csrMath.h

   1 // Copyright (C) 2021 Harry Godden (hgn)
   2
   3 // Util
   4 // ==================================================================================================================
   5
   6 #define CSR_INLINE static inline
   7 #define CSR_PIf 3.14159265358979323846264338327950288f
   8
   9 // Simple min/max replacements
  10 CSR_INLINE float csr_minf( float a, float b )
  11 {
  12         return a < b? a: b;
  13 }
  14
  15 CSR_INLINE float csr_maxf( float a, float b )
  16 {
  17         return a > b? a: b;
  18 }
  19
  20 CSR_INLINE int csr_min( int a, int b )
  21 {
  22         return a < b? a: b;
  23 }
  24
  25 CSR_INLINE int csr_max( int a, int b )
  26 {
  27         return a > b? a: b;
  28 }
  29
  30 // Convert double precision vec3 into single
  31 CSR_INLINE void v3d_v3f( double a[3], float b[3] )
  32 {
  33         b[0] = a[0];
  34         b[1] = a[1];
  35         b[2] = a[2];
  36 }
  37
  38 // Convert degrees to radians
  39 CSR_INLINE float csr_rad( float deg )
  40 {
  41         return deg * CSR_PIf / 180.0f;
  42 }
  43
  44 // Vector 2
  45 // ==================================================================================================================
  46
  47 CSR_INLINE void v2_copy( v2f a, v2f b )
  48 {
  49         b[0] = a[0]; b[1] = a[1];
  50 }
  51
  52 CSR_INLINE void v2_minv( v2f a, v2f b, v2f dest )
  53 {
  54         dest[0] = csr_minf(a[0], b[0]);
  55         dest[1] = csr_minf(a[1], b[1]);
  56 }
  57
  58 CSR_INLINE void v2_maxv( v2f a, v2f b, v2f dest )
  59 {
  60         dest[0] = csr_maxf(a[0], b[0]);
  61         dest[1] = csr_maxf(a[1], b[1]);
  62 }
  63
  64 CSR_INLINE void v2_sub( v2f a, v2f b, v2f d )
  65 {
  66         d[0] = a[0]-b[0]; d[1] = a[1]-b[1];
  67 }
  68
  69 CSR_INLINE float v2_cross( v2f a, v2f b )
  70 {
  71         return a[0] * b[1] - a[1] * b[0];
  72 }
  73
  74 CSR_INLINE void v2_add( v2f a, v2f b, v2f d )
  75 {
  76         d[0] = a[0]+b[0]; d[1] = a[1]+b[1];
  77 }
  78
  79 CSR_INLINE void v2_muls( v2f a, float s, v2f d )
  80 {
  81         d[0] = a[0]*s; d[1] = a[1]*s;
  82 }
  83
  84 CSR_INLINE void v2_mul( v2f a, v2f b, v2f d )
  85 {
  86         d[0] = a[0]*b[0]; d[1] = a[1]*b[1];
  87 }
  88
  89 CSR_INLINE void v2_div( v2f a, v2f b, v2f d )
  90 {
  91         d[0] = a[0]/b[0]; d[1] = a[1]/b[1];
  92 }
  93
  94 // Vector 3
  95 // ==================================================================================================================
  96
  97 CSR_INLINE void v3_zero( v3f a )
  98 {
  99         a[0] = 0.f; a[1] = 0.f; a[2] = 0.f;
 100 }
 101
 102 CSR_INLINE void v3_copy( v3f a, v3f b )
 103 {
 104         b[0] = a[0]; b[1] = a[1]; b[2] = a[2];
 105 }
 106
 107 CSR_INLINE void v3_add( v3f a, v3f b, v3f d )
 108 {
 109         d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; d[2] = a[2]+b[2];
 110 }
 111
 112 CSR_INLINE void v3_sub( v3f a, v3f b, v3f d )
 113 {
 114         d[0] = a[0]-b[0]; d[1] = a[1]-b[1]; d[2] = a[2]-b[2];
 115 }
 116
 117 CSR_INLINE void v3_mul( v3f a, v3f b, v3f d )
 118 {
 119         d[0] = a[0]*b[0]; d[1] = a[1]*b[1]; d[2] = a[2]*b[2];
 120 }
 121
 122 CSR_INLINE void v3_div( v3f a, v3f b, v3f d )
 123 {
 124         d[0] = a[0]/b[0]; d[1] = a[1]/b[1];     d[2] = a[2]/b[2];
 125 }
 126
 127 CSR_INLINE void v3_muls( v3f a, float s, v3f d )
 128 {
 129         d[0] = a[0]*s; d[1] = a[1]*s; d[2] = a[2]*s;
 130 }
 131
 132 CSR_INLINE void v3_divs( v3f a, float s, v3f d )
 133 {
 134         d[0] = a[0]/s; d[1] = a[1]/s; d[2] = a[2]/s;
 135 }
 136
 137 CSR_INLINE void v3_muladds( v3f a, v3f b, float s, v3f d )
 138 {
 139         d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s; d[2] = a[2]+b[2]*s;
 140 }
 141
 142 CSR_INLINE float v3_dot( v3f a, v3f b )
 143 {
 144         return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
 145 }
 146
 147 CSR_INLINE void v3_cross( v3f a, v3f b, v3f d )
 148 {
 149   d[0] = a[1] * b[2] - a[2] * b[1];
 150   d[1] = a[2] * b[0] - a[0] * b[2];
 151   d[2] = a[0] * b[1] - a[1] * b[0];
 152 }
 153
 154 CSR_INLINE float v3_length2( v3f a )
 155 {
 156         return v3_dot( a, a );
 157 }
 158
 159 CSR_INLINE float v3_length( v3f a )
 160 {
 161         return sqrtf( v3_length2( a ) );
 162 }
 163
 164 CSR_INLINE float v3_dist2( v3f a, v3f b )
 165 {
 166         v3f delta;
 167         v3_sub( a, b, delta );
 168         return v3_length2( delta );
 169 }
 170
 171 CSR_INLINE float v3_dist( v3f a, v3f b )
 172 {
 173         return sqrtf( v3_dist2( a, b ) );
 174 }
 175
 176 CSR_INLINE void v3_normalize( v3f a )
 177 {
 178         v3_muls( a, 1.f / v3_length( a ), a );
 179 }
 180
 181 CSR_INLINE float csr_lerpf( float a, float b, float t )
 182 {
 183         return a + t*(b-a);
 184 }
 185
 186 CSR_INLINE void v3_lerp( v3f a, v3f b, float t, v3f d )
 187 {
 188         d[0] = a[0] + t*(b[0]-a[0]);
 189         d[1] = a[1] + t*(b[1]-a[1]);
 190         d[2] = a[2] + t*(b[2]-a[2]);
 191 }
 192
 193 CSR_INLINE void v3_minv( v3f a, v3f b, v3f dest )
 194 {
 195         dest[0] = csr_minf(a[0], b[0]);
 196         dest[1] = csr_minf(a[1], b[1]);
 197         dest[2] = csr_minf(a[2], b[2]);
 198 }
 199
 200 CSR_INLINE void v3_maxv( v3f a, v3f b, v3f dest )
 201 {
 202         dest[0] = csr_maxf(a[0], b[0]);
 203         dest[1] = csr_maxf(a[1], b[1]);
 204         dest[2] = csr_maxf(a[2], b[2]);
 205 }
 206
 207 CSR_INLINE float v3_minf( v3f a )
 208 {
 209         return csr_minf( csr_minf( a[0], a[1] ), a[2] );
 210 }
 211
 212 CSR_INLINE float v3_maxf( v3f a )
 213 {
 214         return csr_maxf( csr_maxf( a[0], a[1] ), a[2] );
 215 }
 216
 217 CSR_INLINE void v3_fill( v3f a, float v )
 218 {
 219         a[0] = v;
 220         a[1] = v;
 221         a[2] = v;
 222 }
 223
 224 // Vector 4
 225 // ==================================================================================================================
 226
 227 CSR_INLINE void v4_copy( v4f a, v4f b )
 228 {
 229         b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; b[3] = a[3];
 230 }
 231
 232 CSR_INLINE void v4_zero( v4f a )
 233 {
 234         a[0] = 0.f; a[1] = 0.f; a[2] = 0.f; a[3] = 0.f;
 235 }
 236
 237 // Matrix 3x3
 238 //======================================================================================================
 239
 240 CSR_INLINE void m3x3_inv_transpose( m3x3f src, m3x3f dest )
 241 {
 242         float a = src[0][0], b = src[0][1], c = src[0][2],
 243                         d = src[1][0], e = src[1][1], f = src[1][2],
 244                         g = src[2][0], h = src[2][1], i = src[2][2];
 245
 246         float det =    1.f /
 247                                         (+a*(e*i-h*f)
 248                 -b*(d*i-f*g)
 249                 +c*(d*h-e*g));
 250
 251         dest[0][0] =  (e*i-h*f)*det;
 252         dest[1][0] = -(b*i-c*h)*det;
 253         dest[2][0] =  (b*f-c*e)*det;
 254         dest[0][1] = -(d*i-f*g)*det;
 255         dest[1][1] =  (a*i-c*g)*det;
 256         dest[2][1] = -(a*f-d*c)*det;
 257         dest[0][2] =  (d*h-g*e)*det;
 258         dest[1][2] = -(a*h-g*b)*det;
 259         dest[2][2] =  (a*e-d*b)*det;
 260 }
 261
 262 CSR_INLINE void m3x3_mulv( m3x3f m, v3f v, v3f d )
 263 {
 264         v3f res;
 265
 266         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
 267         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
 268         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
 269
 270         v3_copy( res, d );
 271 }
 272
 273 // Matrix 4x3
 274 // ==================================================================================================================
 275
 276 #define M4X3_IDENTITY   {{1.0f, 0.0f, 0.0f, },\
 277                                                                 { 0.0f, 1.0f, 0.0f, },\
 278                                                                 { 0.0f, 0.0f, 1.0f, },\
 279                                                                 { 0.0f, 0.0f, 0.0f }}
 280
 281 CSR_INLINE void m4x3_to_3x3( m4x3f a, m3x3f b )
 282 {
 283         v3_copy( a[0], b[0] );
 284         v3_copy( a[1], b[1] );
 285         v3_copy( a[2], b[2] );
 286 }
 287
 288 CSR_INLINE void m4x3_copy( m4x3f a, m4x3f b )
 289 {
 290         v3_copy( a[0], b[0] );
 291         v3_copy( a[1], b[1] );
 292         v3_copy( a[2], b[2] );
 293         v3_copy( a[3], b[3] );
 294 }
 295
 296 CSR_INLINE void m4x3_identity( m4x3f a )
 297 {
 298         m4x3f id = M4X3_IDENTITY;
 299         m4x3_copy( id, a );
 300 }
 301
 302 CSR_INLINE void m4x3_mul( m4x3f a, m4x3f b, m4x3f d )
 303 {
 304         float
 305         a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
 306         a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
 307         a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
 308         a30 = a[3][0], a31 = a[3][1], a32 = a[3][2],
 309         b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
 310         b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
 311         b20 = b[2][0], b21 = b[2][1], b22 = b[2][2],
 312         b30 = b[3][0], b31 = b[3][1], b32 = b[3][2];
 313
 314         d[0][0] = a00*b00 + a10*b01 + a20*b02;
 315         d[0][1] = a01*b00 + a11*b01 + a21*b02;
 316         d[0][2] = a02*b00 + a12*b01 + a22*b02;
 317         d[1][0] = a00*b10 + a10*b11 + a20*b12;
 318         d[1][1] = a01*b10 + a11*b11 + a21*b12;
 319         d[1][2] = a02*b10 + a12*b11 + a22*b12;
 320         d[2][0] = a00*b20 + a10*b21 + a20*b22;
 321         d[2][1] = a01*b20 + a11*b21 + a21*b22;
 322         d[2][2] = a02*b20 + a12*b21 + a22*b22;
 323         d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30;
 324         d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31;
 325         d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32;
 326 }
 327
 328 CSR_INLINE void m4x3_mulv( m4x3f m, v3f v, v3f d )
 329 {
 330         v3f res;
 331
 332         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0];
 333         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1];
 334         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2];
 335
 336         v3_copy( res, d );
 337 }
 338
 339 // Affine transforms
 340
 341 CSR_INLINE void m4x3_translate( m4x3f m, v3f v )
 342 {
 343         v3_muladds( m[3], m[0], v[0], m[3] );
 344         v3_muladds( m[3], m[1], v[1], m[3] );
 345         v3_muladds( m[3], m[2], v[2], m[3] );
 346 }
 347
 348 CSR_INLINE void m4x3_scale( m4x3f m, float s )
 349 {
 350         v3_muls( m[0], s, m[0] );
 351         v3_muls( m[1], s, m[1] );
 352         v3_muls( m[2], s, m[2] );
 353 }
 354
 355 CSR_INLINE void m4x3_rotate_x( m4x3f m, float angle )
 356 {
 357         m4x3f t = M4X3_IDENTITY;
 358         float c, s;
 359
 360         c = cosf( angle );
 361         s = sinf( angle );
 362
 363         t[1][1] =  c;
 364         t[1][2] =  s;
 365         t[2][1] = -s;
 366         t[2][2] =  c;
 367
 368         m4x3_mul( m, t, m );
 369 }
 370
 371 CSR_INLINE void m4x3_rotate_y( m4x3f m, float angle )
 372 {
 373         m4x3f t = M4X3_IDENTITY;
 374         float c, s;
 375
 376         c = cosf( angle );
 377         s = sinf( angle );
 378
 379         t[0][0] =  c;
 380         t[0][2] = -s;
 381         t[2][0] =  s;
 382         t[2][2] =  c;
 383
 384         m4x3_mul( m, t, m );
 385 }
 386
 387 CSR_INLINE void m4x3_rotate_z( m4x3f m, float angle )
 388 {
 389         m4x3f t = M4X3_IDENTITY;
 390         float c, s;
 391
 392         c = cosf( angle );
 393         s = sinf( angle );
 394
 395         t[0][0] =  c;
 396         t[0][1] =  s;
 397         t[1][0] = -s;
 398         t[1][1] =  c;
 399
 400         m4x3_mul( m, t, m );
 401 }
 402
 403 // Warning: These functions are unoptimized..
 404 CSR_INLINE void m4x3_expand_aabb_point( m4x3f m, boxf box, v3f point )
 405 {
 406         v3f v;
 407         m4x3_mulv( m, point, v );
 408
 409         v3_minv( box[0], v, box[0] );
 410         v3_maxv( box[1], v, box[1] );
 411 }
 412
 413 CSR_INLINE void box_concat( boxf a, boxf b )
 414 {
 415         v3_minv( a[0], b[0], a[0] );
 416         v3_maxv( a[1], b[1], a[1] );
 417 }
 418
 419 CSR_INLINE void box_copy( boxf a, boxf b )
 420 {
 421         v3_copy( a[0], b[0] );
 422         v3_copy( a[1], b[1] );
 423 }
 424
 425 CSR_INLINE void m4x3_transform_aabb( m4x3f m, boxf box )
 426 {
 427         v3f a; v3f b;
 428
 429         v3_copy( box[0], a );
 430         v3_copy( box[1], b );
 431         v3_fill( box[0],  INFINITY );
 432         v3_fill( box[1], -INFINITY );
 433
 434         m4x3_expand_aabb_point( m, box, a );
 435         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], a[2] } );
 436         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], a[2] } );
 437         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], a[2] } );
 438         m4x3_expand_aabb_point( m, box, b );
 439         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], b[2] } );
 440         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], b[2] } );
 441         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], b[2] } );
 442 }
 443
 444 // Planes (double precision)
 445 // ==================================================================================================================
 446
 447 CSR_INLINE void tri_to_plane( double a[3], double b[3], double c[3], double p[4] )
 448 {
 449         double edge0[3];
 450         double edge1[3];
 451         double l;
 452
 453         edge0[0] = b[0] - a[0];
 454         edge0[1] = b[1] - a[1];
 455         edge0[2] = b[2] - a[2];
 456
 457         edge1[0] = c[0] - a[0];
 458         edge1[1] = c[1] - a[1];
 459         edge1[2] = c[2] - a[2];
 460
 461         p[0] = edge0[1] * edge1[2] - edge0[2] * edge1[1];
 462         p[1] = edge0[2] * edge1[0] - edge0[0] * edge1[2];
 463         p[2] = edge0[0] * edge1[1] - edge0[1] * edge1[0];
 464
 465         l = sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2]);
 466         p[3] = (p[0] * a[0] + p[1] * a[1] + p[2] * a[2]) / l;
 467
 468         p[0] = p[0] / l;
 469         p[1] = p[1] / l;
 470         p[2] = p[2] / l;
 471 }
 472
 473 CSR_INLINE int plane_intersect( double a[4], double b[4], double c[4], double p[4] )
 474 {
 475         double const epsilon = 1e-8f;
 476
 477         double x[3];
 478         double d;
 479
 480         x[0] = a[1] * b[2] - a[2] * b[1];
 481         x[1] = a[2] * b[0] - a[0] * b[2];
 482         x[2] = a[0] * b[1] - a[1] * b[0];
 483
 484         d = x[0] * c[0] + x[1] * c[1] + x[2] * c[2];
 485
 486         if( d < epsilon && d > -epsilon ) return 0;
 487
 488         p[0] = (b[1] * c[2] - b[2] * c[1]) * -a[3];
 489         p[1] = (b[2] * c[0] - b[0] * c[2]) * -a[3];
 490         p[2] = (b[0] * c[1] - b[1] * c[0]) * -a[3];
 491
 492         p[0] += (c[1] * a[2] - c[2] * a[1]) * -b[3];
 493         p[1] += (c[2] * a[0] - c[0] * a[2]) * -b[3];
 494         p[2] += (c[0] * a[1] - c[1] * a[0]) * -b[3];
 495
 496         p[0] += (a[1] * b[2] - a[2] * b[1]) * -c[3];
 497         p[1] += (a[2] * b[0] - a[0] * b[2]) * -c[3];
 498         p[2] += (a[0] * b[1] - a[1] * b[0]) * -c[3];
 499
 500         p[0] = -p[0] / d;
 501         p[1] = -p[1] / d;
 502         p[2] = -p[2] / d;
 503
 504         return 1;
 505 }
 506
 507 CSR_INLINE double plane_polarity( double p[4], double a[3] )
 508 {
 509         return
 510         (a[0] * p[0] + a[1] * p[1] + a[2] * p[2])
 511         -(p[0]*p[3] * p[0] + p[1]*p[3] * p[1] + p[2]*p[3] * p[2])
 512         ;
 513 }