Austin Schuh | 3333ec7 | 2022-12-29 16:21:06 -0800 | [diff] [blame^] | 1 | /* Copyright (C) 2013-2016, The Regents of The University of Michigan. |
| 2 | All rights reserved. |
| 3 | This software was developed in the APRIL Robotics Lab under the |
| 4 | direction of Edwin Olson, ebolson@umich.edu. This software may be |
| 5 | available under alternative licensing terms; contact the address above. |
| 6 | Redistribution and use in source and binary forms, with or without |
| 7 | modification, are permitted provided that the following conditions are met: |
| 8 | 1. Redistributions of source code must retain the above copyright notice, this |
| 9 | list of conditions and the following disclaimer. |
| 10 | 2. Redistributions in binary form must reproduce the above copyright notice, |
| 11 | this list of conditions and the following disclaimer in the documentation |
| 12 | and/or other materials provided with the distribution. |
| 13 | THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND |
| 14 | ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED |
| 15 | WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE |
| 16 | DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR |
| 17 | ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES |
| 18 | (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| 19 | LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND |
| 20 | ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| 21 | (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| 22 | SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| 23 | The views and conclusions contained in the software and documentation are those |
| 24 | of the authors and should not be interpreted as representing official policies, |
| 25 | either expressed or implied, of the Regents of The University of Michigan. |
| 26 | */ |
| 27 | |
| 28 | #include <stdio.h> |
| 29 | #include <math.h> |
| 30 | #include <string.h> |
| 31 | #include <float.h> |
| 32 | |
| 33 | #include "matd.h" |
| 34 | #include "math_util.h" |
| 35 | |
| 36 | // XXX Write unit tests for me! |
| 37 | // XXX Rewrite matd_coords in terms of this. |
| 38 | |
| 39 | /* |
| 40 | This file provides conversions between the following formats: |
| 41 | |
| 42 | quaternion (TNAME[4], { w, x, y, z}) |
| 43 | |
| 44 | xyt (translation in x, y, and rotation in radians.) |
| 45 | |
| 46 | xytcov (xyt as a TNAME[3] followed by covariance TNAME[9]) |
| 47 | |
| 48 | xy, xyz (translation in x, y, and z) |
| 49 | |
| 50 | mat44 (4x4 rigid-body transformation matrix, row-major |
| 51 | order. Conventions: We assume points are projected via right |
| 52 | multiplication. E.g., p' = Mp.) Note: some functions really do rely |
| 53 | on it being a RIGID, scale=1 transform. |
| 54 | |
| 55 | angleaxis (TNAME[4], { angle-rads, x, y, z } |
| 56 | |
| 57 | xyzrpy (translation x, y, z, euler angles) |
| 58 | |
| 59 | Roll Pitch Yaw are evaluated in the order: roll, pitch, then yaw. I.e., |
| 60 | rollPitchYawToMatrix(rpy) = rotateZ(rpy[2]) * rotateY(rpy[1]) * Rotatex(rpy[0]) |
| 61 | */ |
| 62 | |
| 63 | #define TRRFN(root, suffix) root ## suffix |
| 64 | #define TRFN(root, suffix) TRRFN(root, suffix) |
| 65 | #define TFN(suffix) TRFN(TNAME, suffix) |
| 66 | |
| 67 | // if V is null, returns null. |
| 68 | static inline TNAME *TFN(s_dup)(const TNAME *v, int len) |
| 69 | { |
| 70 | if (!v) |
| 71 | return NULL; |
| 72 | |
| 73 | TNAME *r = (TNAME*)malloc(len * sizeof(TNAME)); |
| 74 | memcpy(r, v, len * sizeof(TNAME)); |
| 75 | return r; |
| 76 | } |
| 77 | |
| 78 | static inline void TFN(s_print)(const TNAME *a, int len, const char *fmt) |
| 79 | { |
| 80 | for (int i = 0; i < len; i++) |
| 81 | printf(fmt, a[i]); |
| 82 | printf("\n"); |
| 83 | } |
| 84 | |
| 85 | static inline void TFN(s_print_mat)(const TNAME *a, int nrows, int ncols, const char *fmt) |
| 86 | { |
| 87 | for (int i = 0; i < nrows * ncols; i++) { |
| 88 | printf(fmt, a[i]); |
| 89 | if ((i % ncols) == (ncols - 1)) |
| 90 | printf("\n"); |
| 91 | } |
| 92 | } |
| 93 | |
| 94 | static inline void TFN(s_print_mat44)(const TNAME *a, const char *fmt) |
| 95 | { |
| 96 | for (int i = 0; i < 4 * 4; i++) { |
| 97 | printf(fmt, a[i]); |
| 98 | if ((i % 4) == 3) |
| 99 | printf("\n"); |
| 100 | } |
| 101 | } |
| 102 | |
| 103 | static inline void TFN(s_add)(const TNAME *a, const TNAME *b, int len, TNAME *r) |
| 104 | { |
| 105 | for (int i = 0; i < len; i++) |
| 106 | r[i] = a[i] + b[i]; |
| 107 | } |
| 108 | |
| 109 | static inline void TFN(s_subtract)(const TNAME *a, const TNAME *b, int len, TNAME *r) |
| 110 | { |
| 111 | for (int i = 0; i < len; i++) |
| 112 | r[i] = a[i] - b[i]; |
| 113 | } |
| 114 | |
| 115 | static inline void TFN(s_scale)(TNAME s, const TNAME *v, int len, TNAME *r) |
| 116 | { |
| 117 | for (int i = 0; i < len; i++) |
| 118 | r[i] = s * v[i]; |
| 119 | } |
| 120 | |
| 121 | static inline TNAME TFN(s_dot)(const TNAME *a, const TNAME *b, int len) |
| 122 | { |
| 123 | TNAME acc = 0; |
| 124 | for (int i = 0; i < len; i++) |
| 125 | acc += a[i] * b[i]; |
| 126 | return acc; |
| 127 | } |
| 128 | |
| 129 | static inline TNAME TFN(s_distance)(const TNAME *a, const TNAME *b, int len) |
| 130 | { |
| 131 | TNAME acc = 0; |
| 132 | for (int i = 0; i < len; i++) |
| 133 | acc += (a[i] - b[i])*(a[i] - b[i]); |
| 134 | return (TNAME)sqrt(acc); |
| 135 | } |
| 136 | |
| 137 | static inline TNAME TFN(s_squared_distance)(const TNAME *a, const TNAME *b, int len) |
| 138 | { |
| 139 | TNAME acc = 0; |
| 140 | for (int i = 0; i < len; i++) |
| 141 | acc += (a[i] - b[i])*(a[i] - b[i]); |
| 142 | return acc; |
| 143 | } |
| 144 | |
| 145 | static inline TNAME TFN(s_squared_magnitude)(const TNAME *v, int len) |
| 146 | { |
| 147 | TNAME acc = 0; |
| 148 | for (int i = 0; i < len; i++) |
| 149 | acc += v[i]*v[i]; |
| 150 | return acc; |
| 151 | } |
| 152 | |
| 153 | static inline TNAME TFN(s_magnitude)(const TNAME *v, int len) |
| 154 | { |
| 155 | TNAME acc = 0; |
| 156 | for (int i = 0; i < len; i++) |
| 157 | acc += v[i]*v[i]; |
| 158 | return (TNAME)sqrt(acc); |
| 159 | } |
| 160 | |
| 161 | static inline void TFN(s_normalize)(const TNAME *v, int len, TNAME *r) |
| 162 | { |
| 163 | TNAME mag = TFN(s_magnitude)(v, len); |
| 164 | for (int i = 0; i < len; i++) |
| 165 | r[i] = v[i] / mag; |
| 166 | } |
| 167 | |
| 168 | static inline void TFN(s_normalize_self)(TNAME *v, int len) |
| 169 | { |
| 170 | TNAME mag = TFN(s_magnitude)(v, len); |
| 171 | for (int i = 0; i < len; i++) |
| 172 | v[i] /= mag; |
| 173 | } |
| 174 | |
| 175 | static inline void TFN(s_scale_self)(TNAME *v, int len, double scale) |
| 176 | { |
| 177 | for (int i = 0; i < len; i++) |
| 178 | v[i] = (TNAME)(v[i] * scale); |
| 179 | } |
| 180 | |
| 181 | static inline void TFN(s_quat_rotate)(const TNAME q[4], const TNAME v[3], TNAME r[3]) |
| 182 | { |
| 183 | TNAME t2, t3, t4, t5, t6, t7, t8, t9, t10; |
| 184 | |
| 185 | t2 = q[0]*q[1]; |
| 186 | t3 = q[0]*q[2]; |
| 187 | t4 = q[0]*q[3]; |
| 188 | t5 = -q[1]*q[1]; |
| 189 | t6 = q[1]*q[2]; |
| 190 | t7 = q[1]*q[3]; |
| 191 | t8 = -q[2]*q[2]; |
| 192 | t9 = q[2]*q[3]; |
| 193 | t10 = -q[3]*q[3]; |
| 194 | |
| 195 | r[0] = 2*((t8+t10)*v[0] + (t6-t4)*v[1] + (t3+t7)*v[2]) + v[0]; |
| 196 | r[1] = 2*((t4+t6)*v[0] + (t5+t10)*v[1] + (t9-t2)*v[2]) + v[1]; |
| 197 | r[2] = 2*((t7-t3)*v[0] + (t2+t9)*v[1] + (t5+t8)*v[2]) + v[2]; |
| 198 | } |
| 199 | |
| 200 | static inline void TFN(s_quat_multiply)(const TNAME a[4], const TNAME b[4], TNAME r[4]) |
| 201 | { |
| 202 | r[0] = a[0]*b[0] - a[1]*b[1] - a[2]*b[2] - a[3]*b[3]; |
| 203 | r[1] = a[0]*b[1] + a[1]*b[0] + a[2]*b[3] - a[3]*b[2]; |
| 204 | r[2] = a[0]*b[2] - a[1]*b[3] + a[2]*b[0] + a[3]*b[1]; |
| 205 | r[3] = a[0]*b[3] + a[1]*b[2] - a[2]*b[1] + a[3]*b[0]; |
| 206 | } |
| 207 | |
| 208 | static inline void TFN(s_quat_inverse)(const TNAME q[4], TNAME r[4]) |
| 209 | { |
| 210 | TNAME mag = TFN(s_magnitude)(q, 4); |
| 211 | r[0] = q[0]/mag; |
| 212 | r[1] = -q[1]/mag; |
| 213 | r[2] = -q[2]/mag; |
| 214 | r[3] = -q[3]/mag; |
| 215 | } |
| 216 | |
| 217 | static inline void TFN(s_copy)(const TNAME *src, TNAME *dst, int n) |
| 218 | { |
| 219 | memcpy(dst, src, n * sizeof(TNAME)); |
| 220 | } |
| 221 | |
| 222 | static inline void TFN(s_xyt_copy)(const TNAME xyt[3], TNAME r[3]) |
| 223 | { |
| 224 | TFN(s_copy)(xyt, r, 3); |
| 225 | } |
| 226 | |
| 227 | static inline void TFN(s_xyt_to_mat44)(const TNAME xyt[3], TNAME r[16]) |
| 228 | { |
| 229 | TNAME s = (TNAME)sin(xyt[2]), c = (TNAME)cos(xyt[2]); |
| 230 | memset(r, 0, sizeof(TNAME)*16); |
| 231 | r[0] = c; |
| 232 | r[1] = -s; |
| 233 | r[3] = xyt[0]; |
| 234 | r[4] = s; |
| 235 | r[5] = c; |
| 236 | r[7] = xyt[1]; |
| 237 | r[10] = 1; |
| 238 | r[15] = 1; |
| 239 | } |
| 240 | |
| 241 | static inline void TFN(s_xyt_transform_xy)(const TNAME xyt[3], const TNAME xy[2], TNAME r[2]) |
| 242 | { |
| 243 | TNAME s = (TNAME)sin(xyt[2]), c = (TNAME)cos(xyt[2]); |
| 244 | r[0] = c*xy[0] - s*xy[1] + xyt[0]; |
| 245 | r[1] = s*xy[0] + c*xy[1] + xyt[1]; |
| 246 | } |
| 247 | |
| 248 | static inline void TFN(s_mat_transform_xyz)(const TNAME M[16], const TNAME xyz[3], TNAME r[3]) |
| 249 | { |
| 250 | r[0] = M[0]*xyz[0] + M[1]*xyz[1] + M[2]*xyz[2] + M[3]; |
| 251 | r[1] = M[4]*xyz[0] + M[5]*xyz[1] + M[6]*xyz[2] + M[7]; |
| 252 | r[2] = M[8]*xyz[0] + M[9]*xyz[1] + M[10]*xyz[2] + M[11]; |
| 253 | } |
| 254 | |
| 255 | static inline void TFN(s_quat_to_angleaxis)(const TNAME _q[4], TNAME r[4]) |
| 256 | { |
| 257 | TNAME q[4]; |
| 258 | TFN(s_normalize)(_q, 4, q); |
| 259 | |
| 260 | // be polite: return an angle from [-pi, pi] |
| 261 | // use atan2 to be 4-quadrant safe |
| 262 | TNAME mag = TFN(s_magnitude)(&q[1], 3); |
| 263 | r[0] = (TNAME)mod2pi(2 * atan2(mag, q[0])); |
| 264 | if (mag != 0) { |
| 265 | r[1] = q[1] / mag; |
| 266 | r[2] = q[2] / mag; |
| 267 | r[3] = q[3] / mag; |
| 268 | } else { |
| 269 | r[1] = 1; |
| 270 | r[2] = 0; |
| 271 | r[3] = 0; |
| 272 | } |
| 273 | } |
| 274 | |
| 275 | static inline void TFN(s_angleaxis_to_quat)(const TNAME aa[4], TNAME q[4]) |
| 276 | { |
| 277 | TNAME rad = aa[0]; |
| 278 | q[0] = (TNAME)cos(rad / 2.0); |
| 279 | TNAME s = (TNAME)sin(rad / 2.0); |
| 280 | |
| 281 | TNAME v[3] = { aa[1], aa[2], aa[3] }; |
| 282 | TFN(s_normalize)(v, 3, v); |
| 283 | |
| 284 | q[1] = s * v[0]; |
| 285 | q[2] = s * v[1]; |
| 286 | q[3] = s * v[2]; |
| 287 | } |
| 288 | |
| 289 | static inline void TFN(s_quat_to_mat44)(const TNAME q[4], TNAME r[16]) |
| 290 | { |
| 291 | TNAME w = q[0], x = q[1], y = q[2], z = q[3]; |
| 292 | |
| 293 | r[0] = w*w + x*x - y*y - z*z; |
| 294 | r[1] = 2*x*y - 2*w*z; |
| 295 | r[2] = 2*x*z + 2*w*y; |
| 296 | r[3] = 0; |
| 297 | |
| 298 | r[4] = 2*x*y + 2*w*z; |
| 299 | r[5] = w*w - x*x + y*y - z*z; |
| 300 | r[6] = 2*y*z - 2*w*x; |
| 301 | r[7] = 0; |
| 302 | |
| 303 | r[8] = 2*x*z - 2*w*y; |
| 304 | r[9] = 2*y*z + 2*w*x; |
| 305 | r[10] = w*w - x*x - y*y + z*z; |
| 306 | r[11] = 0; |
| 307 | |
| 308 | r[12] = 0; |
| 309 | r[13] = 0; |
| 310 | r[14] = 0; |
| 311 | r[15] = 1; |
| 312 | } |
| 313 | |
| 314 | /* Returns the skew-symmetric matrix V such that V*w = v x w (cross product). |
| 315 | Sometimes denoted [v]_x or \hat{v}. |
| 316 | [ 0 -v3 v2 |
| 317 | v3 0 -v1 |
| 318 | -v2 v1 0] |
| 319 | */ |
| 320 | static inline void TFN(s_cross_matrix)(const TNAME v[3], TNAME V[9]) |
| 321 | { |
| 322 | V[0] = 0; |
| 323 | V[1] = -v[2]; |
| 324 | V[2] = v[1]; |
| 325 | V[3] = v[2]; |
| 326 | V[4] = 0; |
| 327 | V[5] = -v[0]; |
| 328 | V[6] = -v[1]; |
| 329 | V[7] = v[0]; |
| 330 | V[8] = 0; |
| 331 | } |
| 332 | |
| 333 | static inline void TFN(s_angleaxis_to_mat44)(const TNAME aa[4], TNAME r[16]) |
| 334 | { |
| 335 | TNAME q[4]; |
| 336 | |
| 337 | TFN(s_angleaxis_to_quat)(aa, q); |
| 338 | TFN(s_quat_to_mat44)(q, r); |
| 339 | } |
| 340 | |
| 341 | static inline void TFN(s_quat_xyz_to_mat44)(const TNAME q[4], const TNAME xyz[3], TNAME r[16]) |
| 342 | { |
| 343 | TFN(s_quat_to_mat44)(q, r); |
| 344 | |
| 345 | if (xyz != NULL) { |
| 346 | r[3] = xyz[0]; |
| 347 | r[7] = xyz[1]; |
| 348 | r[11] = xyz[2]; |
| 349 | } |
| 350 | } |
| 351 | |
| 352 | static inline void TFN(s_rpy_to_quat)(const TNAME rpy[3], TNAME quat[4]) |
| 353 | { |
| 354 | TNAME roll = rpy[0], pitch = rpy[1], yaw = rpy[2]; |
| 355 | |
| 356 | TNAME halfroll = roll / 2; |
| 357 | TNAME halfpitch = pitch / 2; |
| 358 | TNAME halfyaw = yaw / 2; |
| 359 | |
| 360 | TNAME sin_r2 = (TNAME)sin(halfroll); |
| 361 | TNAME sin_p2 = (TNAME)sin(halfpitch); |
| 362 | TNAME sin_y2 = (TNAME)sin(halfyaw); |
| 363 | |
| 364 | TNAME cos_r2 = (TNAME)cos(halfroll); |
| 365 | TNAME cos_p2 = (TNAME)cos(halfpitch); |
| 366 | TNAME cos_y2 = (TNAME)cos(halfyaw); |
| 367 | |
| 368 | quat[0] = cos_r2 * cos_p2 * cos_y2 + sin_r2 * sin_p2 * sin_y2; |
| 369 | quat[1] = sin_r2 * cos_p2 * cos_y2 - cos_r2 * sin_p2 * sin_y2; |
| 370 | quat[2] = cos_r2 * sin_p2 * cos_y2 + sin_r2 * cos_p2 * sin_y2; |
| 371 | quat[3] = cos_r2 * cos_p2 * sin_y2 - sin_r2 * sin_p2 * cos_y2; |
| 372 | } |
| 373 | |
| 374 | // Reference: "A tutorial on SE(3) transformation parameterizations and |
| 375 | // on-manifold optimization" by Jose-Luis Blanco |
| 376 | static inline void TFN(s_quat_to_rpy)(const TNAME q[4], TNAME rpy[3]) |
| 377 | { |
| 378 | const TNAME qr = q[0]; |
| 379 | const TNAME qx = q[1]; |
| 380 | const TNAME qy = q[2]; |
| 381 | const TNAME qz = q[3]; |
| 382 | |
| 383 | TNAME disc = qr*qy - qx*qz; |
| 384 | |
| 385 | if (fabs(disc+0.5) < DBL_EPSILON) { // near -1/2 |
| 386 | rpy[0] = 0; |
| 387 | rpy[1] = (TNAME)(-M_PI/2); |
| 388 | rpy[2] = (TNAME)(2 * atan2(qx, qr)); |
| 389 | } |
| 390 | else if (fabs(disc-0.5) < DBL_EPSILON) { // near 1/2 |
| 391 | rpy[0] = 0; |
| 392 | rpy[1] = (TNAME)(M_PI/2); |
| 393 | rpy[2] = (TNAME)(-2 * atan2(qx, qr)); |
| 394 | } |
| 395 | else { |
| 396 | // roll |
| 397 | TNAME roll_a = 2 * (qr*qx + qy*qz); |
| 398 | TNAME roll_b = 1 - 2 * (qx*qx + qy*qy); |
| 399 | rpy[0] = (TNAME)atan2(roll_a, roll_b); |
| 400 | |
| 401 | // pitch |
| 402 | rpy[1] = (TNAME)asin(2*disc); |
| 403 | |
| 404 | // yaw |
| 405 | TNAME yaw_a = 2 * (qr*qz + qx*qy); |
| 406 | TNAME yaw_b = 1 - 2 * (qy*qy + qz*qz); |
| 407 | rpy[2] = (TNAME)atan2(yaw_a, yaw_b); |
| 408 | } |
| 409 | } |
| 410 | |
| 411 | static inline void TFN(s_rpy_to_mat44)(const TNAME rpy[3], TNAME M[16]) |
| 412 | { |
| 413 | TNAME q[4]; |
| 414 | TFN(s_rpy_to_quat)(rpy, q); |
| 415 | TFN(s_quat_to_mat44)(q, M); |
| 416 | } |
| 417 | |
| 418 | |
| 419 | static inline void TFN(s_xyzrpy_to_mat44)(const TNAME xyzrpy[6], TNAME M[16]) |
| 420 | { |
| 421 | TFN(s_rpy_to_mat44)(&xyzrpy[3], M); |
| 422 | M[3] = xyzrpy[0]; |
| 423 | M[7] = xyzrpy[1]; |
| 424 | M[11] = xyzrpy[2]; |
| 425 | } |
| 426 | |
| 427 | static inline void TFN(s_mat44_transform_xyz)(const TNAME M[16], const TNAME in[3], TNAME out[3]) |
| 428 | { |
| 429 | for (int i = 0; i < 3; i++) |
| 430 | out[i] = M[4*i + 0]*in[0] + M[4*i + 1]*in[1] + M[4*i + 2]*in[2] + M[4*i + 3]; |
| 431 | } |
| 432 | |
| 433 | // out = (upper 3x3 of M) * in |
| 434 | static inline void TFN(s_mat44_rotate_vector)(const TNAME M[16], const TNAME in[3], TNAME out[3]) |
| 435 | { |
| 436 | for (int i = 0; i < 3; i++) |
| 437 | out[i] = M[4*i + 0]*in[0] + M[4*i + 1]*in[1] + M[4*i + 2]*in[2]; |
| 438 | } |
| 439 | |
| 440 | static inline void TFN(s_mat44_to_xyt)(const TNAME M[16], TNAME xyt[3]) |
| 441 | { |
| 442 | // c -s |
| 443 | // s c |
| 444 | xyt[0] = M[3]; |
| 445 | xyt[1] = M[7]; |
| 446 | xyt[2] = (TNAME)atan2(M[4], M[0]); |
| 447 | } |
| 448 | |
| 449 | static inline void TFN(s_mat_to_xyz)(const TNAME M[16], TNAME xyz[3]) |
| 450 | { |
| 451 | xyz[0] = M[3]; |
| 452 | xyz[1] = M[7]; |
| 453 | xyz[2] = M[11]; |
| 454 | } |
| 455 | |
| 456 | static inline void TFN(s_mat_to_quat)(const TNAME M[16], TNAME q[4]) |
| 457 | { |
| 458 | double T = M[0] + M[5] + M[10] + 1.0; |
| 459 | double S; |
| 460 | |
| 461 | if (T > 0.0000001) { |
| 462 | S = sqrt(T) * 2; |
| 463 | q[0] = (TNAME)(0.25 * S); |
| 464 | q[1] = (TNAME)((M[9] - M[6]) / S); |
| 465 | q[2] = (TNAME)((M[2] - M[8]) / S); |
| 466 | q[3] = (TNAME)((M[4] - M[1]) / S); |
| 467 | } else if (M[0] > M[5] && M[0] > M[10]) { // Column 0: |
| 468 | S = sqrt(1.0 + M[0] - M[5] - M[10]) * 2; |
| 469 | q[0] = (TNAME)((M[9] - M[6]) / S); |
| 470 | q[1] = (TNAME)(0.25 * S); |
| 471 | q[2] = (TNAME)((M[4] + M[1]) / S); |
| 472 | q[3] = (TNAME)((M[2] + M[8]) / S); |
| 473 | } else if (M[5] > M[10]) { // Column 1: |
| 474 | S = sqrt(1.0 + M[5] - M[0] - M[10]) * 2; |
| 475 | q[0] = (TNAME)((M[2] - M[8]) / S); |
| 476 | q[1] = (TNAME)((M[4] + M[1]) / S); |
| 477 | q[2] = (TNAME)(0.25 * S); |
| 478 | q[3] = (TNAME)((M[9] + M[6]) / S); |
| 479 | } else { // Column 2: |
| 480 | S = sqrt(1.0 + M[10] - M[0] - M[5]); |
| 481 | q[0] = (TNAME)((M[4] - M[1]) / S); |
| 482 | q[1] = (TNAME)((M[2] + M[8]) / S); |
| 483 | q[2] = (TNAME)((M[9] + M[6]) / S); |
| 484 | q[3] = (TNAME)(0.25 * S); |
| 485 | } |
| 486 | |
| 487 | TFN(s_normalize)(q, 4, q); |
| 488 | } |
| 489 | |
| 490 | static inline void TFN(s_quat_xyz_to_xyt)(const TNAME q[4], const TNAME xyz[3], TNAME xyt[3]) |
| 491 | { |
| 492 | TNAME M[16]; |
| 493 | TFN(s_quat_xyz_to_mat44)(q, xyz, M); |
| 494 | TFN(s_mat44_to_xyt)(M, xyt); |
| 495 | } |
| 496 | |
| 497 | // xytr = xyta * xytb; |
| 498 | static inline void TFN(s_xyt_mul)(const TNAME xyta[3], const TNAME xytb[3], TNAME xytr[3]) |
| 499 | { |
| 500 | TNAME xa = xyta[0], ya = xyta[1], ta = xyta[2]; |
| 501 | TNAME s = (TNAME)sin(ta), c = (TNAME)cos(ta); |
| 502 | |
| 503 | xytr[0] = c*xytb[0] - s*xytb[1] + xa; |
| 504 | xytr[1] = s*xytb[0] + c*xytb[1] + ya; |
| 505 | xytr[2] = ta + xytb[2]; |
| 506 | } |
| 507 | |
| 508 | static inline void TFN(s_xytcov_copy)(const TNAME xyta[3], const TNAME Ca[9], |
| 509 | TNAME xytr[3], TNAME Cr[9]) |
| 510 | { |
| 511 | memcpy(xytr, xyta, 3 * sizeof(TNAME)); |
| 512 | memcpy(Cr, Ca, 9 * sizeof(TNAME)); |
| 513 | } |
| 514 | |
| 515 | static inline void TFN(s_xytcov_mul)(const TNAME xyta[3], const TNAME Ca[9], |
| 516 | const TNAME xytb[3], const TNAME Cb[9], |
| 517 | TNAME xytr[3], TNAME Cr[9]) |
| 518 | { |
| 519 | TNAME xa = xyta[0], ya = xyta[1], ta = xyta[2]; |
| 520 | TNAME xb = xytb[0], yb = xytb[1]; |
| 521 | |
| 522 | TNAME sa = (TNAME)sin(ta), ca = (TNAME)cos(ta); |
| 523 | |
| 524 | TNAME P11 = Ca[0], P12 = Ca[1], P13 = Ca[2]; |
| 525 | TNAME P22 = Ca[4], P23 = Ca[5]; |
| 526 | TNAME P33 = Ca[8]; |
| 527 | |
| 528 | TNAME Q11 = Cb[0], Q12 = Cb[1], Q13 = Cb[2]; |
| 529 | TNAME Q22 = Cb[4], Q23 = Cb[5]; |
| 530 | TNAME Q33 = Cb[8]; |
| 531 | |
| 532 | TNAME JA13 = -sa*xb - ca*yb; |
| 533 | TNAME JA23 = ca*xb - sa*yb; |
| 534 | TNAME JB11 = ca; |
| 535 | TNAME JB12 = -sa; |
| 536 | TNAME JB21 = sa; |
| 537 | TNAME JB22 = ca; |
| 538 | |
| 539 | Cr[0] = P33*JA13*JA13 + 2*P13*JA13 + Q11*JB11*JB11 + 2*Q12*JB11*JB12 + Q22*JB12*JB12 + P11; |
| 540 | Cr[1] = P12 + JA23*(P13 + JA13*P33) + JA13*P23 + JB21*(JB11*Q11 + JB12*Q12) + JB22*(JB11*Q12 + JB12*Q22); |
| 541 | Cr[2] = P13 + JA13*P33 + JB11*Q13 + JB12*Q23; |
| 542 | Cr[3] = Cr[1]; |
| 543 | Cr[4] = P33*JA23*JA23 + 2*P23*JA23 + Q11*JB21*JB21 + 2*Q12*JB21*JB22 + Q22*JB22*JB22 + P22; |
| 544 | Cr[5] = P23 + JA23*P33 + JB21*Q13 + JB22*Q23; |
| 545 | Cr[6] = Cr[2]; |
| 546 | Cr[7] = Cr[5]; |
| 547 | Cr[8] = P33 + Q33; |
| 548 | |
| 549 | xytr[0] = ca*xb - sa*yb + xa; |
| 550 | xytr[1] = sa*xb + ca*yb + ya; |
| 551 | xytr[2] = xyta[2] + xytb[2]; |
| 552 | |
| 553 | /* |
| 554 | // the code above is just an unrolling of the following: |
| 555 | |
| 556 | TNAME JA[][] = new TNAME[][] { { 1, 0, -sa*xb - ca*yb }, |
| 557 | { 0, 1, ca*xb - sa*yb }, |
| 558 | { 0, 0, 1 } }; |
| 559 | TNAME JB[][] = new TNAME[][] { { ca, -sa, 0 }, |
| 560 | { sa, ca, 0 }, |
| 561 | { 0, 0, 1 } }; |
| 562 | |
| 563 | newge.P = LinAlg.add(LinAlg.matrixABCt(JA, P, JA), |
| 564 | LinAlg.matrixABCt(JB, ge.P, JB)); |
| 565 | */ |
| 566 | } |
| 567 | |
| 568 | |
| 569 | static inline void TFN(s_xyt_inv)(const TNAME xyta[3], TNAME xytr[3]) |
| 570 | { |
| 571 | TNAME s = (TNAME)sin(xyta[2]), c = (TNAME)cos(xyta[2]); |
| 572 | xytr[0] = -s*xyta[1] - c*xyta[0]; |
| 573 | xytr[1] = -c*xyta[1] + s*xyta[0]; |
| 574 | xytr[2] = -xyta[2]; |
| 575 | } |
| 576 | |
| 577 | static inline void TFN(s_xytcov_inv)(const TNAME xyta[3], const TNAME Ca[9], |
| 578 | TNAME xytr[3], TNAME Cr[9]) |
| 579 | { |
| 580 | TNAME x = xyta[0], y = xyta[1], theta = xyta[2]; |
| 581 | TNAME s = (TNAME)sin(theta), c = (TNAME)cos(theta); |
| 582 | |
| 583 | TNAME J11 = -c, J12 = -s, J13 = -c*y + s*x; |
| 584 | TNAME J21 = s, J22 = -c, J23 = s*y + c*x; |
| 585 | |
| 586 | TNAME P11 = Ca[0], P12 = Ca[1], P13 = Ca[2]; |
| 587 | TNAME P22 = Ca[4], P23 = Ca[5]; |
| 588 | TNAME P33 = Ca[8]; |
| 589 | |
| 590 | Cr[0] = P11*J11*J11 + 2*P12*J11*J12 + 2*P13*J11*J13 + |
| 591 | P22*J12*J12 + 2*P23*J12*J13 + P33*J13*J13; |
| 592 | Cr[1] = J21*(J11*P11 + J12*P12 + J13*P13) + |
| 593 | J22*(J11*P12 + J12*P22 + J13*P23) + |
| 594 | J23*(J11*P13 + J12*P23 + J13*P33); |
| 595 | Cr[2] = - J11*P13 - J12*P23 - J13*P33; |
| 596 | Cr[3] = Cr[1]; |
| 597 | Cr[4] = P11*J21*J21 + 2*P12*J21*J22 + 2*P13*J21*J23 + |
| 598 | P22*J22*J22 + 2*P23*J22*J23 + P33*J23*J23; |
| 599 | Cr[5] = - J21*P13 - J22*P23 - J23*P33; |
| 600 | Cr[6] = Cr[2]; |
| 601 | Cr[7] = Cr[5]; |
| 602 | Cr[8] = P33; |
| 603 | |
| 604 | /* |
| 605 | // the code above is just an unrolling of the following: |
| 606 | |
| 607 | TNAME J[][] = new TNAME[][] { { -c, -s, -c*y + s*x }, |
| 608 | { s, -c, s*y + c*x }, |
| 609 | { 0, 0, -1 } }; |
| 610 | ge.P = LinAlg.matrixABCt(J, P, J); |
| 611 | */ |
| 612 | |
| 613 | xytr[0] = -s*y - c*x; |
| 614 | xytr[1] = -c*y + s*x; |
| 615 | xytr[2] = -xyta[2]; |
| 616 | } |
| 617 | |
| 618 | // xytr = inv(xyta) * xytb |
| 619 | static inline void TFN(s_xyt_inv_mul)(const TNAME xyta[3], const TNAME xytb[3], TNAME xytr[3]) |
| 620 | { |
| 621 | TNAME theta = xyta[2]; |
| 622 | TNAME ca = (TNAME)cos(theta); |
| 623 | TNAME sa = (TNAME)sin(theta); |
| 624 | TNAME dx = xytb[0] - xyta[0]; |
| 625 | TNAME dy = xytb[1] - xyta[1]; |
| 626 | |
| 627 | xytr[0] = ca*dx + sa*dy; |
| 628 | xytr[1] = -sa*dx + ca*dy; |
| 629 | xytr[2]= xytb[2] - xyta[2]; |
| 630 | } |
| 631 | |
| 632 | static inline void TFN(s_mat_add)(const TNAME *A, int Arows, int Acols, |
| 633 | const TNAME *B, int Brows, int Bcols, |
| 634 | TNAME *R, int Rrows, int Rcols) |
| 635 | { |
| 636 | assert(Arows == Brows); |
| 637 | assert(Arows == Rrows); |
| 638 | assert(Bcols == Bcols); |
| 639 | assert(Bcols == Rcols); |
| 640 | |
| 641 | for (int i = 0; i < Arows; i++) |
| 642 | for (int j = 0; j < Bcols; j++) |
| 643 | R[i*Acols + j] = A[i*Acols + j] + B[i*Acols + j]; |
| 644 | } |
| 645 | |
| 646 | // matrix should be in row-major order, allocated in a single packed |
| 647 | // array. (This is compatible with matd.) |
| 648 | static inline void TFN(s_mat_AB)(const TNAME *A, int Arows, int Acols, |
| 649 | const TNAME *B, int Brows, int Bcols, |
| 650 | TNAME *R, int Rrows, int Rcols) |
| 651 | { |
| 652 | assert(Acols == Brows); |
| 653 | assert(Rrows == Arows); |
| 654 | assert(Bcols == Rcols); |
| 655 | |
| 656 | for (int Rrow = 0; Rrow < Rrows; Rrow++) { |
| 657 | for (int Rcol = 0; Rcol < Rcols; Rcol++) { |
| 658 | TNAME acc = 0; |
| 659 | for (int i = 0; i < Acols; i++) |
| 660 | acc += A[Rrow*Acols + i] * B[i*Bcols + Rcol]; |
| 661 | R[Rrow*Rcols + Rcol] = acc; |
| 662 | } |
| 663 | } |
| 664 | } |
| 665 | |
| 666 | // matrix should be in row-major order, allocated in a single packed |
| 667 | // array. (This is compatible with matd.) |
| 668 | static inline void TFN(s_mat_ABt)(const TNAME *A, int Arows, int Acols, |
| 669 | const TNAME *B, int Brows, int Bcols, |
| 670 | TNAME *R, int Rrows, int Rcols) |
| 671 | { |
| 672 | assert(Acols == Bcols); |
| 673 | assert(Rrows == Arows); |
| 674 | assert(Brows == Rcols); |
| 675 | |
| 676 | for (int Rrow = 0; Rrow < Rrows; Rrow++) { |
| 677 | for (int Rcol = 0; Rcol < Rcols; Rcol++) { |
| 678 | TNAME acc = 0; |
| 679 | for (int i = 0; i < Acols; i++) |
| 680 | acc += A[Rrow*Acols + i] * B[Rcol*Bcols + i]; |
| 681 | R[Rrow*Rcols + Rcol] = acc; |
| 682 | } |
| 683 | } |
| 684 | } |
| 685 | |
| 686 | static inline void TFN(s_mat_ABC)(const TNAME *A, int Arows, int Acols, |
| 687 | const TNAME *B, int Brows, int Bcols, |
| 688 | const TNAME *C, int Crows, int Ccols, |
| 689 | TNAME *R, int Rrows, int Rcols) |
| 690 | { |
| 691 | TNAME *tmp = malloc(sizeof(TNAME)*Arows*Bcols); |
| 692 | |
| 693 | TFN(s_mat_AB)(A, Arows, Acols, B, Brows, Bcols, tmp, Arows, Bcols); |
| 694 | TFN(s_mat_AB)(tmp, Arows, Bcols, C, Crows, Ccols, R, Rrows, Rcols); |
| 695 | free(tmp); |
| 696 | } |
| 697 | |
| 698 | static inline void TFN(s_mat_Ab)(const TNAME *A, int Arows, int Acols, |
| 699 | const TNAME *B, int Blength, |
| 700 | TNAME *R, int Rlength) |
| 701 | { |
| 702 | assert(Acols == Blength); |
| 703 | assert(Arows == Rlength); |
| 704 | |
| 705 | for (int Ridx = 0; Ridx < Rlength; Ridx++) { |
| 706 | TNAME acc = 0; |
| 707 | for (int i = 0; i < Blength; i++) |
| 708 | acc += A[Ridx*Acols + i] * B[i]; |
| 709 | R[Ridx] = acc; |
| 710 | } |
| 711 | } |
| 712 | |
| 713 | static inline void TFN(s_mat_AtB)(const TNAME *A, int Arows, int Acols, |
| 714 | const TNAME *B, int Brows, int Bcols, |
| 715 | TNAME *R, int Rrows, int Rcols) |
| 716 | { |
| 717 | assert(Arows == Brows); |
| 718 | assert(Rrows == Acols); |
| 719 | assert(Bcols == Rcols); |
| 720 | |
| 721 | for (int Rrow = 0; Rrow < Rrows; Rrow++) { |
| 722 | for (int Rcol = 0; Rcol < Rcols; Rcol++) { |
| 723 | TNAME acc = 0; |
| 724 | for (int i = 0; i < Acols; i++) |
| 725 | acc += A[i*Acols + Rrow] * B[i*Bcols + Rcol]; |
| 726 | R[Rrow*Rcols + Rcol] = acc; |
| 727 | } |
| 728 | } |
| 729 | } |
| 730 | |
| 731 | static inline void TFN(s_quat_slerp)(const TNAME q0[4], const TNAME _q1[4], TNAME r[4], TNAME w) |
| 732 | { |
| 733 | TNAME dot = TFN(s_dot)(q0, _q1, 4); |
| 734 | |
| 735 | TNAME q1[4]; |
| 736 | memcpy(q1, _q1, sizeof(TNAME) * 4); |
| 737 | |
| 738 | if (dot < 0) { |
| 739 | // flip sign on one of them so we don't spin the "wrong |
| 740 | // way" around. This doesn't change the rotation that the |
| 741 | // quaternion represents. |
| 742 | dot = -dot; |
| 743 | for (int i = 0; i < 4; i++) |
| 744 | q1[i] *= -1; |
| 745 | } |
| 746 | |
| 747 | // if large dot product (1), slerp will scale both q0 and q1 |
| 748 | // by 0, and normalization will blow up. |
| 749 | if (dot > 0.95) { |
| 750 | |
| 751 | for (int i = 0; i < 4; i++) |
| 752 | r[i] = q0[i]*(1-w) + q1[i]*w; |
| 753 | |
| 754 | } else { |
| 755 | TNAME angle = (TNAME)acos(dot); |
| 756 | |
| 757 | TNAME w0 = (TNAME)sin(angle*(1-w)), w1 = (TNAME)sin(angle*w); |
| 758 | |
| 759 | for (int i = 0; i < 4; i++) |
| 760 | r[i] = q0[i]*w0 + q1[i]*w1; |
| 761 | |
| 762 | TFN(s_normalize)(r, 4, r); |
| 763 | } |
| 764 | } |
| 765 | |
| 766 | static inline void TFN(s_cross_product)(const TNAME v1[3], const TNAME v2[3], TNAME r[3]) |
| 767 | { |
| 768 | r[0] = v1[1]*v2[2] - v1[2]*v2[1]; |
| 769 | r[1] = v1[2]*v2[0] - v1[0]*v2[2]; |
| 770 | r[2] = v1[0]*v2[1] - v1[1]*v2[0]; |
| 771 | } |
| 772 | |
| 773 | //////////////////// |
| 774 | static inline void TFN(s_mat44_identity)(TNAME out[16]) |
| 775 | { |
| 776 | memset(out, 0, 16 * sizeof(TNAME)); |
| 777 | out[0] = 1; |
| 778 | out[5] = 1; |
| 779 | out[10] = 1; |
| 780 | out[15] = 1; |
| 781 | } |
| 782 | |
| 783 | static inline void TFN(s_mat44_translate)(const TNAME txyz[3], TNAME out[16]) |
| 784 | { |
| 785 | TFN(s_mat44_identity)(out); |
| 786 | |
| 787 | for (int i = 0; i < 3; i++) |
| 788 | out[4*i + 3] += txyz[i]; |
| 789 | } |
| 790 | |
| 791 | static inline void TFN(s_mat44_scale)(const TNAME sxyz[3], TNAME out[16]) |
| 792 | { |
| 793 | TFN(s_mat44_identity)(out); |
| 794 | |
| 795 | for (int i = 0; i < 3; i++) |
| 796 | out[4*i + i] = sxyz[i]; |
| 797 | } |
| 798 | |
| 799 | static inline void TFN(s_mat44_rotate_z)(TNAME rad, TNAME out[16]) |
| 800 | { |
| 801 | TFN(s_mat44_identity)(out); |
| 802 | TNAME s = (TNAME)sin(rad), c = (TNAME)cos(rad); |
| 803 | out[0*4 + 0] = c; |
| 804 | out[0*4 + 1] = -s; |
| 805 | out[1*4 + 0] = s; |
| 806 | out[1*4 + 1] = c; |
| 807 | } |
| 808 | |
| 809 | static inline void TFN(s_mat44_rotate_y)(TNAME rad, TNAME out[16]) |
| 810 | { |
| 811 | TFN(s_mat44_identity)(out); |
| 812 | TNAME s = (TNAME)sin(rad), c = (TNAME)cos(rad); |
| 813 | out[0*4 + 0] = c; |
| 814 | out[0*4 + 2] = s; |
| 815 | out[2*4 + 0] = -s; |
| 816 | out[2*4 + 2] = c; |
| 817 | } |
| 818 | |
| 819 | static inline void TFN(s_mat44_rotate_x)(TNAME rad, TNAME out[16]) |
| 820 | { |
| 821 | TFN(s_mat44_identity)(out); |
| 822 | TNAME s = (TNAME)sin(rad), c = (TNAME)cos(rad); |
| 823 | out[1*4 + 1] = c; |
| 824 | out[1*4 + 2] = -s; |
| 825 | out[2*4 + 1] = s; |
| 826 | out[2*4 + 2] = c; |
| 827 | } |
| 828 | |
| 829 | // out = out * translate(txyz) |
| 830 | static inline void TFN(s_mat44_translate_self)(const TNAME txyz[3], TNAME out[16]) |
| 831 | { |
| 832 | TNAME tmp[16], prod[16]; |
| 833 | TFN(s_mat44_translate(txyz, tmp)); |
| 834 | TFN(s_mat_AB)(out, 4, 4, tmp, 4, 4, prod, 4, 4); |
| 835 | memcpy(out, prod, sizeof(TNAME)*16); |
| 836 | } |
| 837 | |
| 838 | static inline void TFN(s_mat44_scale_self)(const TNAME sxyz[3], TNAME out[16]) |
| 839 | { |
| 840 | TNAME tmp[16], prod[16]; |
| 841 | TFN(s_mat44_scale(sxyz, tmp)); |
| 842 | TFN(s_mat_AB)(out, 4, 4, tmp, 4, 4, prod, 4, 4); |
| 843 | memcpy(out, prod, sizeof(TNAME)*16); |
| 844 | } |
| 845 | |
| 846 | static inline void TFN(s_mat44_rotate_z_self)(TNAME rad, TNAME out[16]) |
| 847 | { |
| 848 | TNAME tmp[16], prod[16]; |
| 849 | TFN(s_mat44_rotate_z(rad, tmp)); |
| 850 | TFN(s_mat_AB)(out, 4, 4, tmp, 4, 4, prod, 4, 4); |
| 851 | memcpy(out, prod, sizeof(TNAME)*16); |
| 852 | } |
| 853 | |
| 854 | // out = inv(M)*in. Note: this assumes that mat44 is a rigid-body transformation. |
| 855 | static inline void TFN(s_mat44_inv)(const TNAME M[16], TNAME out[16]) |
| 856 | { |
| 857 | // NB: M = T*R, inv(M) = inv(R) * inv(T) |
| 858 | |
| 859 | // transpose of upper-left corner |
| 860 | for (int i = 0; i < 3; i++) |
| 861 | for (int j = 0; j < 3; j++) |
| 862 | out[4*i + j] = M[4*j + i]; |
| 863 | |
| 864 | out[4*0 + 3] = 0; |
| 865 | out[4*1 + 3] = 0; |
| 866 | out[4*2 + 3] = 0; |
| 867 | |
| 868 | for (int i = 0; i < 3; i++) |
| 869 | for (int j = 0; j < 3; j++) |
| 870 | out[4*i + 3] -= out[4*i + j] * M[4*j + 3]; |
| 871 | |
| 872 | out[4*3 + 0] = 0; |
| 873 | out[4*3 + 1] = 0; |
| 874 | out[4*3 + 2] = 0; |
| 875 | out[4*3 + 3] = 1; |
| 876 | |
| 877 | /* TNAME tmp[16]; |
| 878 | TFN(s_mat_AB)(M, 4, 4, out, 4, 4, tmp, 4, 4); |
| 879 | printf("identity: "); |
| 880 | TFN(s_print_mat)(tmp, 4, 4, "%15f"); */ |
| 881 | } |
| 882 | |
| 883 | // out = inv(M)*in |
| 884 | static inline void TFN(s_mat44_inv_transform_xyz)(const TNAME M[16], const TNAME in[3], TNAME out[3]) |
| 885 | { |
| 886 | TNAME T[16]; |
| 887 | TFN(s_mat44_inv)(M, T); |
| 888 | |
| 889 | TFN(s_mat44_transform_xyz)(T, in, out); |
| 890 | } |
| 891 | |
| 892 | // out = (upper 3x3 of inv(M)) * in |
| 893 | static inline void TFN(s_mat44_inv_rotate_vector)(const TNAME M[16], const TNAME in[3], TNAME out[3]) |
| 894 | { |
| 895 | TNAME T[16]; |
| 896 | TFN(s_mat44_inv)(M, T); |
| 897 | |
| 898 | TFN(s_mat44_rotate_vector)(T, in, out); |
| 899 | } |
| 900 | |
| 901 | static inline void TFN(s_elu_to_mat44)(const TNAME eye[3], const TNAME lookat[3], const TNAME _up[3], |
| 902 | TNAME M[16]) |
| 903 | { |
| 904 | TNAME f[3]; |
| 905 | TFN(s_subtract)(lookat, eye, 3, f); |
| 906 | TFN(s_normalize)(f, 3, f); |
| 907 | |
| 908 | TNAME up[3]; |
| 909 | |
| 910 | // remove any component of 'up' that isn't perpendicular to the look direction. |
| 911 | TFN(s_normalize)(_up, 3, up); |
| 912 | |
| 913 | TNAME up_dot = TFN(s_dot)(f, up, 3); |
| 914 | for (int i = 0; i < 3; i++) |
| 915 | up[i] -= up_dot*f[i]; |
| 916 | |
| 917 | TFN(s_normalize_self)(up, 3); |
| 918 | |
| 919 | TNAME s[3], u[3]; |
| 920 | TFN(s_cross_product)(f, up, s); |
| 921 | TFN(s_cross_product)(s, f, u); |
| 922 | |
| 923 | TNAME R[16] = { s[0], s[1], s[2], 0, |
| 924 | u[0], u[1], u[2], 0, |
| 925 | -f[0], -f[1], -f[2], 0, |
| 926 | 0, 0, 0, 1}; |
| 927 | |
| 928 | TNAME T[16] = {1, 0, 0, -eye[0], |
| 929 | 0, 1, 0, -eye[1], |
| 930 | 0, 0, 1, -eye[2], |
| 931 | 0, 0, 0, 1}; |
| 932 | |
| 933 | // M is the extrinsics matrix [R | t] where t = -R*c |
| 934 | TNAME tmp[16]; |
| 935 | TFN(s_mat_AB)(R, 4, 4, T, 4, 4, tmp, 4, 4); |
| 936 | TFN(s_mat44_inv)(tmp, M); |
| 937 | } |
| 938 | |
| 939 | // Computes the cholesky factorization of A, putting the lower |
| 940 | // triangular matrix into R. |
| 941 | static inline void TFN(s_mat33_chol)(const TNAME *A, int Arows, int Acols, |
| 942 | TNAME *R, int Brows, int Bcols) |
| 943 | { |
| 944 | assert(Arows == Brows); |
| 945 | assert(Bcols == Bcols); |
| 946 | |
| 947 | // A[0] = R[0]*R[0] |
| 948 | R[0] = (TNAME)sqrt(A[0]); |
| 949 | |
| 950 | // A[1] = R[0]*R[3]; |
| 951 | R[3] = A[1] / R[0]; |
| 952 | |
| 953 | // A[2] = R[0]*R[6]; |
| 954 | R[6] = A[2] / R[0]; |
| 955 | |
| 956 | // A[4] = R[3]*R[3] + R[4]*R[4] |
| 957 | R[4] = (TNAME)sqrt(A[4] - R[3]*R[3]); |
| 958 | |
| 959 | // A[5] = R[3]*R[6] + R[4]*R[7] |
| 960 | R[7] = (A[5] - R[3]*R[6]) / R[4]; |
| 961 | |
| 962 | // A[8] = R[6]*R[6] + R[7]*R[7] + R[8]*R[8] |
| 963 | R[8] = (TNAME)sqrt(A[8] - R[6]*R[6] - R[7]*R[7]); |
| 964 | |
| 965 | R[1] = 0; |
| 966 | R[2] = 0; |
| 967 | R[5] = 0; |
| 968 | } |
| 969 | |
| 970 | static inline void TFN(s_mat33_lower_tri_inv)(const TNAME *A, int Arows, int Acols, |
| 971 | TNAME *R, int Rrows, int Rcols) |
| 972 | { |
| 973 | // A[0]*R[0] = 1 |
| 974 | R[0] = 1 / A[0]; |
| 975 | |
| 976 | // A[3]*R[0] + A[4]*R[3] = 0 |
| 977 | R[3] = -A[3]*R[0] / A[4]; |
| 978 | |
| 979 | // A[4]*R[4] = 1 |
| 980 | R[4] = 1 / A[4]; |
| 981 | |
| 982 | // A[6]*R[0] + A[7]*R[3] + A[8]*R[6] = 0 |
| 983 | R[6] = (-A[6]*R[0] - A[7]*R[3]) / A[8]; |
| 984 | |
| 985 | // A[7]*R[4] + A[8]*R[7] = 0 |
| 986 | R[7] = -A[7]*R[4] / A[8]; |
| 987 | |
| 988 | // A[8]*R[8] = 1 |
| 989 | R[8] = 1 / A[8]; |
| 990 | } |
| 991 | |
| 992 | |
| 993 | static inline void TFN(s_mat33_sym_solve)(const TNAME *A, int Arows, int Acols, |
| 994 | const TNAME *B, int Brows, int Bcols, |
| 995 | TNAME *R, int Rrows, int Rcols) |
| 996 | { |
| 997 | assert(Arows == Acols); |
| 998 | assert(Acols == 3); |
| 999 | assert(Brows == 3); |
| 1000 | assert(Bcols == 1); |
| 1001 | assert(Rrows == 3); |
| 1002 | assert(Rcols == 1); |
| 1003 | |
| 1004 | TNAME L[9]; |
| 1005 | TFN(s_mat33_chol)(A, 3, 3, L, 3, 3); |
| 1006 | |
| 1007 | TNAME M[9]; |
| 1008 | TFN(s_mat33_lower_tri_inv)(L, 3, 3, M, 3, 3); |
| 1009 | |
| 1010 | double tmp[3]; |
| 1011 | tmp[0] = M[0]*B[0]; |
| 1012 | tmp[1] = M[3]*B[0] + M[4]*B[1]; |
| 1013 | tmp[2] = M[6]*B[0] + M[7]*B[1] + M[8]*B[2]; |
| 1014 | |
| 1015 | R[0] = (TNAME)(M[0]*tmp[0] + M[3]*tmp[1] + M[6]*tmp[2]); |
| 1016 | R[1] = (TNAME)(M[4]*tmp[1] + M[7]*tmp[2]); |
| 1017 | R[2] = (TNAME)(M[8]*tmp[2]); |
| 1018 | } |
| 1019 | |
| 1020 | /* |
| 1021 | // solve Ax = B. Assumes A is symmetric; uses cholesky factorization |
| 1022 | static inline void TFN(s_mat_solve_chol)(const TNAME *A, int Arows, int Acols, |
| 1023 | const TNAME *B, int Brows, int Bcols, |
| 1024 | TNAME *R, int Rrows, int Rcols) |
| 1025 | { |
| 1026 | assert(Arows == Acols); |
| 1027 | assert(Arows == Brows); |
| 1028 | assert(Acols == Rrows); |
| 1029 | assert(Bcols == Rcols); |
| 1030 | |
| 1031 | // |
| 1032 | } |
| 1033 | */ |
| 1034 | #undef TRRFN |
| 1035 | #undef TRFN |
| 1036 | #undef TFN |