src/cxr_math.h

   1 // Copyright (C) 2021 Harry Godden (hgn)
   2
   3 #define CXR_INLINE static inline
   4 #define CXR_PIf 3.14159265358979323846264338327950288f
   5
   6 // Simple min/max replacements
   7 CXR_INLINE double cxr_minf( double a, double b )
   8 {
   9         return a < b? a: b;
  10 }
  11
  12 CXR_INLINE double cxr_maxf( double a, double b )
  13 {
  14         return a > b? a: b;
  15 }
  16
  17 CXR_INLINE int cxr_min( int a, int b )
  18 {
  19         return a < b? a: b;
  20 }
  21
  22 CXR_INLINE int cxr_max( int a, int b )
  23 {
  24         return a > b? a: b;
  25 }
  26
  27 // Convert degrees to radians
  28 CXR_INLINE double cxr_rad( double deg )
  29 {
  30         return deg * CXR_PIf / 180.0f;
  31 }
  32
  33 // Vector 2
  34 // ==================================================================================================================
  35
  36 CXR_INLINE void v2_zero( v2f a )
  37 {
  38    a[0] = 0.0; a[1] = 0.0;
  39 }
  40
  41 CXR_INLINE void v2_fill( v2f a, double v )
  42 {
  43    a[0] = v; a[1] = v;
  44 }
  45
  46 CXR_INLINE void v2_copy( v2f a, v2f b )
  47 {
  48         b[0] = a[0]; b[1] = a[1];
  49 }
  50
  51 CXR_INLINE void v2_minv( v2f a, v2f b, v2f dest )
  52 {
  53         dest[0] = cxr_minf(a[0], b[0]);
  54         dest[1] = cxr_minf(a[1], b[1]);
  55 }
  56
  57 CXR_INLINE void v2_maxv( v2f a, v2f b, v2f dest )
  58 {
  59         dest[0] = cxr_maxf(a[0], b[0]);
  60         dest[1] = cxr_maxf(a[1], b[1]);
  61 }
  62
  63 CXR_INLINE void v2_sub( v2f a, v2f b, v2f d )
  64 {
  65         d[0] = a[0]-b[0]; d[1] = a[1]-b[1];
  66 }
  67
  68 CXR_INLINE double v2_cross( v2f a, v2f b )
  69 {
  70         return a[0] * b[1] - a[1] * b[0];
  71 }
  72
  73 CXR_INLINE void v2_add( v2f a, v2f b, v2f d )
  74 {
  75         d[0] = a[0]+b[0]; d[1] = a[1]+b[1];
  76 }
  77
  78 CXR_INLINE void v2_muls( v2f a, double s, v2f d )
  79 {
  80         d[0] = a[0]*s; d[1] = a[1]*s;
  81 }
  82
  83 CXR_INLINE void v2_mul( v2f a, v2f b, v2f d )
  84 {
  85         d[0] = a[0]*b[0]; d[1] = a[1]*b[1];
  86 }
  87
  88 CXR_INLINE void v2_muladds( v2f a, v2f b, double s, v2f d )
  89 {
  90         d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s;
  91 }
  92
  93 CXR_INLINE double v2_dot( v2f a, v2f b )
  94 {
  95         return a[0] * b[0] + a[1] * b[1];
  96 }
  97
  98 CXR_INLINE void v2_div( v2f a, v2f b, v2f d )
  99 {
 100         d[0] = a[0]/b[0]; d[1] = a[1]/b[1];
 101 }
 102
 103 CXR_INLINE double v2_length2( v2f a )
 104 {
 105         return v2_dot( a, a );
 106 }
 107
 108 CXR_INLINE double v2_length( v2f a )
 109 {
 110         return sqrt( v2_length2( a ) );
 111 }
 112
 113 CXR_INLINE double v2_dist2( v2f a, v2f b )
 114 {
 115         v2f delta;
 116         v2_sub( a, b, delta );
 117         return v2_length2( delta );
 118 }
 119
 120 CXR_INLINE double v2_dist( v2f a, v2f b )
 121 {
 122         return sqrt( v2_dist2( a, b ) );
 123 }
 124
 125 CXR_INLINE void v2_normalize( v2f a )
 126 {
 127         v2_muls( a, 1.0 / v2_length( a ), a );
 128 }
 129
 130 // Vector 3
 131 // ==================================================================================================================
 132
 133 CXR_INLINE void v3_zero( v3f a )
 134 {
 135         a[0] = 0.f; a[1] = 0.f; a[2] = 0.f;
 136 }
 137
 138 CXR_INLINE void v3_copy( v3f a, v3f b )
 139 {
 140         b[0] = a[0]; b[1] = a[1]; b[2] = a[2];
 141 }
 142
 143 CXR_INLINE void v3_add( v3f a, v3f b, v3f d )
 144 {
 145         d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; d[2] = a[2]+b[2];
 146 }
 147
 148 CXR_INLINE void v3_sub( v3f a, v3f b, v3f d )
 149 {
 150         d[0] = a[0]-b[0]; d[1] = a[1]-b[1]; d[2] = a[2]-b[2];
 151 }
 152
 153 CXR_INLINE void v3_mul( v3f a, v3f b, v3f d )
 154 {
 155         d[0] = a[0]*b[0]; d[1] = a[1]*b[1]; d[2] = a[2]*b[2];
 156 }
 157
 158 CXR_INLINE void v3_div( v3f a, v3f b, v3f d )
 159 {
 160         d[0] = a[0]/b[0]; d[1] = a[1]/b[1];     d[2] = a[2]/b[2];
 161 }
 162
 163 CXR_INLINE void v3_muls( v3f a, double s, v3f d )
 164 {
 165         d[0] = a[0]*s; d[1] = a[1]*s; d[2] = a[2]*s;
 166 }
 167
 168 CXR_INLINE void v3_divs( v3f a, double s, v3f d )
 169 {
 170         d[0] = a[0]/s; d[1] = a[1]/s; d[2] = a[2]/s;
 171 }
 172
 173 CXR_INLINE void v3_muladds( v3f a, v3f b, double s, v3f d )
 174 {
 175         d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s; d[2] = a[2]+b[2]*s;
 176 }
 177
 178 CXR_INLINE double v3_dot( v3f a, v3f b )
 179 {
 180         return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
 181 }
 182
 183 CXR_INLINE void v3_cross( v3f a, v3f b, v3f d )
 184 {
 185   d[0] = a[1] * b[2] - a[2] * b[1];
 186   d[1] = a[2] * b[0] - a[0] * b[2];
 187   d[2] = a[0] * b[1] - a[1] * b[0];
 188 }
 189
 190 CXR_INLINE double v3_length2( v3f a )
 191 {
 192         return v3_dot( a, a );
 193 }
 194
 195 CXR_INLINE double v3_length( v3f a )
 196 {
 197         return sqrt( v3_length2( a ) );
 198 }
 199
 200 CXR_INLINE double v3_dist2( v3f a, v3f b )
 201 {
 202         v3f delta;
 203         v3_sub( a, b, delta );
 204         return v3_length2( delta );
 205 }
 206
 207 CXR_INLINE double v3_dist( v3f a, v3f b )
 208 {
 209         return sqrt( v3_dist2( a, b ) );
 210 }
 211
 212 CXR_INLINE void v3_normalize( v3f a )
 213 {
 214         v3_muls( a, 1.0 / v3_length( a ), a );
 215 }
 216
 217 CXR_INLINE void v3_negate( v3f a, v3f dest )
 218 {
 219    v3_muls( a, -1.0, dest );
 220 }
 221
 222 CXR_INLINE double cxr_lerpf( double a, double b, double t )
 223 {
 224         return a + t*(b-a);
 225 }
 226
 227 CXR_INLINE void v3_lerp( v3f a, v3f b, double t, v3f d )
 228 {
 229         d[0] = a[0] + t*(b[0]-a[0]);
 230         d[1] = a[1] + t*(b[1]-a[1]);
 231         d[2] = a[2] + t*(b[2]-a[2]);
 232 }
 233
 234 CXR_INLINE void v3_minv( v3f a, v3f b, v3f dest )
 235 {
 236         dest[0] = cxr_minf(a[0], b[0]);
 237         dest[1] = cxr_minf(a[1], b[1]);
 238         dest[2] = cxr_minf(a[2], b[2]);
 239 }
 240
 241 CXR_INLINE void v3_maxv( v3f a, v3f b, v3f dest )
 242 {
 243         dest[0] = cxr_maxf(a[0], b[0]);
 244         dest[1] = cxr_maxf(a[1], b[1]);
 245         dest[2] = cxr_maxf(a[2], b[2]);
 246 }
 247
 248 CXR_INLINE double v3_minf( v3f a )
 249 {
 250         return cxr_minf( cxr_minf( a[0], a[1] ), a[2] );
 251 }
 252
 253 CXR_INLINE double v3_maxf( v3f a )
 254 {
 255         return cxr_maxf( cxr_maxf( a[0], a[1] ), a[2] );
 256 }
 257
 258 CXR_INLINE void v3_fill( v3f a, double v )
 259 {
 260         a[0] = v;
 261         a[1] = v;
 262         a[2] = v;
 263 }
 264
 265 // Vector 4
 266 // ==================================================================================================================
 267
 268 CXR_INLINE void v4_copy( v4f a, v4f b )
 269 {
 270         b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; b[3] = a[3];
 271 }
 272
 273 CXR_INLINE void v4_zero( v4f a )
 274 {
 275         a[0] = 0.f; a[1] = 0.f; a[2] = 0.f; a[3] = 0.f;
 276 }
 277
 278 CXR_INLINE void v4_muls( v4f a, double s, v4f d )
 279 {
 280         d[0] = a[0]*s; d[1] = a[1]*s; d[2] = a[2]*s; d[3] = a[3]*s;
 281 }
 282
 283 // Matrix 3x3
 284 //======================================================================================================
 285
 286 CXR_INLINE void m3x3_inv_transpose( m3x3f src, m3x3f dest )
 287 {
 288         double a = src[0][0], b = src[0][1], c = src[0][2],
 289                         d = src[1][0], e = src[1][1], f = src[1][2],
 290                         g = src[2][0], h = src[2][1], i = src[2][2];
 291
 292         double det =    1.f /
 293                                         (+a*(e*i-h*f)
 294                 -b*(d*i-f*g)
 295                 +c*(d*h-e*g));
 296
 297         dest[0][0] =  (e*i-h*f)*det;
 298         dest[1][0] = -(b*i-c*h)*det;
 299         dest[2][0] =  (b*f-c*e)*det;
 300         dest[0][1] = -(d*i-f*g)*det;
 301         dest[1][1] =  (a*i-c*g)*det;
 302         dest[2][1] = -(a*f-d*c)*det;
 303         dest[0][2] =  (d*h-g*e)*det;
 304         dest[1][2] = -(a*h-g*b)*det;
 305         dest[2][2] =  (a*e-d*b)*det;
 306 }
 307
 308 CXR_INLINE void m3x3_mulv( m3x3f m, v3f v, v3f d )
 309 {
 310         v3f res;
 311
 312         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
 313         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
 314         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
 315
 316         v3_copy( res, d );
 317 }
 318
 319 // Matrix 4x3
 320 // ==================================================================================================================
 321
 322 #define M4X3_IDENTITY   {{1.0f, 0.0f, 0.0f, },\
 323                                                                 { 0.0f, 1.0f, 0.0f, },\
 324                                                                 { 0.0f, 0.0f, 1.0f, },\
 325                                                                 { 0.0f, 0.0f, 0.0f }}
 326
 327 CXR_INLINE void m4x3_to_3x3( m4x3f a, m3x3f b )
 328 {
 329         v3_copy( a[0], b[0] );
 330         v3_copy( a[1], b[1] );
 331         v3_copy( a[2], b[2] );
 332 }
 333
 334 CXR_INLINE void m4x3_copy( m4x3f a, m4x3f b )
 335 {
 336         v3_copy( a[0], b[0] );
 337         v3_copy( a[1], b[1] );
 338         v3_copy( a[2], b[2] );
 339         v3_copy( a[3], b[3] );
 340 }
 341
 342 CXR_INLINE void m4x3_identity( m4x3f a )
 343 {
 344         m4x3f id = M4X3_IDENTITY;
 345         m4x3_copy( id, a );
 346 }
 347
 348 CXR_INLINE void m4x3_mul( m4x3f a, m4x3f b, m4x3f d )
 349 {
 350         double
 351         a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
 352         a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
 353         a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
 354         a30 = a[3][0], a31 = a[3][1], a32 = a[3][2],
 355         b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
 356         b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
 357         b20 = b[2][0], b21 = b[2][1], b22 = b[2][2],
 358         b30 = b[3][0], b31 = b[3][1], b32 = b[3][2];
 359
 360         d[0][0] = a00*b00 + a10*b01 + a20*b02;
 361         d[0][1] = a01*b00 + a11*b01 + a21*b02;
 362         d[0][2] = a02*b00 + a12*b01 + a22*b02;
 363         d[1][0] = a00*b10 + a10*b11 + a20*b12;
 364         d[1][1] = a01*b10 + a11*b11 + a21*b12;
 365         d[1][2] = a02*b10 + a12*b11 + a22*b12;
 366         d[2][0] = a00*b20 + a10*b21 + a20*b22;
 367         d[2][1] = a01*b20 + a11*b21 + a21*b22;
 368         d[2][2] = a02*b20 + a12*b21 + a22*b22;
 369         d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30;
 370         d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31;
 371         d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32;
 372 }
 373
 374 CXR_INLINE void m4x3_mulv( m4x3f m, v3f v, v3f d )
 375 {
 376         v3f res;
 377
 378         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0];
 379         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1];
 380         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2];
 381
 382         v3_copy( res, d );
 383 }
 384
 385 // Affine transforms
 386
 387 CXR_INLINE void m4x3_translate( m4x3f m, v3f v )
 388 {
 389         v3_muladds( m[3], m[0], v[0], m[3] );
 390         v3_muladds( m[3], m[1], v[1], m[3] );
 391         v3_muladds( m[3], m[2], v[2], m[3] );
 392 }
 393
 394 CXR_INLINE void m4x3_scale( m4x3f m, double s )
 395 {
 396         v3_muls( m[0], s, m[0] );
 397         v3_muls( m[1], s, m[1] );
 398         v3_muls( m[2], s, m[2] );
 399 }
 400
 401 CXR_INLINE void m4x3_rotate_x( m4x3f m, double angle )
 402 {
 403         m4x3f t = M4X3_IDENTITY;
 404         double c, s;
 405
 406         c = cosf( angle );
 407         s = sinf( angle );
 408
 409         t[1][1] =  c;
 410         t[1][2] =  s;
 411         t[2][1] = -s;
 412         t[2][2] =  c;
 413
 414         m4x3_mul( m, t, m );
 415 }
 416
 417 CXR_INLINE void m4x3_rotate_y( m4x3f m, double angle )
 418 {
 419         m4x3f t = M4X3_IDENTITY;
 420         double c, s;
 421
 422         c = cosf( angle );
 423         s = sinf( angle );
 424
 425         t[0][0] =  c;
 426         t[0][2] = -s;
 427         t[2][0] =  s;
 428         t[2][2] =  c;
 429
 430         m4x3_mul( m, t, m );
 431 }
 432
 433 CXR_INLINE void m4x3_rotate_z( m4x3f m, double angle )
 434 {
 435         m4x3f t = M4X3_IDENTITY;
 436         double c, s;
 437
 438         c = cosf( angle );
 439         s = sinf( angle );
 440
 441         t[0][0] =  c;
 442         t[0][1] =  s;
 443         t[1][0] = -s;
 444         t[1][1] =  c;
 445
 446         m4x3_mul( m, t, m );
 447 }
 448
 449 // Warning: These functions are unoptimized..
 450 CXR_INLINE void m4x3_expand_aabb_point( m4x3f m, boxf box, v3f point )
 451 {
 452         v3f v;
 453         m4x3_mulv( m, point, v );
 454
 455         v3_minv( box[0], v, box[0] );
 456         v3_maxv( box[1], v, box[1] );
 457 }
 458
 459 CXR_INLINE void box_concat( boxf a, boxf b )
 460 {
 461         v3_minv( a[0], b[0], a[0] );
 462         v3_maxv( a[1], b[1], a[1] );
 463 }
 464
 465 CXR_INLINE void box_copy( boxf a, boxf b )
 466 {
 467         v3_copy( a[0], b[0] );
 468         v3_copy( a[1], b[1] );
 469 }
 470
 471 CXR_INLINE void m4x3_transform_aabb( m4x3f m, boxf box )
 472 {
 473         v3f a; v3f b;
 474
 475         v3_copy( box[0], a );
 476         v3_copy( box[1], b );
 477         v3_fill( box[0],  INFINITY );
 478         v3_fill( box[1], -INFINITY );
 479
 480         m4x3_expand_aabb_point( m, box, a );
 481         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], a[2] } );
 482         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], a[2] } );
 483         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], a[2] } );
 484         m4x3_expand_aabb_point( m, box, b );
 485         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], b[2] } );
 486         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], b[2] } );
 487         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], b[2] } );
 488 }
 489
 490 CXR_INLINE void tri_normal( v3f p0, v3f p1, v3f p2, v3f normal )
 491 {
 492    v3f v0, v1;
 493    v3_sub( p1, p0, v0 );
 494    v3_sub( p2, p0, v1 );
 495    v3_cross( v0, v1, normal );
 496    v3_normalize( normal );
 497 }
 498
 499 CXR_INLINE void tri_to_plane( v3f a, v3f b, v3f c, v4f plane )
 500 {
 501    tri_normal( a,b,c, plane );
 502    plane[3] = v3_dot( plane, a );
 503 }
 504
 505 // TODO update this code to use normal v3_x functions
 506 CXR_INLINE void tri_to_plane1( double a[3], double b[3], double c[3], double p[4] )
 507 {
 508         double edge0[3];
 509         double edge1[3];
 510         double l;
 511
 512         edge0[0] = b[0] - a[0];
 513         edge0[1] = b[1] - a[1];
 514         edge0[2] = b[2] - a[2];
 515
 516         edge1[0] = c[0] - a[0];
 517         edge1[1] = c[1] - a[1];
 518         edge1[2] = c[2] - a[2];
 519
 520         p[0] = edge0[1] * edge1[2] - edge0[2] * edge1[1];
 521         p[1] = edge0[2] * edge1[0] - edge0[0] * edge1[2];
 522         p[2] = edge0[0] * edge1[1] - edge0[1] * edge1[0];
 523
 524         l = sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2]);
 525         p[3] = (p[0] * a[0] + p[1] * a[1] + p[2] * a[2]) / l;
 526
 527         p[0] = p[0] / l;
 528         p[1] = p[1] / l;
 529         p[2] = p[2] / l;
 530 }
 531
 532 CXR_INLINE int plane_intersect( double a[4], double b[4], double c[4], double p[3] )
 533 {
 534         double const epsilon = 0.001;
 535
 536         double x[3];
 537         double d;
 538
 539         x[0] = a[1] * b[2] - a[2] * b[1];
 540         x[1] = a[2] * b[0] - a[0] * b[2];
 541         x[2] = a[0] * b[1] - a[1] * b[0];
 542
 543         d = x[0] * c[0] + x[1] * c[1] + x[2] * c[2];
 544
 545         if( d < epsilon && d > -epsilon ) return 0;
 546
 547         p[0] = (b[1] * c[2] - b[2] * c[1]) * -a[3];
 548         p[1] = (b[2] * c[0] - b[0] * c[2]) * -a[3];
 549         p[2] = (b[0] * c[1] - b[1] * c[0]) * -a[3];
 550
 551         p[0] += (c[1] * a[2] - c[2] * a[1]) * -b[3];
 552         p[1] += (c[2] * a[0] - c[0] * a[2]) * -b[3];
 553         p[2] += (c[0] * a[1] - c[1] * a[0]) * -b[3];
 554
 555         p[0] += (a[1] * b[2] - a[2] * b[1]) * -c[3];
 556         p[1] += (a[2] * b[0] - a[0] * b[2]) * -c[3];
 557         p[2] += (a[0] * b[1] - a[1] * b[0]) * -c[3];
 558
 559         p[0] = -p[0] / d;
 560         p[1] = -p[1] / d;
 561         p[2] = -p[2] / d;
 562
 563         return 1;
 564 }
 565
 566 CXR_INLINE void normal_to_plane( v3f normal, v3f p, v4f plane )
 567 {
 568    v3_copy( normal, plane );
 569    plane[3] = v3_dot( normal, p );
 570 }
 571
 572 CXR_INLINE double plane_polarity( double p[4], double a[3] )
 573 {
 574         return
 575         (a[0] * p[0] + a[1] * p[1] + a[2] * p[2])
 576         -(p[0]*p[3] * p[0] + p[1]*p[3] * p[1] + p[2]*p[3] * p[2])
 577         ;
 578 }
 579
 580 CXR_INLINE void plane_project_point( v4f plane, v3f a, v3f d )
 581 {
 582    v3f ref, delta;
 583    v3_muls( plane, plane[3], ref );
 584
 585    v3_sub( a, ref, delta );
 586    v3_muladds( a, plane, -v3_dot(delta,plane), d );
 587 }