 557 static inline void m4x3_rotate_y( m4x3f m, float angle )
 558 {
 559         m4x3f t = M4X3_IDENTITY;
 560         float c, s;
 561
 562         c = cosf( angle );
 563         s = sinf( angle );
 564
 565         t[0][0] =  c;
 566         t[0][2] = -s;
 567         t[2][0] =  s;
 568         t[2][2] =  c;
 569
 570         m4x3_mul( m, t, m );
 571 }
 572
 573 static inline void m4x3_rotate_z( m4x3f m, float angle )
 574 {
 575         m4x3f t = M4X3_IDENTITY;
 576         float c, s;
 577
 578         c = cosf( angle );
 579         s = sinf( angle );
 580
 581         t[0][0] =  c;
 582         t[0][1] =  s;
 583         t[1][0] = -s;
 584         t[1][1] =  c;
 585
 586         m4x3_mul( m, t, m );
 587 }
 588
 589 // Warning: These functions are unoptimized..
 590 static inline void m4x3_expand_aabb_point( m4x3f m, boxf box, v3f point )
 591 {
 592         v3f v;
 593         m4x3_mulv( m, point, v );
 594
 595         v3_minv( box[0], v, box[0] );
 596         v3_maxv( box[1], v, box[1] );
 597 }
 598
 599 static inline void box_concat( boxf a, boxf b )
 600 {
 601         v3_minv( a[0], b[0], a[0] );
 602         v3_maxv( a[1], b[1], a[1] );
 603 }
 604
 605 static inline void box_copy( boxf a, boxf b )
 606 {
 607         v3_copy( a[0], b[0] );
 608         v3_copy( a[1], b[1] );
 609 }
 610
 611 static inline void m4x3_transform_aabb( m4x3f m, boxf box )
 612 {
 613         v3f a; v3f b;
 614
 615         v3_copy( box[0], a );
 616         v3_copy( box[1], b );
 617         v3_fill( box[0],  INFINITY );
 618         v3_fill( box[1], -INFINITY );
 619
 620         m4x3_expand_aabb_point( m, box, a );
 621         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], a[2] } );
 622         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], a[2] } );
 623         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], a[2] } );
 624         m4x3_expand_aabb_point( m, box, b );
 625         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], b[2] } );
 626         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], b[2] } );
 627         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], b[2] } );
 628 }
 629
 630 // Planes (double precision)
 631 // ==================================================================================================================
 632
 633 static inline void tri_to_plane( double a[3], double b[3], double c[3], double p[4] )
 634 {
 635         double edge0[3];
 636         double edge1[3];
 637         double l;
 638
 639         edge0[0] = b[0] - a[0];
 640         edge0[1] = b[1] - a[1];
 641         edge0[2] = b[2] - a[2];
 642
 643         edge1[0] = c[0] - a[0];
 644         edge1[1] = c[1] - a[1];
 645         edge1[2] = c[2] - a[2];
 646
 647         p[0] = edge0[1] * edge1[2] - edge0[2] * edge1[1];
 648         p[1] = edge0[2] * edge1[0] - edge0[0] * edge1[2];
 649         p[2] = edge0[0] * edge1[1] - edge0[1] * edge1[0];
 650
 651         l = sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2]);
 652         p[3] = (p[0] * a[0] + p[1] * a[1] + p[2] * a[2]) / l;
 653
 654         p[0] = p[0] / l;
 655         p[1] = p[1] / l;
 656         p[2] = p[2] / l;
 657 }
 658
 659 static inline int plane_intersect( double a[4], double b[4], double c[4], double p[4] )
 660 {
 661         double const epsilon = 1e-8f;
 662
 663         double x[3];
 664         double d;
 665
 666         x[0] = a[1] * b[2] - a[2] * b[1];
 667         x[1] = a[2] * b[0] - a[0] * b[2];
 668         x[2] = a[0] * b[1] - a[1] * b[0];
 669
 670         d = x[0] * c[0] + x[1] * c[1] + x[2] * c[2];
 671
 672         if( d < epsilon && d > -epsilon ) return 0;
 673
 674         p[0] = (b[1] * c[2] - b[2] * c[1]) * -a[3];
 675         p[1] = (b[2] * c[0] - b[0] * c[2]) * -a[3];
 676         p[2] = (b[0] * c[1] - b[1] * c[0]) * -a[3];
 677
 678         p[0] += (c[1] * a[2] - c[2] * a[1]) * -b[3];
 679         p[1] += (c[2] * a[0] - c[0] * a[2]) * -b[3];
 680         p[2] += (c[0] * a[1] - c[1] * a[0]) * -b[3];
 681
 682         p[0] += (a[1] * b[2] - a[2] * b[1]) * -c[3];
 683         p[1] += (a[2] * b[0] - a[0] * b[2]) * -c[3];
 684         p[2] += (a[0] * b[1] - a[1] * b[0]) * -c[3];
 685
 686         p[0] = -p[0] / d;
 687         p[1] = -p[1] / d;
 688         p[2] = -p[2] / d;
 689
 690         return 1;
 691 }
 692
 693 static inline double plane_polarity( double p[4], double a[3] )
 694 {
 695         return
 696         (a[0] * p[0] + a[1] * p[1] + a[2] * p[2])
 697         -(p[0]*p[3] * p[0] + p[1]*p[3] * p[1] + p[2]*p[3] * p[2])
 698         ;
 699 }