| 1 |
greg |
1.1 |
#ifndef lint |
| 2 |
|
|
static char SCCSid[] = "$SunId$ LBL"; |
| 3 |
|
|
#endif |
| 4 |
|
|
|
| 5 |
|
|
#include <math.h> |
| 6 |
|
|
#include <string.h> |
| 7 |
|
|
#include "vect.h" |
| 8 |
|
|
|
| 9 |
|
|
#ifndef M_PI |
| 10 |
|
|
#define M_PI 3.14159265358979323846 |
| 11 |
|
|
#endif |
| 12 |
gregl |
1.2 |
#define PI ((double)M_PI) |
| 13 |
greg |
1.1 |
|
| 14 |
|
|
#define EPSILON 1e-6 |
| 15 |
|
|
|
| 16 |
|
|
void adjoint (Matrix mat); |
| 17 |
|
|
double det4x4 (Matrix mat); |
| 18 |
|
|
double det3x3 (double a1, double a2, double a3, double b1, double b2, |
| 19 |
|
|
double b3, double c1, double c2, double c3); |
| 20 |
|
|
double det2x2 (double a, double b, double c, double d); |
| 21 |
|
|
|
| 22 |
|
|
|
| 23 |
|
|
void vect_init (Vector v, float x, float y, float z) |
| 24 |
|
|
{ |
| 25 |
|
|
v[X] = x; |
| 26 |
|
|
v[Y] = y; |
| 27 |
|
|
v[Z] = z; |
| 28 |
|
|
} |
| 29 |
|
|
|
| 30 |
|
|
|
| 31 |
|
|
void vect_copy (Vector v1, Vector v2) |
| 32 |
|
|
{ |
| 33 |
|
|
v1[X] = v2[X]; |
| 34 |
|
|
v1[Y] = v2[Y]; |
| 35 |
|
|
v1[Z] = v2[Z]; |
| 36 |
|
|
} |
| 37 |
|
|
|
| 38 |
|
|
|
| 39 |
|
|
int vect_equal (Vector v1, Vector v2) |
| 40 |
|
|
{ |
| 41 |
|
|
if (v1[X] == v2[X] && v1[Y] == v2[Y] && v1[Z] == v2[Z]) |
| 42 |
|
|
return 1; |
| 43 |
|
|
else |
| 44 |
|
|
return 0; |
| 45 |
|
|
} |
| 46 |
|
|
|
| 47 |
|
|
|
| 48 |
|
|
void vect_add (Vector v1, Vector v2, Vector v3) |
| 49 |
|
|
{ |
| 50 |
|
|
v1[X] = v2[X] + v3[X]; |
| 51 |
|
|
v1[Y] = v2[Y] + v3[Y]; |
| 52 |
|
|
v1[Z] = v2[Z] + v3[Z]; |
| 53 |
|
|
} |
| 54 |
|
|
|
| 55 |
|
|
|
| 56 |
|
|
void vect_sub (Vector v1, Vector v2, Vector v3) |
| 57 |
|
|
{ |
| 58 |
|
|
v1[X] = v2[X] - v3[X]; |
| 59 |
|
|
v1[Y] = v2[Y] - v3[Y]; |
| 60 |
|
|
v1[Z] = v2[Z] - v3[Z]; |
| 61 |
|
|
} |
| 62 |
|
|
|
| 63 |
|
|
|
| 64 |
|
|
void vect_scale (Vector v1, Vector v2, float k) |
| 65 |
|
|
{ |
| 66 |
|
|
v1[X] = k * v2[X]; |
| 67 |
|
|
v1[Y] = k * v2[Y]; |
| 68 |
|
|
v1[Z] = k * v2[Z]; |
| 69 |
|
|
} |
| 70 |
|
|
|
| 71 |
|
|
|
| 72 |
|
|
float vect_mag (Vector v) |
| 73 |
|
|
{ |
| 74 |
|
|
float mag = sqrt(v[X]*v[X] + v[Y]*v[Y] + v[Z]*v[Z]); |
| 75 |
|
|
|
| 76 |
|
|
return mag; |
| 77 |
|
|
} |
| 78 |
|
|
|
| 79 |
|
|
|
| 80 |
|
|
void vect_normalize (Vector v) |
| 81 |
|
|
{ |
| 82 |
|
|
float mag = vect_mag (v); |
| 83 |
|
|
|
| 84 |
|
|
if (mag > 0.0) |
| 85 |
|
|
vect_scale (v, v, 1.0/mag); |
| 86 |
|
|
} |
| 87 |
|
|
|
| 88 |
|
|
|
| 89 |
|
|
float vect_dot (Vector v1, Vector v2) |
| 90 |
|
|
{ |
| 91 |
|
|
return (v1[X]*v2[X] + v1[Y]*v2[Y] + v1[Z]*v2[Z]); |
| 92 |
|
|
} |
| 93 |
|
|
|
| 94 |
|
|
|
| 95 |
|
|
void vect_cross (Vector v1, Vector v2, Vector v3) |
| 96 |
|
|
{ |
| 97 |
|
|
v1[X] = (v2[Y] * v3[Z]) - (v2[Z] * v3[Y]); |
| 98 |
|
|
v1[Y] = (v2[Z] * v3[X]) - (v2[X] * v3[Z]); |
| 99 |
|
|
v1[Z] = (v2[X] * v3[Y]) - (v2[Y] * v3[X]); |
| 100 |
|
|
} |
| 101 |
|
|
|
| 102 |
|
|
void vect_min (Vector v1, Vector v2, Vector v3) |
| 103 |
|
|
{ |
| 104 |
|
|
v1[X] = (v2[X] < v3[X]) ? v2[X] : v3[X]; |
| 105 |
|
|
v1[Y] = (v2[Y] < v3[Y]) ? v2[Y] : v3[Y]; |
| 106 |
|
|
v1[Z] = (v2[Z] < v3[Z]) ? v2[Z] : v3[Z]; |
| 107 |
|
|
} |
| 108 |
|
|
|
| 109 |
|
|
|
| 110 |
|
|
void vect_max (Vector v1, Vector v2, Vector v3) |
| 111 |
|
|
{ |
| 112 |
|
|
v1[X] = (v2[X] > v3[X]) ? v2[X] : v3[X]; |
| 113 |
|
|
v1[Y] = (v2[Y] > v3[Y]) ? v2[Y] : v3[Y]; |
| 114 |
|
|
v1[Z] = (v2[Z] > v3[Z]) ? v2[Z] : v3[Z]; |
| 115 |
|
|
} |
| 116 |
|
|
|
| 117 |
|
|
|
| 118 |
|
|
/* Return the angle between two vectors */ |
| 119 |
|
|
float vect_angle (Vector v1, Vector v2) |
| 120 |
|
|
{ |
| 121 |
|
|
float mag1, mag2, angle, cos_theta; |
| 122 |
|
|
|
| 123 |
|
|
mag1 = vect_mag(v1); |
| 124 |
|
|
mag2 = vect_mag(v2); |
| 125 |
|
|
|
| 126 |
|
|
if (mag1 * mag2 == 0.0) |
| 127 |
|
|
angle = 0.0; |
| 128 |
|
|
else { |
| 129 |
|
|
cos_theta = vect_dot(v1,v2) / (mag1 * mag2); |
| 130 |
|
|
|
| 131 |
|
|
if (cos_theta <= -1.0) |
| 132 |
|
|
angle = 180.0; |
| 133 |
|
|
else if (cos_theta >= +1.0) |
| 134 |
|
|
angle = 0.0; |
| 135 |
|
|
else |
| 136 |
gregl |
1.2 |
angle = (180.0/PI) * acos(cos_theta); |
| 137 |
greg |
1.1 |
} |
| 138 |
|
|
|
| 139 |
|
|
return angle; |
| 140 |
|
|
} |
| 141 |
|
|
|
| 142 |
|
|
|
| 143 |
|
|
void vect_print (FILE *f, Vector v, int dec, char sep) |
| 144 |
|
|
{ |
| 145 |
|
|
char fstr[] = "%.4f, %.4f, %.4f"; |
| 146 |
|
|
|
| 147 |
|
|
if (dec < 0) dec = 0; |
| 148 |
|
|
if (dec > 9) dec = 9; |
| 149 |
|
|
|
| 150 |
|
|
fstr[2] = '0' + dec; |
| 151 |
|
|
fstr[8] = '0' + dec; |
| 152 |
|
|
fstr[14] = '0' + dec; |
| 153 |
|
|
|
| 154 |
|
|
fstr[4] = sep; |
| 155 |
|
|
fstr[10] = sep; |
| 156 |
|
|
|
| 157 |
|
|
fprintf (f, fstr, v[X], v[Y], v[Z]); |
| 158 |
|
|
} |
| 159 |
|
|
|
| 160 |
|
|
|
| 161 |
|
|
/* Rotate a vector about the X, Y or Z axis */ |
| 162 |
|
|
void vect_rotate (Vector v1, Vector v2, int axis, float angle) |
| 163 |
|
|
{ |
| 164 |
|
|
float cosa, sina; |
| 165 |
|
|
|
| 166 |
gregl |
1.2 |
cosa = cos ((PI/180.0) * angle); |
| 167 |
|
|
sina = sin ((PI/180.0) * angle); |
| 168 |
greg |
1.1 |
|
| 169 |
|
|
switch (axis) { |
| 170 |
|
|
case X: |
| 171 |
|
|
v1[X] = v2[X]; |
| 172 |
|
|
v1[Y] = v2[Y] * cosa + v2[Z] * sina; |
| 173 |
|
|
v1[Z] = v2[Z] * cosa - v2[Y] * sina; |
| 174 |
|
|
break; |
| 175 |
|
|
|
| 176 |
|
|
case Y: |
| 177 |
|
|
v1[X] = v2[X] * cosa - v2[Z] * sina; |
| 178 |
|
|
v1[Y] = v2[Y]; |
| 179 |
|
|
v1[Z] = v2[Z] * cosa + v2[X] * sina; |
| 180 |
|
|
break; |
| 181 |
|
|
|
| 182 |
|
|
case Z: |
| 183 |
|
|
v1[X] = v2[X] * cosa + v2[Y] * sina; |
| 184 |
|
|
v1[Y] = v2[Y] * cosa - v2[X] * sina; |
| 185 |
|
|
v1[Z] = v2[Z]; |
| 186 |
|
|
break; |
| 187 |
|
|
} |
| 188 |
|
|
} |
| 189 |
|
|
|
| 190 |
|
|
|
| 191 |
|
|
/* Rotate a vector about a specific axis */ |
| 192 |
|
|
void vect_axis_rotate (Vector v1, Vector v2, Vector axis, float angle) |
| 193 |
|
|
{ |
| 194 |
|
|
float cosa, sina; |
| 195 |
|
|
Matrix mat; |
| 196 |
|
|
|
| 197 |
gregl |
1.2 |
cosa = cos ((PI/180.0) * angle); |
| 198 |
|
|
sina = sin ((PI/180.0) * angle); |
| 199 |
greg |
1.1 |
|
| 200 |
|
|
mat[0][0] = (axis[X] * axis[X]) + ((1.0 - (axis[X] * axis[X]))*cosa); |
| 201 |
|
|
mat[0][1] = (axis[X] * axis[Y] * (1.0 - cosa)) - (axis[Z] * sina); |
| 202 |
|
|
mat[0][2] = (axis[X] * axis[Z] * (1.0 - cosa)) + (axis[Y] * sina); |
| 203 |
|
|
mat[0][3] = 0.0; |
| 204 |
|
|
|
| 205 |
|
|
mat[1][0] = (axis[X] * axis[Y] * (1.0 - cosa)) + (axis[Z] * sina); |
| 206 |
|
|
mat[1][1] = (axis[Y] * axis[Y]) + ((1.0 - (axis[Y] * axis[Y])) * cosa); |
| 207 |
|
|
mat[1][2] = (axis[Y] * axis[Z] * (1.0 - cosa)) - (axis[X] * sina); |
| 208 |
|
|
mat[1][3] = 0.0; |
| 209 |
|
|
|
| 210 |
|
|
mat[2][0] = (axis[X] * axis[Z] * (1.0 - cosa)) - (axis[Y] * sina); |
| 211 |
|
|
mat[2][1] = (axis[Y] * axis[Z] * (1.0 - cosa)) + (axis[X] * sina); |
| 212 |
|
|
mat[2][2] = (axis[Z] * axis[Z]) + ((1.0 - (axis[Z] * axis[Z])) * cosa); |
| 213 |
|
|
mat[2][3] = 0.0; |
| 214 |
|
|
|
| 215 |
|
|
mat[3][0] = mat[3][1] = mat[3][2] = mat[3][3] = 0.0; |
| 216 |
|
|
|
| 217 |
|
|
vect_transform (v1, v2, mat); |
| 218 |
|
|
} |
| 219 |
|
|
|
| 220 |
|
|
|
| 221 |
|
|
/* Transform the given vector */ |
| 222 |
|
|
void vect_transform (Vector v1, Vector v2, Matrix mat) |
| 223 |
|
|
{ |
| 224 |
|
|
Vector tmp; |
| 225 |
|
|
|
| 226 |
|
|
tmp[X] = (v2[X] * mat[0][0]) + (v2[Y] * mat[1][0]) + (v2[Z] * mat[2][0]) + mat[3][0]; |
| 227 |
|
|
tmp[Y] = (v2[X] * mat[0][1]) + (v2[Y] * mat[1][1]) + (v2[Z] * mat[2][1]) + mat[3][1]; |
| 228 |
|
|
tmp[Z] = (v2[X] * mat[0][2]) + (v2[Y] * mat[1][2]) + (v2[Z] * mat[2][2]) + mat[3][2]; |
| 229 |
|
|
|
| 230 |
|
|
vect_copy (v1, tmp); |
| 231 |
|
|
} |
| 232 |
|
|
|
| 233 |
|
|
|
| 234 |
|
|
/* Create an identity matrix */ |
| 235 |
|
|
void mat_identity (Matrix mat) |
| 236 |
|
|
{ |
| 237 |
|
|
int i, j; |
| 238 |
|
|
|
| 239 |
|
|
for (i = 0; i < 4; i++) |
| 240 |
|
|
for (j = 0; j < 4; j++) |
| 241 |
|
|
mat[i][j] = 0.0; |
| 242 |
|
|
|
| 243 |
|
|
for (i = 0; i < 4; i++) |
| 244 |
|
|
mat[i][i] = 1.0; |
| 245 |
|
|
} |
| 246 |
|
|
|
| 247 |
|
|
|
| 248 |
|
|
void mat_copy (Matrix mat1, Matrix mat2) |
| 249 |
|
|
{ |
| 250 |
|
|
int i, j; |
| 251 |
|
|
|
| 252 |
|
|
for (i = 0; i < 4; i++) |
| 253 |
|
|
for (j = 0; j < 4; j++) |
| 254 |
|
|
mat1[i][j] = mat2[i][j]; |
| 255 |
|
|
} |
| 256 |
|
|
|
| 257 |
|
|
|
| 258 |
|
|
/* Rotate a matrix about the X, Y or Z axis */ |
| 259 |
|
|
void mat_rotate (Matrix mat1, Matrix mat2, int axis, float angle) |
| 260 |
|
|
{ |
| 261 |
|
|
Matrix mat; |
| 262 |
|
|
float cosa, sina; |
| 263 |
|
|
|
| 264 |
gregl |
1.2 |
cosa = cos ((PI/180.0) * angle); |
| 265 |
|
|
sina = sin ((PI/180.0) * angle); |
| 266 |
greg |
1.1 |
|
| 267 |
|
|
mat_identity (mat); |
| 268 |
|
|
|
| 269 |
|
|
switch (axis) { |
| 270 |
|
|
case X: |
| 271 |
|
|
mat[1][1] = cosa; |
| 272 |
|
|
mat[1][2] = sina; |
| 273 |
|
|
mat[2][1] = -sina; |
| 274 |
|
|
mat[2][2] = cosa; |
| 275 |
|
|
break; |
| 276 |
|
|
|
| 277 |
|
|
case Y: |
| 278 |
|
|
mat[0][0] = cosa; |
| 279 |
|
|
mat[0][2] = -sina; |
| 280 |
|
|
mat[2][0] = sina; |
| 281 |
|
|
mat[2][2] = cosa; |
| 282 |
|
|
break; |
| 283 |
|
|
|
| 284 |
|
|
case Z: |
| 285 |
|
|
mat[0][0] = cosa; |
| 286 |
|
|
mat[0][1] = sina; |
| 287 |
|
|
mat[1][0] = -sina; |
| 288 |
|
|
mat[1][1] = cosa; |
| 289 |
|
|
break; |
| 290 |
|
|
} |
| 291 |
|
|
|
| 292 |
|
|
mat_mult (mat1, mat2, mat); |
| 293 |
|
|
} |
| 294 |
|
|
|
| 295 |
|
|
|
| 296 |
|
|
void mat_axis_rotate (Matrix mat1, Matrix mat2, Vector axis, float angle) |
| 297 |
|
|
{ |
| 298 |
|
|
float cosa, sina; |
| 299 |
|
|
Matrix mat; |
| 300 |
|
|
|
| 301 |
gregl |
1.2 |
cosa = cos ((PI/180.0) * angle); |
| 302 |
|
|
sina = sin ((PI/180.0) * angle); |
| 303 |
greg |
1.1 |
|
| 304 |
|
|
mat[0][0] = (axis[X] * axis[X]) + ((1.0 - (axis[X] * axis[X]))*cosa); |
| 305 |
|
|
mat[0][1] = (axis[X] * axis[Y] * (1.0 - cosa)) - (axis[Z] * sina); |
| 306 |
|
|
mat[0][2] = (axis[X] * axis[Z] * (1.0 - cosa)) + (axis[Y] * sina); |
| 307 |
|
|
mat[0][3] = 0.0; |
| 308 |
|
|
|
| 309 |
|
|
mat[1][0] = (axis[X] * axis[Y] * (1.0 - cosa)) + (axis[Z] * sina); |
| 310 |
|
|
mat[1][1] = (axis[Y] * axis[Y]) + ((1.0 - (axis[Y] * axis[Y])) * cosa); |
| 311 |
|
|
mat[1][2] = (axis[Y] * axis[Z] * (1.0 - cosa)) - (axis[X] * sina); |
| 312 |
|
|
mat[1][3] = 0.0; |
| 313 |
|
|
|
| 314 |
|
|
mat[2][0] = (axis[X] * axis[Z] * (1.0 - cosa)) - (axis[Y] * sina); |
| 315 |
|
|
mat[2][1] = (axis[Y] * axis[Z] * (1.0 - cosa)) + (axis[X] * sina); |
| 316 |
|
|
mat[2][2] = (axis[Z] * axis[Z]) + ((1.0 - (axis[Z] * axis[Z])) * cosa); |
| 317 |
|
|
mat[2][3] = 0.0; |
| 318 |
|
|
|
| 319 |
|
|
mat[3][0] = mat[3][1] = mat[3][2] = mat[3][3] = 0.0; |
| 320 |
|
|
|
| 321 |
|
|
mat_mult (mat1, mat2, mat); |
| 322 |
|
|
} |
| 323 |
|
|
|
| 324 |
|
|
|
| 325 |
|
|
/* mat1 <-- mat2 * mat3 */ |
| 326 |
|
|
void mat_mult (Matrix mat1, Matrix mat2, Matrix mat3) |
| 327 |
|
|
{ |
| 328 |
|
|
float sum; |
| 329 |
|
|
int i, j, k; |
| 330 |
|
|
Matrix result; |
| 331 |
|
|
|
| 332 |
|
|
for (i = 0; i < 4; i++) { |
| 333 |
|
|
for (j = 0; j < 4; j++) { |
| 334 |
|
|
sum = 0.0; |
| 335 |
|
|
|
| 336 |
|
|
for (k = 0; k < 4; k++) |
| 337 |
|
|
sum = sum + mat2[i][k] * mat3[k][j]; |
| 338 |
|
|
|
| 339 |
|
|
result[i][j] = sum; |
| 340 |
|
|
} |
| 341 |
|
|
} |
| 342 |
|
|
|
| 343 |
|
|
for (i = 0; i < 4; i++) |
| 344 |
|
|
for (j = 0; j < 4; j++) |
| 345 |
|
|
mat1[i][j] = result[i][j]; |
| 346 |
|
|
} |
| 347 |
|
|
|
| 348 |
|
|
|
| 349 |
|
|
/* |
| 350 |
|
|
Decodes a 3x4 transformation matrix into separate scale, rotation, |
| 351 |
|
|
translation, and shear vectors. Based on a program by Spencer W. |
| 352 |
|
|
Thomas (Graphics Gems II) |
| 353 |
|
|
*/ |
| 354 |
|
|
void mat_decode (Matrix mat, Vector scale, Vector shear, Vector rotate, |
| 355 |
|
|
Vector transl) |
| 356 |
|
|
{ |
| 357 |
|
|
int i; |
| 358 |
|
|
Vector row[3], temp; |
| 359 |
|
|
|
| 360 |
|
|
for (i = 0; i < 3; i++) |
| 361 |
|
|
transl[i] = mat[3][i]; |
| 362 |
|
|
|
| 363 |
|
|
for (i = 0; i < 3; i++) { |
| 364 |
|
|
row[i][X] = mat[i][0]; |
| 365 |
|
|
row[i][Y] = mat[i][1]; |
| 366 |
|
|
row[i][Z] = mat[i][2]; |
| 367 |
|
|
} |
| 368 |
|
|
|
| 369 |
|
|
scale[X] = vect_mag (row[0]); |
| 370 |
|
|
vect_normalize (row[0]); |
| 371 |
|
|
|
| 372 |
|
|
shear[X] = vect_dot (row[0], row[1]); |
| 373 |
|
|
row[1][X] = row[1][X] - shear[X]*row[0][X]; |
| 374 |
|
|
row[1][Y] = row[1][Y] - shear[X]*row[0][Y]; |
| 375 |
|
|
row[1][Z] = row[1][Z] - shear[X]*row[0][Z]; |
| 376 |
|
|
|
| 377 |
|
|
scale[Y] = vect_mag (row[1]); |
| 378 |
|
|
vect_normalize (row[1]); |
| 379 |
|
|
|
| 380 |
|
|
if (scale[Y] != 0.0) |
| 381 |
|
|
shear[X] /= scale[Y]; |
| 382 |
|
|
|
| 383 |
|
|
shear[Y] = vect_dot (row[0], row[2]); |
| 384 |
|
|
row[2][X] = row[2][X] - shear[Y]*row[0][X]; |
| 385 |
|
|
row[2][Y] = row[2][Y] - shear[Y]*row[0][Y]; |
| 386 |
|
|
row[2][Z] = row[2][Z] - shear[Y]*row[0][Z]; |
| 387 |
|
|
|
| 388 |
|
|
shear[Z] = vect_dot (row[1], row[2]); |
| 389 |
|
|
row[2][X] = row[2][X] - shear[Z]*row[1][X]; |
| 390 |
|
|
row[2][Y] = row[2][Y] - shear[Z]*row[1][Y]; |
| 391 |
|
|
row[2][Z] = row[2][Z] - shear[Z]*row[1][Z]; |
| 392 |
|
|
|
| 393 |
|
|
scale[Z] = vect_mag (row[2]); |
| 394 |
|
|
vect_normalize (row[2]); |
| 395 |
|
|
|
| 396 |
|
|
if (scale[Z] != 0.0) { |
| 397 |
|
|
shear[Y] /= scale[Z]; |
| 398 |
|
|
shear[Z] /= scale[Z]; |
| 399 |
|
|
} |
| 400 |
|
|
|
| 401 |
|
|
vect_cross (temp, row[1], row[2]); |
| 402 |
|
|
if (vect_dot (row[0], temp) < 0.0) { |
| 403 |
|
|
for (i = 0; i < 3; i++) { |
| 404 |
|
|
scale[i] *= -1.0; |
| 405 |
|
|
row[i][X] *= -1.0; |
| 406 |
|
|
row[i][Y] *= -1.0; |
| 407 |
|
|
row[i][Z] *= -1.0; |
| 408 |
|
|
} |
| 409 |
|
|
} |
| 410 |
|
|
|
| 411 |
|
|
if (row[0][Z] < -1.0) row[0][Z] = -1.0; |
| 412 |
|
|
if (row[0][Z] > +1.0) row[0][Z] = +1.0; |
| 413 |
|
|
|
| 414 |
|
|
rotate[Y] = asin(-row[0][Z]); |
| 415 |
|
|
|
| 416 |
|
|
if (fabs(cos(rotate[Y])) > EPSILON) { |
| 417 |
|
|
rotate[X] = atan2 (row[1][Z], row[2][Z]); |
| 418 |
|
|
rotate[Z] = atan2 (row[0][Y], row[0][X]); |
| 419 |
|
|
} |
| 420 |
|
|
else { |
| 421 |
|
|
rotate[X] = atan2 (row[1][X], row[1][Y]); |
| 422 |
|
|
rotate[Z] = 0.0; |
| 423 |
|
|
} |
| 424 |
|
|
|
| 425 |
|
|
/* Convert the rotations to degrees */ |
| 426 |
gregl |
1.2 |
rotate[X] = (180.0/PI)*rotate[X]; |
| 427 |
|
|
rotate[Y] = (180.0/PI)*rotate[Y]; |
| 428 |
|
|
rotate[Z] = (180.0/PI)*rotate[Z]; |
| 429 |
greg |
1.1 |
} |
| 430 |
|
|
|
| 431 |
|
|
|
| 432 |
|
|
/* Matrix inversion code from Graphics Gems */ |
| 433 |
|
|
|
| 434 |
|
|
/* mat1 <-- mat2^-1 */ |
| 435 |
|
|
float mat_inv (Matrix mat1, Matrix mat2) |
| 436 |
|
|
{ |
| 437 |
|
|
int i, j; |
| 438 |
|
|
float det; |
| 439 |
|
|
|
| 440 |
|
|
if (mat1 != mat2) { |
| 441 |
|
|
for (i = 0; i < 4; i++) |
| 442 |
|
|
for (j = 0; j < 4; j++) |
| 443 |
|
|
mat1[i][j] = mat2[i][j]; |
| 444 |
|
|
} |
| 445 |
|
|
|
| 446 |
|
|
det = det4x4 (mat1); |
| 447 |
|
|
|
| 448 |
|
|
if (fabs (det) < EPSILON) |
| 449 |
|
|
return 0.0; |
| 450 |
|
|
|
| 451 |
|
|
adjoint (mat1); |
| 452 |
|
|
|
| 453 |
|
|
for (i = 0; i < 4; i++) |
| 454 |
|
|
for(j = 0; j < 4; j++) |
| 455 |
|
|
mat1[i][j] = mat1[i][j] / det; |
| 456 |
|
|
|
| 457 |
|
|
return det; |
| 458 |
|
|
} |
| 459 |
|
|
|
| 460 |
|
|
|
| 461 |
|
|
void adjoint (Matrix mat) |
| 462 |
|
|
{ |
| 463 |
|
|
double a1, a2, a3, a4, b1, b2, b3, b4; |
| 464 |
|
|
double c1, c2, c3, c4, d1, d2, d3, d4; |
| 465 |
|
|
|
| 466 |
|
|
a1 = mat[0][0]; b1 = mat[0][1]; |
| 467 |
|
|
c1 = mat[0][2]; d1 = mat[0][3]; |
| 468 |
|
|
|
| 469 |
|
|
a2 = mat[1][0]; b2 = mat[1][1]; |
| 470 |
|
|
c2 = mat[1][2]; d2 = mat[1][3]; |
| 471 |
|
|
|
| 472 |
|
|
a3 = mat[2][0]; b3 = mat[2][1]; |
| 473 |
|
|
c3 = mat[2][2]; d3 = mat[2][3]; |
| 474 |
|
|
|
| 475 |
|
|
a4 = mat[3][0]; b4 = mat[3][1]; |
| 476 |
|
|
c4 = mat[3][2]; d4 = mat[3][3]; |
| 477 |
|
|
|
| 478 |
|
|
/* row column labeling reversed since we transpose rows & columns */ |
| 479 |
|
|
mat[0][0] = det3x3 (b2, b3, b4, c2, c3, c4, d2, d3, d4); |
| 480 |
|
|
mat[1][0] = -det3x3 (a2, a3, a4, c2, c3, c4, d2, d3, d4); |
| 481 |
|
|
mat[2][0] = det3x3 (a2, a3, a4, b2, b3, b4, d2, d3, d4); |
| 482 |
|
|
mat[3][0] = -det3x3 (a2, a3, a4, b2, b3, b4, c2, c3, c4); |
| 483 |
|
|
|
| 484 |
|
|
mat[0][1] = -det3x3 (b1, b3, b4, c1, c3, c4, d1, d3, d4); |
| 485 |
|
|
mat[1][1] = det3x3 (a1, a3, a4, c1, c3, c4, d1, d3, d4); |
| 486 |
|
|
mat[2][1] = -det3x3 (a1, a3, a4, b1, b3, b4, d1, d3, d4); |
| 487 |
|
|
mat[3][1] = det3x3 (a1, a3, a4, b1, b3, b4, c1, c3, c4); |
| 488 |
|
|
|
| 489 |
|
|
mat[0][2] = det3x3 (b1, b2, b4, c1, c2, c4, d1, d2, d4); |
| 490 |
|
|
mat[1][2] = -det3x3 (a1, a2, a4, c1, c2, c4, d1, d2, d4); |
| 491 |
|
|
mat[2][2] = det3x3 (a1, a2, a4, b1, b2, b4, d1, d2, d4); |
| 492 |
|
|
mat[3][2] = -det3x3 (a1, a2, a4, b1, b2, b4, c1, c2, c4); |
| 493 |
|
|
|
| 494 |
|
|
mat[0][3] = -det3x3 (b1, b2, b3, c1, c2, c3, d1, d2, d3); |
| 495 |
|
|
mat[1][3] = det3x3 (a1, a2, a3, c1, c2, c3, d1, d2, d3); |
| 496 |
|
|
mat[2][3] = -det3x3 (a1, a2, a3, b1, b2, b3, d1, d2, d3); |
| 497 |
|
|
mat[3][3] = det3x3 (a1, a2, a3, b1, b2, b3, c1, c2, c3); |
| 498 |
|
|
} |
| 499 |
|
|
|
| 500 |
|
|
|
| 501 |
|
|
double det4x4 (Matrix mat) |
| 502 |
|
|
{ |
| 503 |
|
|
double ans; |
| 504 |
|
|
double a1, a2, a3, a4, b1, b2, b3, b4, c1, c2, c3, c4, d1, d2, d3, d4; |
| 505 |
|
|
|
| 506 |
|
|
a1 = mat[0][0]; b1 = mat[0][1]; |
| 507 |
|
|
c1 = mat[0][2]; d1 = mat[0][3]; |
| 508 |
|
|
|
| 509 |
|
|
a2 = mat[1][0]; b2 = mat[1][1]; |
| 510 |
|
|
c2 = mat[1][2]; d2 = mat[1][3]; |
| 511 |
|
|
|
| 512 |
|
|
a3 = mat[2][0]; b3 = mat[2][1]; |
| 513 |
|
|
c3 = mat[2][2]; d3 = mat[2][3]; |
| 514 |
|
|
|
| 515 |
|
|
a4 = mat[3][0]; b4 = mat[3][1]; |
| 516 |
|
|
c4 = mat[3][2]; d4 = mat[3][3]; |
| 517 |
|
|
|
| 518 |
|
|
ans = a1 * det3x3 (b2, b3, b4, c2, c3, c4, d2, d3, d4) - |
| 519 |
|
|
b1 * det3x3 (a2, a3, a4, c2, c3, c4, d2, d3, d4) + |
| 520 |
|
|
c1 * det3x3 (a2, a3, a4, b2, b3, b4, d2, d3, d4) - |
| 521 |
|
|
d1 * det3x3 (a2, a3, a4, b2, b3, b4, c2, c3, c4); |
| 522 |
|
|
|
| 523 |
|
|
return ans; |
| 524 |
|
|
} |
| 525 |
|
|
|
| 526 |
|
|
|
| 527 |
|
|
double det3x3 (double a1, double a2, double a3, double b1, double b2, |
| 528 |
|
|
double b3, double c1, double c2, double c3) |
| 529 |
|
|
{ |
| 530 |
|
|
double ans; |
| 531 |
|
|
|
| 532 |
|
|
ans = a1 * det2x2 (b2, b3, c2, c3) |
| 533 |
|
|
- b1 * det2x2 (a2, a3, c2, c3) |
| 534 |
|
|
+ c1 * det2x2 (a2, a3, b2, b3); |
| 535 |
|
|
|
| 536 |
|
|
return ans; |
| 537 |
|
|
} |
| 538 |
|
|
|
| 539 |
|
|
|
| 540 |
|
|
double det2x2 (double a, double b, double c, double d) |
| 541 |
|
|
{ |
| 542 |
|
|
double ans; |
| 543 |
|
|
ans = a * d - b * c; |
| 544 |
|
|
return ans; |
| 545 |
|
|
} |
| 546 |
|
|
|
