src/vg/vg_m.h

   1 /* Copyright (C) 2021 Harry Godden (hgn) - All Rights Reserved */
   2
   3 #define VG_PIf  3.14159265358979323846264338327950288f
   4 #define VG_TAUf 6.28318530717958647692528676655900576f
   5
   6 static inline float vg_minf( float a, float b )
   7 {
   8         return a < b? a: b;
   9 }
  10
  11 static inline float vg_maxf( float a, float b )
  12 {
  13         return a > b? a: b;
  14 }
  15
  16 static inline float vg_clampf( float a, float min, float max )
  17 {
  18         return vg_minf( max, vg_maxf( a, min ) );
  19 }
  20
  21 static inline float vg_signf( float a )
  22 {
  23    return a < 0.0f? -1.0f: 1.0f;
  24 }
  25
  26 #define VG_MIN( A, B ) ((A)<(B)?(A):(B))
  27 #define VG_MAX( A, B ) ((A)>(B)?(A):(B))
  28
  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 static inline float vg_rad( float deg )
  40 {
  41         return deg * VG_PIf / 180.0f;
  42 }
  43
  44 /*
  45  * Vector 3
  46  */
  47 static inline void v2_copy( v2f a, v2f b )
  48 {
  49         b[0] = a[0]; b[1] = a[1];
  50 }
  51
  52 static inline void v2i_copy( v2i a, v2i b )
  53 {
  54         b[0] = a[0]; b[1] = a[1];
  55 }
  56
  57 static inline int v2i_eq( v2i a, v2i b )
  58 {
  59         return ((a[0] == b[0]) && (a[1] == b[1]));
  60 }
  61
  62 static inline void v2i_add( v2i a, v2i b, v2i d )
  63 {
  64         d[0] = a[0]+b[0]; d[1] = a[1]+b[1];
  65 }
  66
  67 static inline void v2i_sub( v2i a, v2i b, v2i d )
  68 {
  69         d[0] = a[0]-b[0]; d[1] = a[1]-b[1];
  70 }
  71
  72 static inline void v2_minv( v2f a, v2f b, v2f dest )
  73 {
  74         dest[0] = vg_minf(a[0], b[0]);
  75         dest[1] = vg_minf(a[1], b[1]);
  76 }
  77
  78 static inline void v2_maxv( v2f a, v2f b, v2f dest )
  79 {
  80         dest[0] = vg_maxf(a[0], b[0]);
  81         dest[1] = vg_maxf(a[1], b[1]);
  82 }
  83
  84 static inline void v2_sub( v2f a, v2f b, v2f d )
  85 {
  86         d[0] = a[0]-b[0]; d[1] = a[1]-b[1];
  87 }
  88
  89 static inline float v2_cross( v2f a, v2f b )
  90 {
  91         return a[0] * b[1] - a[1] * b[0];
  92 }
  93
  94 static inline void v2_add( v2f a, v2f b, v2f d )
  95 {
  96         d[0] = a[0]+b[0]; d[1] = a[1]+b[1];
  97 }
  98
  99 static inline void v2_muls( v2f a, float s, v2f d )
 100 {
 101         d[0] = a[0]*s; d[1] = a[1]*s;
 102 }
 103
 104 static inline void v2_divs( v2f a, float s, v2f d )
 105 {
 106         d[0] = a[0]/s; d[1] = a[1]/s;
 107 }
 108
 109 static inline void v2_mul( v2f a, v2f b, v2f d )
 110 {
 111         d[0] = a[0]*b[0];
 112         d[1] = a[1]*b[1];
 113 }
 114
 115 static inline void v2_div( v2f a, v2f b, v2f d )
 116 {
 117         d[0] = a[0]/b[0]; d[1] = a[1]/b[1];
 118 }
 119
 120 static inline void v2_muladd( v2f a, v2f b, v2f s, v2f d )
 121 {
 122         d[0] = a[0]+b[0]*s[0];
 123         d[1] = a[1]+b[1]*s[1];
 124 }
 125
 126 static inline void v2_muladds( v2f a, v2f b, float s, v2f d )
 127 {
 128         d[0] = a[0]+b[0]*s;
 129         d[1] = a[1]+b[1]*s;
 130 }
 131
 132 static inline float v2_length2( v2f a )
 133 {
 134         return a[0]*a[0] + a[1]*a[1];
 135 }
 136
 137 static inline float v2_length( v2f a )
 138 {
 139         return sqrtf( v2_length2( a ) );
 140 }
 141
 142 static inline float v2_dist2( v2f a, v2f b )
 143 {
 144         v2f delta;
 145         v2_sub( a, b, delta );
 146         return v2_length2( delta );
 147 }
 148
 149 static inline float v2_dist( v2f a, v2f b )
 150 {
 151         return sqrtf( v2_dist2( a, b ) );
 152 }
 153
 154 static inline void v2_lerp( v2f a, v2f b, float t, v2f d )
 155 {
 156         d[0] = a[0] + t*(b[0]-a[0]);
 157         d[1] = a[1] + t*(b[1]-a[1]);
 158 }
 159
 160 /*
 161  * Vector 3
 162  */
 163 static inline void v3_zero( v3f a )
 164 {
 165         a[0] = 0.f; a[1] = 0.f; a[2] = 0.f;
 166 }
 167
 168 static inline void v3_copy( v3f a, v3f b )
 169 {
 170         b[0] = a[0]; b[1] = a[1]; b[2] = a[2];
 171 }
 172
 173 static inline void v3_add( v3f a, v3f b, v3f d )
 174 {
 175         d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; d[2] = a[2]+b[2];
 176 }
 177
 178 static inline void v3_sub( v3f a, v3f b, v3f d )
 179 {
 180         d[0] = a[0]-b[0]; d[1] = a[1]-b[1]; d[2] = a[2]-b[2];
 181 }
 182
 183 static inline void v3_mul( v3f a, v3f b, v3f d )
 184 {
 185         d[0] = a[0]*b[0]; d[1] = a[1]*b[1]; d[2] = a[2]*b[2];
 186 }
 187
 188 static inline void v3_div( v3f a, v3f b, v3f d )
 189 {
 190         d[0] = a[0]/b[0]; d[1] = a[1]/b[1];     d[2] = a[2]/b[2];
 191 }
 192
 193 static inline void v3_muls( v3f a, float s, v3f d )
 194 {
 195         d[0] = a[0]*s; d[1] = a[1]*s; d[2] = a[2]*s;
 196 }
 197
 198 static inline void v3_divs( v3f a, float s, v3f d )
 199 {
 200         d[0] = a[0]/s; d[1] = a[1]/s; d[2] = a[2]/s;
 201 }
 202
 203 static inline void v3_muladds( v3f a, v3f b, float s, v3f d )
 204 {
 205         d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s; d[2] = a[2]+b[2]*s;
 206 }
 207
 208 static inline float v3_dot( v3f a, v3f b )
 209 {
 210         return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
 211 }
 212
 213 static inline void v3_cross( v3f a, v3f b, v3f d )
 214 {
 215   d[0] = a[1] * b[2] - a[2] * b[1];
 216   d[1] = a[2] * b[0] - a[0] * b[2];
 217   d[2] = a[0] * b[1] - a[1] * b[0];
 218 }
 219
 220 static inline float v3_length2( v3f a )
 221 {
 222         return v3_dot( a, a );
 223 }
 224
 225 static inline float v3_length( v3f a )
 226 {
 227         return sqrtf( v3_length2( a ) );
 228 }
 229
 230 static inline float v3_dist2( v3f a, v3f b )
 231 {
 232         v3f delta;
 233         v3_sub( a, b, delta );
 234         return v3_length2( delta );
 235 }
 236
 237 static inline float v3_dist( v3f a, v3f b )
 238 {
 239         return sqrtf( v3_dist2( a, b ) );
 240 }
 241
 242 static inline void v3_normalize( v3f a )
 243 {
 244         v3_muls( a, 1.f / v3_length( a ), a );
 245 }
 246
 247 static inline float vg_lerpf( float a, float b, float t )
 248 {
 249         return a + t*(b-a);
 250 }
 251
 252 static inline void v3_lerp( v3f a, v3f b, float t, v3f d )
 253 {
 254         d[0] = a[0] + t*(b[0]-a[0]);
 255         d[1] = a[1] + t*(b[1]-a[1]);
 256         d[2] = a[2] + t*(b[2]-a[2]);
 257 }
 258
 259 static inline void v3_minv( v3f a, v3f b, v3f dest )
 260 {
 261         dest[0] = vg_minf(a[0], b[0]);
 262         dest[1] = vg_minf(a[1], b[1]);
 263         dest[2] = vg_minf(a[2], b[2]);
 264 }
 265
 266 static inline void v3_maxv( v3f a, v3f b, v3f dest )
 267 {
 268         dest[0] = vg_maxf(a[0], b[0]);
 269         dest[1] = vg_maxf(a[1], b[1]);
 270         dest[2] = vg_maxf(a[2], b[2]);
 271 }
 272
 273 static inline float v3_minf( v3f a )
 274 {
 275         return vg_minf( vg_minf( a[0], a[1] ), a[2] );
 276 }
 277
 278 static inline float v3_maxf( v3f a )
 279 {
 280         return vg_maxf( vg_maxf( a[0], a[1] ), a[2] );
 281 }
 282
 283 static inline void v3_fill( v3f a, float v )
 284 {
 285         a[0] = v;
 286         a[1] = v;
 287         a[2] = v;
 288 }
 289
 290 static inline void v3_floor( v3f a, v3f b )
 291 {
 292    b[0] = floorf( a[0] );
 293    b[1] = floorf( a[1] );
 294    b[2] = floorf( a[2] );
 295 }
 296
 297 static inline void v3_negate( v3f a, v3f b )
 298 {
 299    b[0] = -a[0];
 300    b[1] = -a[1];
 301    b[2] = -a[2];
 302 }
 303
 304 /*
 305  * Vector 4
 306  */
 307 static inline void v4_copy( v4f a, v4f b )
 308 {
 309         b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; b[3] = a[3];
 310 }
 311
 312 static inline void v4_zero( v4f a )
 313 {
 314         a[0] = 0.f; a[1] = 0.f; a[2] = 0.f; a[3] = 0.f;
 315 }
 316
 317 static inline void v4_muladds( v3f a, v3f b, float s, v3f d )
 318 {
 319         d[0] = a[0]+b[0]*s;
 320    d[1] = a[1]+b[1]*s;
 321    d[2] = a[2]+b[2]*s;
 322    d[3] = a[3]+b[3]*s;
 323 }
 324
 325 /*
 326  * Matrix 2x2
 327  */
 328
 329 #define M2X2_INDENTIY   {{1.0f, 0.0f, }, \
 330                                                                 { 0.0f, 1.0f, }}
 331
 332 #define M2X2_ZERO                       {{0.0f, 0.0f, }, \
 333                                                                 { 0.0f, 0.0f, }}
 334
 335 static inline void m2x2_copy( m2x2f a, m2x2f b )
 336 {
 337         v2_copy( a[0], b[0] );
 338         v2_copy( a[1], b[1] );
 339 }
 340
 341 static inline void m2x2_identity( m2x2f a )
 342 {
 343         m2x2f id = M2X2_INDENTIY;
 344         m2x2_copy( id, a );
 345 }
 346
 347 static inline void m2x2_create_rotation( m2x2f a, float theta )
 348 {
 349         float s, c;
 350
 351         s = sinf( theta );
 352         c = cosf( theta );
 353
 354         a[0][0] =  c;
 355         a[0][1] = -s;
 356         a[1][0] =  s;
 357         a[1][1] =  c;
 358 }
 359
 360 /*
 361  * Matrix 3x3
 362  */
 363
 364 #define M3X3_IDENTITY   {{1.0f, 0.0f, 0.0f, },\
 365                                                                 { 0.0f, 1.0f, 0.0f, },\
 366                                                                 { 0.0f, 0.0f, 1.0f, }}
 367
 368 #define M3X3_ZERO                       {{0.0f, 0.0f, 0.0f, },\
 369                                                                 { 0.0f, 0.0f, 0.0f, },\
 370                                                                 { 0.0f, 0.0f, 0.0f, }}
 371
 372
 373 static inline void m3x3_copy( m3x3f a, m3x3f b )
 374 {
 375         v3_copy( a[0], b[0] );
 376         v3_copy( a[1], b[1] );
 377         v3_copy( a[2], b[2] );
 378 }
 379
 380 static inline void m3x3_identity( m3x3f a )
 381 {
 382         m3x3f id = M3X3_IDENTITY;
 383         m3x3_copy( id, a );
 384 }
 385
 386 static inline void m3x3_zero( m3x3f a )
 387 {
 388         m3x3f z = M3X3_ZERO;
 389         m3x3_copy( z, a );
 390 }
 391
 392 static inline void m3x3_inv( m3x3f src, m3x3f dest )
 393 {
 394         float a = src[0][0], b = src[0][1], c = src[0][2],
 395                         d = src[1][0], e = src[1][1], f = src[1][2],
 396                         g = src[2][0], h = src[2][1], i = src[2][2];
 397
 398         float det =    1.f /
 399                                         (+a*(e*i-h*f)
 400                 -b*(d*i-f*g)
 401                 +c*(d*h-e*g));
 402
 403         dest[0][0] =  (e*i-h*f)*det;
 404         dest[0][1] = -(b*i-c*h)*det;
 405         dest[0][2] =  (b*f-c*e)*det;
 406         dest[1][0] = -(d*i-f*g)*det;
 407         dest[1][1] =  (a*i-c*g)*det;
 408         dest[1][2] = -(a*f-d*c)*det;
 409         dest[2][0] =  (d*h-g*e)*det;
 410         dest[2][1] = -(a*h-g*b)*det;
 411         dest[2][2] =  (a*e-d*b)*det;
 412 }
 413
 414 static inline void m3x3_transpose( m3x3f src, m3x3f dest )
 415 {
 416         float a = src[0][0], b = src[0][1], c = src[0][2],
 417                         d = src[1][0], e = src[1][1], f = src[1][2],
 418                         g = src[2][0], h = src[2][1], i = src[2][2];
 419
 420         dest[0][0] = a;
 421         dest[0][1] = d;
 422         dest[0][2] = g;
 423         dest[1][0] = b;
 424         dest[1][1] = e;
 425         dest[1][2] = h;
 426         dest[2][0] = c;
 427         dest[2][1] = f;
 428         dest[2][2] = i;
 429 }
 430
 431 static inline void m3x3_mul( m3x3f a, m3x3f b, m3x3f d )
 432 {
 433         float a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
 434                         a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
 435                         a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
 436
 437                         b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
 438                         b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
 439                         b20 = b[2][0], b21 = b[2][1], b22 = b[2][2];
 440
 441         d[0][0] = a00*b00 + a10*b01 + a20*b02;
 442         d[0][1] = a01*b00 + a11*b01 + a21*b02;
 443         d[0][2] = a02*b00 + a12*b01 + a22*b02;
 444         d[1][0] = a00*b10 + a10*b11 + a20*b12;
 445         d[1][1] = a01*b10 + a11*b11 + a21*b12;
 446         d[1][2] = a02*b10 + a12*b11 + a22*b12;
 447         d[2][0] = a00*b20 + a10*b21 + a20*b22;
 448         d[2][1] = a01*b20 + a11*b21 + a21*b22;
 449         d[2][2] = a02*b20 + a12*b21 + a22*b22;
 450 }
 451
 452 static inline void m3x3_mulv( m3x3f m, v3f v, v3f d )
 453 {
 454         v3f res;
 455
 456         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
 457         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
 458         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
 459
 460         v3_copy( res, d );
 461 }
 462
 463 static inline void m3x3_projection( m3x3f dst,
 464       float const left, float const right, float const bottom, float const top )
 465 {
 466         float rl, tb;
 467
 468         m3x3_zero( dst );
 469
 470         rl = 1.0f / (right - left);
 471         tb = 1.0f / (top   - bottom);
 472
 473         dst[0][0] = 2.0f * rl;
 474         dst[1][1] = 2.0f * tb;
 475         dst[2][2] = 1.0f;
 476 }
 477
 478 static inline void m3x3_translate( m3x3f m, v3f v )
 479 {
 480         m[2][0] = m[0][0] * v[0] + m[1][0] * v[1] + m[2][0];
 481         m[2][1] = m[0][1] * v[0] + m[1][1] * v[1] + m[2][1];
 482         m[2][2] = m[0][2] * v[0] + m[1][2] * v[1] + m[2][2];
 483 }
 484
 485 static inline void m3x3_scale( m3x3f m, v3f v )
 486 {
 487         m[0][0] = m[0][0] * v[0];
 488         m[0][1] = m[0][1] * v[0];
 489         m[0][2] = m[0][2] * v[0];
 490
 491         m[1][0] = m[1][0] * v[1];
 492         m[1][1] = m[1][1] * v[1];
 493         m[1][2] = m[1][2] * v[1];
 494 }
 495
 496 static inline void m3x3_rotate( m3x3f m, float angle )
 497 {
 498         float m00 = m[0][0], m10 = m[1][0],
 499                         m01 = m[0][1], m11 = m[1][1],
 500                         m02 = m[0][2], m12 = m[1][2];
 501         float c, s;
 502
 503         s = sinf( angle );
 504         c = cosf( angle );
 505
 506         m[0][0] = m00 * c + m10 * s;
 507         m[0][1] = m01 * c + m11 * s;
 508         m[0][2] = m02 * c + m12 * s;
 509
 510         m[1][0] = m00 * -s + m10 * c;
 511         m[1][1] = m01 * -s + m11 * c;
 512         m[1][2] = m02 * -s + m12 * c;
 513 }
 514
 515 /*
 516  * Matrix 4x3
 517  */
 518
 519 #define M4X3_IDENTITY   {{1.0f, 0.0f, 0.0f, },\
 520                                                                 { 0.0f, 1.0f, 0.0f, },\
 521                                                                 { 0.0f, 0.0f, 1.0f, },\
 522                                                                 { 0.0f, 0.0f, 0.0f }}
 523
 524 static inline void m4x3_to_3x3( m4x3f a, m3x3f b )
 525 {
 526         v3_copy( a[0], b[0] );
 527         v3_copy( a[1], b[1] );
 528         v3_copy( a[2], b[2] );
 529 }
 530
 531 static inline void m4x3_copy( m4x3f a, m4x3f b )
 532 {
 533         v3_copy( a[0], b[0] );
 534         v3_copy( a[1], b[1] );
 535         v3_copy( a[2], b[2] );
 536         v3_copy( a[3], b[3] );
 537 }
 538
 539 static inline void m4x3_identity( m4x3f a )
 540 {
 541         m4x3f id = M4X3_IDENTITY;
 542         m4x3_copy( id, a );
 543 }
 544
 545 static inline void m4x3_mul( m4x3f a, m4x3f b, m4x3f d )
 546 {
 547         float
 548         a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
 549         a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
 550         a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
 551         a30 = a[3][0], a31 = a[3][1], a32 = a[3][2],
 552         b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
 553         b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
 554         b20 = b[2][0], b21 = b[2][1], b22 = b[2][2],
 555         b30 = b[3][0], b31 = b[3][1], b32 = b[3][2];
 556
 557         d[0][0] = a00*b00 + a10*b01 + a20*b02;
 558         d[0][1] = a01*b00 + a11*b01 + a21*b02;
 559         d[0][2] = a02*b00 + a12*b01 + a22*b02;
 560         d[1][0] = a00*b10 + a10*b11 + a20*b12;
 561         d[1][1] = a01*b10 + a11*b11 + a21*b12;
 562         d[1][2] = a02*b10 + a12*b11 + a22*b12;
 563         d[2][0] = a00*b20 + a10*b21 + a20*b22;
 564         d[2][1] = a01*b20 + a11*b21 + a21*b22;
 565         d[2][2] = a02*b20 + a12*b21 + a22*b22;
 566         d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30;
 567         d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31;
 568         d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32;
 569 }
 570
 571 static inline void m4x3_mulv( m4x3f m, v3f v, v3f d )
 572 {
 573         v3f res;
 574
 575         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0];
 576         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1];
 577         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2];
 578
 579         v3_copy( res, d );
 580 }
 581
 582 /*
 583  * Affine transforms
 584  */
 585
 586 static inline void m4x3_translate( m4x3f m, v3f v )
 587 {
 588         v3_muladds( m[3], m[0], v[0], m[3] );
 589         v3_muladds( m[3], m[1], v[1], m[3] );
 590         v3_muladds( m[3], m[2], v[2], m[3] );
 591 }
 592
 593 static inline void m4x3_scale( m4x3f m, float s )
 594 {
 595         v3_muls( m[0], s, m[0] );
 596         v3_muls( m[1], s, m[1] );
 597         v3_muls( m[2], s, m[2] );
 598 }
 599
 600 static inline void m4x3_rotate_x( m4x3f m, float angle )
 601 {
 602         m4x3f t = M4X3_IDENTITY;
 603         float c, s;
 604
 605         c = cosf( angle );
 606         s = sinf( angle );
 607
 608         t[1][1] =  c;
 609         t[1][2] =  s;
 610         t[2][1] = -s;
 611         t[2][2] =  c;
 612
 613         m4x3_mul( m, t, m );
 614 }
 615
 616 static inline void m4x3_rotate_y( m4x3f m, float angle )
 617 {
 618         m4x3f t = M4X3_IDENTITY;
 619         float c, s;
 620
 621         c = cosf( angle );
 622         s = sinf( angle );
 623
 624         t[0][0] =  c;
 625         t[0][2] = -s;
 626         t[2][0] =  s;
 627         t[2][2] =  c;
 628
 629         m4x3_mul( m, t, m );
 630 }
 631
 632 static inline void m4x3_rotate_z( m4x3f m, float angle )
 633 {
 634         m4x3f t = M4X3_IDENTITY;
 635         float c, s;
 636
 637         c = cosf( angle );
 638         s = sinf( angle );
 639
 640         t[0][0] =  c;
 641         t[0][1] =  s;
 642         t[1][0] = -s;
 643         t[1][1] =  c;
 644
 645         m4x3_mul( m, t, m );
 646 }
 647
 648 static inline void m4x3_expand( m4x3f m, m4x4f d )
 649 {
 650    v3_copy( m[0], d[0] );
 651    v3_copy( m[1], d[1] );
 652    v3_copy( m[2], d[2] );
 653    v3_copy( m[3], d[3] );
 654    d[0][3] = 0.0f;
 655    d[1][3] = 0.0f;
 656    d[2][3] = 0.0f;
 657    d[3][3] = 1.0f;
 658 }
 659
 660 static inline void m4x3_expand_aabb_point( m4x3f m, boxf box, v3f point )
 661 {
 662         v3f v;
 663         m4x3_mulv( m, point, v );
 664
 665         v3_minv( box[0], v, box[0] );
 666         v3_maxv( box[1], v, box[1] );
 667 }
 668
 669 static inline void box_concat( boxf a, boxf b )
 670 {
 671         v3_minv( a[0], b[0], a[0] );
 672         v3_maxv( a[1], b[1], a[1] );
 673 }
 674
 675 static inline void box_copy( boxf a, boxf b )
 676 {
 677         v3_copy( a[0], b[0] );
 678         v3_copy( a[1], b[1] );
 679 }
 680
 681 static inline void m4x3_transform_aabb( m4x3f m, boxf box )
 682 {
 683         v3f a; v3f b;
 684
 685         v3_copy( box[0], a );
 686         v3_copy( box[1], b );
 687         v3_fill( box[0],  INFINITY );
 688         v3_fill( box[1], -INFINITY );
 689
 690         m4x3_expand_aabb_point( m, box, a );
 691         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], a[2] } );
 692         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], a[2] } );
 693         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], a[2] } );
 694         m4x3_expand_aabb_point( m, box, b );
 695         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], b[2] } );
 696         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], b[2] } );
 697         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], b[2] } );
 698 }
 699
 700 /*
 701  * Matrix 4x4
 702  */
 703
 704 #define M4X4_IDENTITY   {{1.0f, 0.0f, 0.0f, 0.0f },\
 705                                                                 { 0.0f, 1.0f, 0.0f, 0.0f },\
 706                                                                 { 0.0f, 0.0f, 1.0f, 0.0f },\
 707                                                                 { 0.0f, 0.0f, 0.0f, 1.0f }}
 708
 709 static void m4x4_projection( m4x4f m, float angle,
 710       float ratio, float near, float far )
 711 {
 712    float scale = tanf( angle * 0.5f * VG_PIf / 180.0f ) * near,
 713          r = ratio * scale,
 714          l = -r,
 715          t = scale,
 716          b = -t;
 717
 718    m[0][0] =  2.0f * near / (r - l);
 719    m[0][1] =  0.0f;
 720    m[0][2] =  0.0f;
 721    m[0][3] =  0.0f;
 722    m[1][0] =  0.0f;
 723    m[1][1] =  2.0f * near / (t - b);
 724    m[1][2] =  0.0f;
 725    m[1][3] =  0.0f;
 726    m[2][0] =  (r + l) / (r - l);
 727    m[2][1] =  (t + b) / (t - b);
 728    m[2][2] = -(far + near) / (far - near);
 729    m[2][3] = -1.0f;
 730    m[3][0] =  0.0f;
 731    m[3][1] =  0.0f;
 732    m[3][2] = -2.0f * far * near / (far - near);
 733    m[3][3] =  0.0f;
 734 }
 735
 736 static void m4x4_translate( m4x4f m, v3f v )
 737 {
 738    v4_muladds( m[3], m[0], v[0], m[3] );
 739    v4_muladds( m[3], m[1], v[1], m[3] );
 740    v4_muladds( m[3], m[2], v[2], m[3] );
 741 }
 742
 743 static inline void m4x4_copy( m4x4f a, m4x4f b )
 744 {
 745         v4_copy( a[0], b[0] );
 746         v4_copy( a[1], b[1] );
 747         v4_copy( a[2], b[2] );
 748         v4_copy( a[3], b[3] );
 749 }
 750
 751 static inline void m4x4_identity( m4x4f a )
 752 {
 753         m4x4f id = M4X4_IDENTITY;
 754         m4x4_copy( id, a );
 755 }
 756
 757 static inline void m4x4_mul( m4x4f a, m4x4f b, m4x4f d )
 758 {
 759    float a00 = a[0][0], a01 = a[0][1], a02 = a[0][2], a03 = a[0][3],
 760          a10 = a[1][0], a11 = a[1][1], a12 = a[1][2], a13 = a[1][3],
 761          a20 = a[2][0], a21 = a[2][1], a22 = a[2][2], a23 = a[2][3],
 762          a30 = a[3][0], a31 = a[3][1], a32 = a[3][2], a33 = a[3][3],
 763
 764          b00 = b[0][0], b01 = b[0][1], b02 = b[0][2], b03 = b[0][3],
 765          b10 = b[1][0], b11 = b[1][1], b12 = b[1][2], b13 = b[1][3],
 766          b20 = b[2][0], b21 = b[2][1], b22 = b[2][2], b23 = b[2][3],
 767          b30 = b[3][0], b31 = b[3][1], b32 = b[3][2], b33 = b[3][3];
 768
 769   d[0][0] = a00*b00 + a10*b01 + a20*b02 + a30*b03;
 770   d[0][1] = a01*b00 + a11*b01 + a21*b02 + a31*b03;
 771   d[0][2] = a02*b00 + a12*b01 + a22*b02 + a32*b03;
 772   d[0][3] = a03*b00 + a13*b01 + a23*b02 + a33*b03;
 773   d[1][0] = a00*b10 + a10*b11 + a20*b12 + a30*b13;
 774   d[1][1] = a01*b10 + a11*b11 + a21*b12 + a31*b13;
 775   d[1][2] = a02*b10 + a12*b11 + a22*b12 + a32*b13;
 776   d[1][3] = a03*b10 + a13*b11 + a23*b12 + a33*b13;
 777   d[2][0] = a00*b20 + a10*b21 + a20*b22 + a30*b23;
 778   d[2][1] = a01*b20 + a11*b21 + a21*b22 + a31*b23;
 779   d[2][2] = a02*b20 + a12*b21 + a22*b22 + a32*b23;
 780   d[2][3] = a03*b20 + a13*b21 + a23*b22 + a33*b23;
 781   d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30*b33;
 782   d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31*b33;
 783   d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32*b33;
 784   d[3][3] = a03*b30 + a13*b31 + a23*b32 + a33*b33;
 785 }
 786
 787 /*
 788  * Planes (double precision)
 789  */
 790 static inline void tri_to_plane( double a[3], double b[3],
 791       double c[3], double p[4] )
 792 {
 793         double edge0[3];
 794         double edge1[3];
 795         double l;
 796
 797         edge0[0] = b[0] - a[0];
 798         edge0[1] = b[1] - a[1];
 799         edge0[2] = b[2] - a[2];
 800
 801         edge1[0] = c[0] - a[0];
 802         edge1[1] = c[1] - a[1];
 803         edge1[2] = c[2] - a[2];
 804
 805         p[0] = edge0[1] * edge1[2] - edge0[2] * edge1[1];
 806         p[1] = edge0[2] * edge1[0] - edge0[0] * edge1[2];
 807         p[2] = edge0[0] * edge1[1] - edge0[1] * edge1[0];
 808
 809         l = sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2]);
 810         p[3] = (p[0] * a[0] + p[1] * a[1] + p[2] * a[2]) / l;
 811
 812         p[0] = p[0] / l;
 813         p[1] = p[1] / l;
 814         p[2] = p[2] / l;
 815 }
 816
 817 static inline int plane_intersect( double a[4], double b[4],
 818       double c[4], double p[4] )
 819 {
 820         double const epsilon = 1e-8f;
 821
 822         double x[3];
 823         double d;
 824
 825         x[0] = a[1] * b[2] - a[2] * b[1];
 826         x[1] = a[2] * b[0] - a[0] * b[2];
 827         x[2] = a[0] * b[1] - a[1] * b[0];
 828
 829         d = x[0] * c[0] + x[1] * c[1] + x[2] * c[2];
 830
 831         if( d < epsilon && d > -epsilon ) return 0;
 832
 833         p[0] = (b[1] * c[2] - b[2] * c[1]) * -a[3];
 834         p[1] = (b[2] * c[0] - b[0] * c[2]) * -a[3];
 835         p[2] = (b[0] * c[1] - b[1] * c[0]) * -a[3];
 836
 837         p[0] += (c[1] * a[2] - c[2] * a[1]) * -b[3];
 838         p[1] += (c[2] * a[0] - c[0] * a[2]) * -b[3];
 839         p[2] += (c[0] * a[1] - c[1] * a[0]) * -b[3];
 840
 841         p[0] += (a[1] * b[2] - a[2] * b[1]) * -c[3];
 842         p[1] += (a[2] * b[0] - a[0] * b[2]) * -c[3];
 843         p[2] += (a[0] * b[1] - a[1] * b[0]) * -c[3];
 844
 845         p[0] = -p[0] / d;
 846         p[1] = -p[1] / d;
 847         p[2] = -p[2] / d;
 848
 849         return 1;
 850 }
 851
 852 static inline double plane_polarity( double p[4], double a[3] )
 853 {
 854         return
 855         (a[0] * p[0] + a[1] * p[1] + a[2] * p[2])
 856         -(p[0]*p[3] * p[0] + p[1]*p[3] * p[1] + p[2]*p[3] * p[2])
 857         ;
 858 }