Dogcows Code - chaz/rasterize/blob - mat.h

   1
   2 /*
   3  * CS5600 University of Utah
   4  * Charles McGarvey
   5  * mcgarvey@eng.utah.edu
   6  */
   7
   8 #ifndef _MAT_H_
   9 #define _MAT_H_
  10
  11 #include "common.h"
  12 #include "vec.h"
  13
  14
  15 /*
  16  * A simple matrix class with column-major storage and notation.
  17  */
  18 struct mat
  19 {
  20     vec_t v[4];
  21 };
  22 typedef struct mat mat_t;
  23
  24 /*
  25  * Initialize a matrix with individual components, row by row.
  26  */
  27 INLINE_MAYBE
  28 void mat_init(mat_t* m, scal_t m11, scal_t m12, scal_t m13, scal_t m14,
  29                         scal_t m21, scal_t m22, scal_t m23, scal_t m24,
  30                         scal_t m31, scal_t m32, scal_t m33, scal_t m34,
  31                         scal_t m41, scal_t m42, scal_t m43, scal_t m44)
  32 {
  33     m->v[0] = vec_new2(m11, m21, m31, m41);
  34     m->v[1] = vec_new2(m12, m22, m32, m42);
  35     m->v[2] = vec_new2(m13, m23, m33, m43);
  36     m->v[3] = vec_new2(m14, m24, m34, m44);
  37 }
  38
  39
  40 /*
  41  * Create a new matrix with individual components, row by row.
  42  */
  43 INLINE_MAYBE
  44 mat_t mat_new(scal_t m11, scal_t m12, scal_t m13, scal_t m14,
  45               scal_t m21, scal_t m22, scal_t m23, scal_t m24,
  46               scal_t m31, scal_t m32, scal_t m33, scal_t m34,
  47               scal_t m41, scal_t m42, scal_t m43, scal_t m44)
  48 {
  49     mat_t m;
  50     mat_init(&m, m11, m12, m13, m14,
  51                  m21, m22, m23, m24,
  52                  m31, m32, m33, m34,
  53                  m41, m42, m43, m44);
  54     return m;
  55 }
  56
  57 /*
  58  * Create a new matrix with four column vectors.
  59  */
  60 INLINE_MAYBE
  61 mat_t mat_new2(vec_t a, vec_t b, vec_t c, vec_t d)
  62 {
  63     mat_t m;
  64     m.v[0] = a;
  65     m.v[1] = b;
  66     m.v[2] = c;
  67     m.v[3] = d;
  68     return m;
  69 }
  70
  71 #define MAT_IDENTITY mat_new(S(1.0), S(0.0), S(0.0), S(0.0), \
  72                              S(0.0), S(1.0), S(0.0), S(0.0), \
  73                              S(0.0), S(0.0), S(1.0), S(0.0), \
  74                              S(0.0), S(0.0), S(0.0), S(1.0))
  75
  76
  77 /*
  78  * Get a pointer to the matrix data.
  79  */
  80 INLINE_MAYBE
  81 const scal_t* mat_data(const mat_t* m)
  82 {
  83     return &m->v[0].x;
  84 }
  85
  86
  87 /*
  88  * Get a column vector (can also access the vector array directly).
  89  */
  90 INLINE_MAYBE
  91 vec_t mat_col(mat_t m, int i)
  92 {
  93     return m.v[i];
  94 }
  95
  96 /*
  97  * Get a row vector.
  98  */
  99 INLINE_MAYBE
 100 vec_t mat_row(mat_t m, int i)
 101 {
 102     switch (i) {
 103     case 0:
 104         return vec_new2(m.v[0].x, m.v[1].x, m.v[2].x, m.v[3].x);
 105     case 1:
 106         return vec_new2(m.v[0].y, m.v[1].y, m.v[2].y, m.v[3].y);
 107     case 2:
 108         return vec_new2(m.v[0].z, m.v[1].z, m.v[2].z, m.v[3].z);
 109     case 3:
 110         return vec_new2(m.v[0].w, m.v[1].w, m.v[2].w, m.v[3].w);
 111     }
 112 }
 113
 114
 115 /*
 116  * Print the matrix to stdout.
 117  */
 118 INLINE_MAYBE
 119 void mat_print(mat_t m)
 120 {
 121     printf("|");
 122     vec_print(mat_row(m, 0));
 123     printf("|\n|");
 124     vec_print(mat_row(m, 1));
 125     printf("|\n|");
 126     vec_print(mat_row(m, 2));
 127     printf("|\n|");
 128     vec_print(mat_row(m, 3));
 129     printf("|");
 130 }
 131
 132
 133 /*
 134  * Multiply two matrices together.
 135  */
 136 INLINE_MAYBE
 137 mat_t mat_mult(mat_t a, mat_t b)
 138 {
 139 #define _DOT(I,J) vec_dot2(mat_row(a,I), mat_col(b,J))
 140     return mat_new(_DOT(0,0), _DOT(0,1), _DOT(0,2), _DOT(0,3),
 141                    _DOT(1,0), _DOT(1,1), _DOT(1,2), _DOT(1,3),
 142                    _DOT(2,0), _DOT(2,1), _DOT(2,2), _DOT(2,3),
 143                    _DOT(3,0), _DOT(3,1), _DOT(3,2), _DOT(3,3));
 144 #undef _DOT
 145 }
 146
 147 /*
 148  * Transform a vector using a matrix.
 149  */
 150 INLINE_MAYBE
 151 vec_t mat_apply(mat_t m, vec_t v)
 152 {
 153     return vec_new2(vec_dot2(v,mat_row(m,0)),
 154                     vec_dot2(v,mat_row(m,1)),
 155                     vec_dot2(v,mat_row(m,2)),
 156                     vec_dot2(v,mat_row(m,3)));
 157 }
 158
 159
 160 /*
 161  * Create a new translate matrix.
 162  */
 163 INLINE_MAYBE
 164 mat_t MAT_TRANSLATE(scal_t x, scal_t y, scal_t z)
 165 {
 166     return mat_new(S(1.0), S(0.0), S(0.0),      x,
 167                    S(0.0), S(1.0), S(0.0),      y,
 168                    S(0.0), S(0.0), S(1.0),      z,
 169                    S(0.0), S(0.0), S(0.0), S(1.0));
 170 }
 171
 172 /*
 173  * Create a new translate matrix from a vector.
 174  */
 175 INLINE_MAYBE
 176 mat_t MAT_TRANSLATE2(vec_t v)
 177 {
 178     return MAT_TRANSLATE(v.x, v.y, v.z);
 179 }
 180
 181 /*
 182  * Create a new scale matrix.
 183  */
 184 INLINE_MAYBE
 185 mat_t MAT_SCALE(scal_t x, scal_t y, scal_t z)
 186 {
 187     return mat_new(x, S(0.0), S(0.0), S(0.0),
 188               S(0.0),      y, S(0.0), S(0.0),
 189               S(0.0), S(0.0),      z, S(0.0),
 190               S(0.0), S(0.0), S(0.0), S(1.0));
 191 }
 192
 193 /*
 194  * Create a new scale matrix from a vector.
 195  */
 196 INLINE_MAYBE
 197 mat_t MAT_SCALE2(vec_t v)
 198 {
 199     return MAT_SCALE(v.x, v.y, v.z);
 200 }
 201
 202 /*
 203  * Create a rotation matrix (around the X axis).
 204  */
 205 INLINE_MAYBE
 206 mat_t MAT_ROTATE_X(scal_t theta)
 207 {
 208     scal_t sin_a = scal_sin(theta);
 209     scal_t cos_a = scal_cos(theta);
 210     return mat_new(S(1.0), S(0.0), S(0.0), S(0.0),
 211                    S(0.0),  cos_a, -sin_a, S(0.0),
 212                    S(0.0),  sin_a,  cos_a, S(0.0),
 213                    S(0.0), S(0.0), S(0.0), S(1.0));
 214 }
 215
 216 /*
 217  * Create a rotation matrix (around the Y axis).
 218  */
 219 INLINE_MAYBE
 220 mat_t MAT_ROTATE_Y(scal_t theta)
 221 {
 222     scal_t sin_a = scal_sin(theta);
 223     scal_t cos_a = scal_cos(theta);
 224     return mat_new(cos_a, S(0.0),  sin_a, S(0.0),
 225                   S(0.0), S(1.0), S(0.0), S(0.0),
 226                   -sin_a, S(0.0),  cos_a, S(0.0),
 227                   S(0.0), S(0.0), S(0.0), S(1.0));
 228 }
 229
 230 /*
 231  * Create a rotation matrix (around the Z axis).
 232  */
 233 INLINE_MAYBE
 234 mat_t MAT_ROTATE_Z(scal_t theta)
 235 {
 236     scal_t sin_a = scal_sin(theta);
 237     scal_t cos_a = scal_cos(theta);
 238     return mat_new(cos_a, -sin_a, S(0.0), S(0.0),
 239                    sin_a,  cos_a, S(0.0), S(0.0),
 240                   S(0.0), S(0.0), S(1.0), S(0.0),
 241                   S(0.0), S(0.0), S(0.0), S(1.0));
 242 }
 243
 244 /*
 245  * Create a rotation matrix (around an arbitrary axis).
 246  */
 247 INLINE_MAYBE
 248 mat_t MAT_ROTATE(scal_t theta, scal_t x, scal_t y, scal_t z)
 249 {
 250     vec_t v = vec_normalize(vec_new(x, y, z));
 251     x = v.x;
 252     y = v.y;
 253     z = v.z;
 254     scal_t c = scal_cos(-theta);
 255     scal_t s = scal_sin(-theta);
 256     scal_t t = S(1.0) - c;
 257     return mat_new(t * x * x + c, t * x * y + s * z, t * x * z - s * y, S(0.0),
 258                    t * x * y - s * z, t * y * y + c, t * y * z + s * x, S(0.0),
 259                    t * x * z + s * y, t * y * z - s * x, t * z * z + c, S(0.0),
 260                    S(0.0), S(0.0), S(0.0), S(1.0));
 261 }
 262
 263 /*
 264  * Create a view matrix based on eye, spot, and an up vector.
 265  */
 266 INLINE_MAYBE
 267 mat_t MAT_LOOKAT(vec_t eye, vec_t spot, vec_t up)
 268 {
 269     vec_t f = vec_normalize(vec_sub(spot, eye));
 270     vec_t s = vec_normalize(vec_cross(f, up));
 271     vec_t u = vec_cross(s, f);
 272     return mat_mult(mat_new(s.x,    s.y,    s.z, S(0.0),
 273                             u.x,    u.y,    u.z, S(0.0),
 274                            -f.x,   -f.y,   -f.z, S(0.0),
 275                          S(0.0), S(0.0), S(0.0), S(1.0)), MAT_TRANSLATE2(vec_neg(eye)));
 276 }
 277
 278 /*
 279  * Create a 3D orthogonal projection matrix.
 280  */
 281 INLINE_MAYBE
 282 mat_t MAT_ORTHO(scal_t left, scal_t right,
 283                 scal_t bottom, scal_t top,
 284                 scal_t near, scal_t far)
 285 {
 286     scal_t rml = right - left;
 287     scal_t rpl = right + left;
 288     scal_t tmb = top - bottom;
 289     scal_t tpb = top + bottom;
 290     scal_t fmn = far - near;
 291     scal_t fpn = far + near;
 292     return mat_new(S(2.0)/rml,     S(0.0),      S(0.0), -rpl / rml,
 293                        S(0.0), S(2.0)/tmb,      S(0.0), -tpb / tmb,
 294                        S(0.0),     S(0.0), S(-2.0)/fmn, -fpn / fmn,
 295                        S(0.0),     S(0.0),      S(0.0),     S(1.0));
 296 }
 297
 298 /*
 299  * Create a frustum-based projection matrix.
 300  */
 301 INLINE_MAYBE
 302 mat_t MAT_FRUSTUM(scal_t left, scal_t right,
 303                   scal_t bottom, scal_t top,
 304                   scal_t near, scal_t far)
 305 {
 306     scal_t rml = right - left;
 307     scal_t rpl = right + left;
 308     scal_t tmb = top - bottom;
 309     scal_t tpb = top + bottom;
 310     scal_t fmn = far - near;
 311     scal_t fpn = far + near;
 312     scal_t n2  = near * S(2.0);
 313     return mat_new(n2/rml, S(0.0),  rpl/rml,      S(0.0),
 314                    S(0.0), n2/tmb,  tpb/tmb,      S(0.0),
 315                    S(0.0), S(0.0), -fpn/fmn, -n2*far/fmn,
 316                    S(0.0), S(0.0),  S(-1.0),      S(0.0));
 317 }
 318
 319 /*
 320  * Create a perspective projection matrix.
 321  */
 322 INLINE_MAYBE
 323 mat_t MAT_PERSPECTIVE(scal_t fovy, scal_t aspect, scal_t near, scal_t far)
 324 {
 325     scal_t top    = near * scal_tan(fovy * S(0.5));
 326     scal_t bottom = -top;
 327     scal_t left   = bottom * aspect;
 328     scal_t right  = top * aspect;
 329     return MAT_FRUSTUM(left, right, bottom, top, near, far);
 330 }
 331
 332 /*
 333  * Create a viewport matrix.
 334  */
 335 INLINE_MAYBE
 336 mat_t MAT_VIEWPORT(int x, int y, int w, int h)
 337 {
 338     scal_t xs = (scal_t)x;
 339     scal_t ys = (scal_t)y;
 340     scal_t ws = (scal_t)w * S(0.5);
 341     scal_t hs = (scal_t)h * S(0.5);
 342     return mat_new(ws, S(0.0), S(0.0),  ws+xs,
 343                S(0.0),     hs, S(0.0),  hs+ys,
 344                S(0.0), S(0.0), S(1.0), S(0.0),
 345                S(0.0), S(0.0), S(0.0), S(1.0));
 346 }
 347
 348
 349 #endif // _MAT_H_
 350