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 int vg_min( int a, int b )
  21 {
  22         return a < b? a: b;
  23 }
  24
  25 static inline int vg_max( int a, int b )
  26 {
  27         return a > b? a: b;
  28 }
  29
  30 // Convert degrees to radians
  31 static inline float vg_rad( float deg )
  32 {
  33         return deg * VG_PIf / 180.0f;
  34 }
  35
  36 // Vector 2
  37 // ==================================================================================================================
  38
  39 static inline void v2_copy( v2f a, v2f b )
  40 {
  41         b[0] = a[0]; b[1] = a[1];
  42 }
  43
  44 static inline void v2_minv( v2f a, v2f b, v2f dest )
  45 {
  46         dest[0] = vg_minf(a[0], b[0]);
  47         dest[1] = vg_minf(a[1], b[1]);
  48 }
  49
  50 static inline void v2_maxv( v2f a, v2f b, v2f dest )
  51 {
  52         dest[0] = vg_maxf(a[0], b[0]);
  53         dest[1] = vg_maxf(a[1], b[1]);
  54 }
  55
  56 static inline void v2_sub( v2f a, v2f b, v2f d )
  57 {
  58         d[0] = a[0]-b[0]; d[1] = a[1]-b[1];
  59 }
  60
  61 static inline float v2_cross( v2f a, v2f b )
  62 {
  63         return a[0] * b[1] - a[1] * b[0];
  64 }
  65
  66 static inline void v2_add( v2f a, v2f b, v2f d )
  67 {
  68         d[0] = a[0]+b[0]; d[1] = a[1]+b[1];
  69 }
  70
  71 static inline void v2_muls( v2f a, float s, v2f d )
  72 {
  73         d[0] = a[0]*s; d[1] = a[1]*s;
  74 }
  75
  76 static inline void v2_mul( v2f a, v2f b, v2f d )
  77 {
  78         d[0] = a[0]*b[0]; d[1] = a[1]*b[1];
  79 }
  80
  81 static inline void v2_div( v2f a, v2f b, v2f d )
  82 {
  83         d[0] = a[0]/b[0]; d[1] = a[1]/b[1];
  84 }
  85
  86 // Vector 3
  87 // ==================================================================================================================
  88
  89 static inline void v3_zero( v3f a )
  90 {
  91         a[0] = 0.f; a[1] = 0.f; a[2] = 0.f;
  92 }
  93
  94 static inline void v3_copy( v3f a, v3f b )
  95 {
  96         b[0] = a[0]; b[1] = a[1]; b[2] = a[2];
  97 }
  98
  99 static inline void v3_add( v3f a, v3f b, v3f d )
 100 {
 101         d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; d[2] = a[2]+b[2];
 102 }
 103
 104 static inline void v3_sub( v3f a, v3f b, v3f d )
 105 {
 106         d[0] = a[0]-b[0]; d[1] = a[1]-b[1]; d[2] = a[2]-b[2];
 107 }
 108
 109 static inline void v3_mul( v3f a, v3f b, v3f d )
 110 {
 111         d[0] = a[0]*b[0]; d[1] = a[1]*b[1]; d[2] = a[2]*b[2];
 112 }
 113
 114 static inline void v3_div( v3f a, v3f b, v3f d )
 115 {
 116         d[0] = a[0]/b[0]; d[1] = a[1]/b[1];     d[2] = a[2]/b[2];
 117 }
 118
 119 static inline void v3_muls( v3f a, float s, v3f d )
 120 {
 121         d[0] = a[0]*s; d[1] = a[1]*s; d[2] = a[2]*s;
 122 }
 123
 124 static inline void v3_divs( v3f a, float s, v3f d )
 125 {
 126         d[0] = a[0]/s; d[1] = a[1]/s; d[2] = a[2]/s;
 127 }
 128
 129 static inline void v3_muladds( v3f a, v3f b, float s, v3f d )
 130 {
 131         d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s; d[2] = a[2]+b[2]*s;
 132 }
 133
 134 static inline float v3_dot( v3f a, v3f b )
 135 {
 136         return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
 137 }
 138
 139 static inline void v3_cross( v3f a, v3f b, v3f d )
 140 {
 141   d[0] = a[1] * b[2] - a[2] * b[1];
 142   d[1] = a[2] * b[0] - a[0] * b[2];
 143   d[2] = a[0] * b[1] - a[1] * b[0];
 144 }
 145
 146 static inline float v3_length2( v3f a )
 147 {
 148         return v3_dot( a, a );
 149 }
 150
 151 static inline float v3_length( v3f a )
 152 {
 153         return sqrtf( v3_length2( a ) );
 154 }
 155
 156 static inline float v3_dist2( v3f a, v3f b )
 157 {
 158         v3f delta;
 159         v3_sub( a, b, delta );
 160         return v3_length2( delta );
 161 }
 162
 163 static inline float v3_dist( v3f a, v3f b )
 164 {
 165         return sqrtf( v3_dist2( a, b ) );
 166 }
 167
 168 static inline void v3_normalize( v3f a )
 169 {
 170         v3_muls( a, 1.f / v3_length( a ), a );
 171 }
 172
 173 static inline float csr_lerpf( float a, float b, float t )
 174 {
 175         return a + t*(b-a);
 176 }
 177
 178 static inline void v3_lerp( v3f a, v3f b, float t, v3f d )
 179 {
 180         d[0] = a[0] + t*(b[0]-a[0]);
 181         d[1] = a[1] + t*(b[1]-a[1]);
 182         d[2] = a[2] + t*(b[2]-a[2]);
 183 }
 184
 185 static inline void v3_minv( v3f a, v3f b, v3f dest )
 186 {
 187         dest[0] = vg_minf(a[0], b[0]);
 188         dest[1] = vg_minf(a[1], b[1]);
 189         dest[2] = vg_minf(a[2], b[2]);
 190 }
 191
 192 static inline void v3_maxv( v3f a, v3f b, v3f dest )
 193 {
 194         dest[0] = vg_maxf(a[0], b[0]);
 195         dest[1] = vg_maxf(a[1], b[1]);
 196         dest[2] = vg_maxf(a[2], b[2]);
 197 }
 198
 199 static inline float v3_minf( v3f a )
 200 {
 201         return vg_minf( vg_minf( a[0], a[1] ), a[2] );
 202 }
 203
 204 static inline float v3_maxf( v3f a )
 205 {
 206         return vg_maxf( vg_maxf( a[0], a[1] ), a[2] );
 207 }
 208
 209 static inline void v3_fill( v3f a, float v )
 210 {
 211         a[0] = v;
 212         a[1] = v;
 213         a[2] = v;
 214 }
 215
 216 // Vector 4
 217 // ==================================================================================================================
 218
 219 static inline void v4_copy( v4f a, v4f b )
 220 {
 221         b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; b[3] = a[3];
 222 }
 223
 224 static inline void v4_zero( v4f a )
 225 {
 226         a[0] = 0.f; a[1] = 0.f; a[2] = 0.f; a[3] = 0.f;
 227 }
 228
 229 // Matrix 3x3
 230 //======================================================================================================
 231
 232 #define M3X3_IDENTITY   {{1.0f, 0.0f, 0.0f, },\
 233                                                                 { 0.0f, 1.0f, 0.0f, },\
 234                                                                 { 0.0f, 0.0f, 1.0f, }}
 235
 236 #define M3X3_ZERO                       {{0.0f, 0.0f, 0.0f, },\
 237                                                                 { 0.0f, 0.0f, 0.0f, },\
 238                                                                 { 0.0f, 0.0f, 0.0f, }}
 239
 240
 241 static inline void m3x3_copy( m3x3f a, m3x3f b )
 242 {
 243         v3_copy( a[0], b[0] );
 244         v3_copy( a[1], b[1] );
 245         v3_copy( a[2], b[2] );
 246 }
 247
 248 static inline void m3x3_identity( m3x3f a )
 249 {
 250         m3x3f id = M3X3_IDENTITY;
 251         m3x3_copy( id, a );
 252 }
 253
 254 static inline void m3x3_zero( m3x3f a )
 255 {
 256         m3x3f z = M3X3_ZERO;
 257         m3x3_copy( z, a );
 258 }
 259
 260 static inline void m3x3_inv( m3x3f src, m3x3f dest )
 261 {
 262         float a = src[0][0], b = src[0][1], c = src[0][2],
 263                         d = src[1][0], e = src[1][1], f = src[1][2],
 264                         g = src[2][0], h = src[2][1], i = src[2][2];
 265
 266         float det =    1.f /
 267                                         (+a*(e*i-h*f)
 268                 -b*(d*i-f*g)
 269                 +c*(d*h-e*g));
 270
 271         dest[0][0] =  (e*i-h*f)*det;
 272         dest[0][1] = -(b*i-c*h)*det;
 273         dest[0][2] =  (b*f-c*e)*det;
 274         dest[1][0] = -(d*i-f*g)*det;
 275         dest[1][1] =  (a*i-c*g)*det;
 276         dest[1][2] = -(a*f-d*c)*det;
 277         dest[2][0] =  (d*h-g*e)*det;
 278         dest[2][1] = -(a*h-g*b)*det;
 279         dest[2][2] =  (a*e-d*b)*det;
 280 }
 281
 282 static inline void m3x3_transpose( m3x3f src, m3x3f dest )
 283 {
 284         float a = src[0][0], b = src[0][1], c = src[0][2],
 285                         d = src[1][0], e = src[1][1], f = src[1][2],
 286                         g = src[2][0], h = src[2][1], i = src[2][2];
 287
 288         dest[0][0] = a;
 289         dest[0][1] = d;
 290         dest[0][2] = g;
 291         dest[1][0] = b;
 292         dest[1][1] = e;
 293         dest[1][2] = h;
 294         dest[2][0] = c;
 295         dest[2][1] = f;
 296         dest[2][2] = i;
 297 }
 298
 299 static inline void m3x3_mul( m3x3f a, m3x3f b, m3x3f d )
 300 {
 301         float a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
 302                         a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
 303                         a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
 304
 305                         b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
 306                         b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
 307                         b20 = b[2][0], b21 = b[2][1], b22 = b[2][2];
 308
 309         d[0][0] = a00*b00 + a10*b01 + a20*b02;
 310         d[0][1] = a01*b00 + a11*b01 + a21*b02;
 311         d[0][2] = a02*b00 + a12*b01 + a22*b02;
 312         d[1][0] = a00*b10 + a10*b11 + a20*b12;
 313         d[1][1] = a01*b10 + a11*b11 + a21*b12;
 314         d[1][2] = a02*b10 + a12*b11 + a22*b12;
 315         d[2][0] = a00*b20 + a10*b21 + a20*b22;
 316         d[2][1] = a01*b20 + a11*b21 + a21*b22;
 317         d[2][2] = a02*b20 + a12*b21 + a22*b22;
 318 }
 319
 320 static inline void m3x3_mulv( m3x3f m, v3f v, v3f d )
 321 {
 322         v3f res;
 323
 324         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
 325         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
 326         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
 327
 328         v3_copy( res, d );
 329 }
 330
 331 static inline void m3x3_projection( m3x3f dst, float const left, float const right, float const bottom, float const top )
 332 {
 333         float rl, tb;
 334
 335         m3x3_zero( dst );
 336
 337         rl = 1.0f / (right - left);
 338         tb = 1.0f / (top   - bottom);
 339
 340         dst[0][0] = 2.0f * rl;
 341         dst[1][1] = 2.0f * tb;
 342         dst[2][2] = 1.0f;
 343 }
 344
 345 static inline void m3x3_translate( m3x3f m, v3f v )
 346 {
 347         m[2][0] = m[0][0] * v[0] + m[1][0] * v[1] + m[2][0];
 348         m[2][1] = m[0][1] * v[0] + m[1][1] * v[1] + m[2][1];
 349         m[2][2] = m[0][2] * v[0] + m[1][2] * v[1] + m[2][2];
 350 }
 351
 352 static inline void m3x3_scale( m3x3f m, v3f v )
 353 {
 354         m[0][0] = m[0][0] * v[0];
 355         m[0][1] = m[0][1] * v[0];
 356         m[0][2] = m[0][2] * v[0];
 357
 358         m[1][0] = m[1][0] * v[1];
 359         m[1][1] = m[1][1] * v[1];
 360         m[1][2] = m[1][2] * v[1];
 361 }
 362
 363 static inline void m3x3_rotate( m3x3f m, float angle )
 364 {
 365         float m00 = m[0][0], m10 = m[1][0],
 366                         m01 = m[0][1], m11 = m[1][1],
 367                         m02 = m[0][2], m12 = m[1][2];
 368         float c, s;
 369
 370         s = sinf( angle );
 371         c = cosf( angle );
 372
 373         m[0][0] = m00 * c + m10 * s;
 374         m[0][1] = m01 * c + m11 * s;
 375         m[0][2] = m02 * c + m12 * s;
 376
 377         m[1][0] = m00 * -s + m10 * c;
 378         m[1][1] = m01 * -s + m11 * c;
 379         m[1][2] = m02 * -s + m12 * c;
 380 }
 381
 382 // Matrix 4x3
 383 // ==================================================================================================================
 384
 385 #define M4X3_IDENTITY   {{1.0f, 0.0f, 0.0f, },\
 386                                                                 { 0.0f, 1.0f, 0.0f, },\
 387                                                                 { 0.0f, 0.0f, 1.0f, },\
 388                                                                 { 0.0f, 0.0f, 0.0f }}
 389
 390 static inline void m4x3_to_3x3( m4x3f a, m3x3f b )
 391 {
 392         v3_copy( a[0], b[0] );
 393         v3_copy( a[1], b[1] );
 394         v3_copy( a[2], b[2] );
 395 }
 396
 397 static inline void m4x3_copy( m4x3f a, m4x3f b )
 398 {
 399         v3_copy( a[0], b[0] );
 400         v3_copy( a[1], b[1] );
 401         v3_copy( a[2], b[2] );
 402         v3_copy( a[3], b[3] );
 403 }
 404
 405 static inline void m4x3_identity( m4x3f a )
 406 {
 407         m4x3f id = M4X3_IDENTITY;
 408         m4x3_copy( id, a );
 409 }
 410
 411 static inline void m4x3_mul( m4x3f a, m4x3f b, m4x3f d )
 412 {
 413         float
 414         a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
 415         a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
 416         a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
 417         a30 = a[3][0], a31 = a[3][1], a32 = a[3][2],
 418         b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
 419         b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
 420         b20 = b[2][0], b21 = b[2][1], b22 = b[2][2],
 421         b30 = b[3][0], b31 = b[3][1], b32 = b[3][2];
 422
 423         d[0][0] = a00*b00 + a10*b01 + a20*b02;
 424         d[0][1] = a01*b00 + a11*b01 + a21*b02;
 425         d[0][2] = a02*b00 + a12*b01 + a22*b02;
 426         d[1][0] = a00*b10 + a10*b11 + a20*b12;
 427         d[1][1] = a01*b10 + a11*b11 + a21*b12;
 428         d[1][2] = a02*b10 + a12*b11 + a22*b12;
 429         d[2][0] = a00*b20 + a10*b21 + a20*b22;
 430         d[2][1] = a01*b20 + a11*b21 + a21*b22;
 431         d[2][2] = a02*b20 + a12*b21 + a22*b22;
 432         d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30;
 433         d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31;
 434         d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32;
 435 }
 436
 437 static inline void m4x3_mulv( m4x3f m, v3f v, v3f d )
 438 {
 439         v3f res;
 440
 441         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0];
 442         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1];
 443         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2];
 444
 445         v3_copy( res, d );
 446 }
 447
 448 // Affine transforms
 449 // ====================================================================================================================
 450
 451 static inline void m4x3_translate( m4x3f m, v3f v )
 452 {
 453         v3_muladds( m[3], m[0], v[0], m[3] );
 454         v3_muladds( m[3], m[1], v[1], m[3] );
 455         v3_muladds( m[3], m[2], v[2], m[3] );
 456 }
 457
 458 static inline void m4x3_scale( m4x3f m, float s )
 459 {
 460         v3_muls( m[0], s, m[0] );
 461         v3_muls( m[1], s, m[1] );
 462         v3_muls( m[2], s, m[2] );
 463 }
 464
 465 static inline void m4x3_rotate_x( m4x3f m, float angle )
 466 {
 467         m4x3f t = M4X3_IDENTITY;
 468         float c, s;
 469
 470         c = cosf( angle );
 471         s = sinf( angle );
 472
 473         t[1][1] =  c;
 474         t[1][2] =  s;
 475         t[2][1] = -s;
 476         t[2][2] =  c;
 477
 478         m4x3_mul( m, t, m );
 479 }
 480
 481 static inline void m4x3_rotate_y( m4x3f m, float angle )
 482 {
 483         m4x3f t = M4X3_IDENTITY;
 484         float c, s;
 485
 486         c = cosf( angle );
 487         s = sinf( angle );
 488
 489         t[0][0] =  c;
 490         t[0][2] = -s;
 491         t[2][0] =  s;
 492         t[2][2] =  c;
 493
 494         m4x3_mul( m, t, m );
 495 }
 496
 497 static inline void m4x3_rotate_z( m4x3f m, float angle )
 498 {
 499         m4x3f t = M4X3_IDENTITY;
 500         float c, s;
 501
 502         c = cosf( angle );
 503         s = sinf( angle );
 504
 505         t[0][0] =  c;
 506         t[0][1] =  s;
 507         t[1][0] = -s;
 508         t[1][1] =  c;
 509
 510         m4x3_mul( m, t, m );
 511 }
 512
 513 // Warning: These functions are unoptimized..
 514 static inline void m4x3_expand_aabb_point( m4x3f m, boxf box, v3f point )
 515 {
 516         v3f v;
 517         m4x3_mulv( m, point, v );
 518
 519         v3_minv( box[0], v, box[0] );
 520         v3_maxv( box[1], v, box[1] );
 521 }
 522
 523 static inline void box_concat( boxf a, boxf b )
 524 {
 525         v3_minv( a[0], b[0], a[0] );
 526         v3_maxv( a[1], b[1], a[1] );
 527 }
 528
 529 static inline void box_copy( boxf a, boxf b )
 530 {
 531         v3_copy( a[0], b[0] );
 532         v3_copy( a[1], b[1] );
 533 }
 534
 535 static inline void m4x3_transform_aabb( m4x3f m, boxf box )
 536 {
 537         v3f a; v3f b;
 538
 539         v3_copy( box[0], a );
 540         v3_copy( box[1], b );
 541         v3_fill( box[0],  INFINITY );
 542         v3_fill( box[1], -INFINITY );
 543
 544         m4x3_expand_aabb_point( m, box, a );
 545         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], a[2] } );
 546         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], a[2] } );
 547         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], a[2] } );
 548         m4x3_expand_aabb_point( m, box, b );
 549         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], b[2] } );
 550         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], b[2] } );
 551         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], b[2] } );
 552 }
 553
 554 // Planes (double precision)
 555 // ==================================================================================================================
 556
 557 static inline void tri_to_plane( double a[3], double b[3], double c[3], double p[4] )
 558 {
 559         double edge0[3];
 560         double edge1[3];
 561         double l;
 562
 563         edge0[0] = b[0] - a[0];
 564         edge0[1] = b[1] - a[1];
 565         edge0[2] = b[2] - a[2];
 566
 567         edge1[0] = c[0] - a[0];
 568         edge1[1] = c[1] - a[1];
 569         edge1[2] = c[2] - a[2];
 570
 571         p[0] = edge0[1] * edge1[2] - edge0[2] * edge1[1];
 572         p[1] = edge0[2] * edge1[0] - edge0[0] * edge1[2];
 573         p[2] = edge0[0] * edge1[1] - edge0[1] * edge1[0];
 574
 575         l = sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2]);
 576         p[3] = (p[0] * a[0] + p[1] * a[1] + p[2] * a[2]) / l;
 577
 578         p[0] = p[0] / l;
 579         p[1] = p[1] / l;
 580         p[2] = p[2] / l;
 581 }
 582
 583 static inline int plane_intersect( double a[4], double b[4], double c[4], double p[4] )
 584 {
 585         double const epsilon = 1e-8f;
 586
 587         double x[3];
 588         double d;
 589
 590         x[0] = a[1] * b[2] - a[2] * b[1];
 591         x[1] = a[2] * b[0] - a[0] * b[2];
 592         x[2] = a[0] * b[1] - a[1] * b[0];
 593
 594         d = x[0] * c[0] + x[1] * c[1] + x[2] * c[2];
 595
 596         if( d < epsilon && d > -epsilon ) return 0;
 597
 598         p[0] = (b[1] * c[2] - b[2] * c[1]) * -a[3];
 599         p[1] = (b[2] * c[0] - b[0] * c[2]) * -a[3];
 600         p[2] = (b[0] * c[1] - b[1] * c[0]) * -a[3];
 601
 602         p[0] += (c[1] * a[2] - c[2] * a[1]) * -b[3];
 603         p[1] += (c[2] * a[0] - c[0] * a[2]) * -b[3];
 604         p[2] += (c[0] * a[1] - c[1] * a[0]) * -b[3];
 605
 606         p[0] += (a[1] * b[2] - a[2] * b[1]) * -c[3];
 607         p[1] += (a[2] * b[0] - a[0] * b[2]) * -c[3];
 608         p[2] += (a[0] * b[1] - a[1] * b[0]) * -c[3];
 609
 610         p[0] = -p[0] / d;
 611         p[1] = -p[1] / d;
 612         p[2] = -p[2] / d;
 613
 614         return 1;
 615 }
 616
 617 static inline double plane_polarity( double p[4], double a[3] )
 618 {
 619         return
 620         (a[0] * p[0] + a[1] * p[1] + a[2] * p[2])
 621         -(p[0]*p[3] * p[0] + p[1]*p[3] * p[1] + p[2]*p[3] * p[2])
 622         ;
 623 }