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 <math.h> |
| 29 | |
| 30 | #include "common/matd.h" |
| 31 | #include "common/zarray.h" |
| 32 | #include "common/homography.h" |
| 33 | #include "common/math_util.h" |
| 34 | |
| 35 | // correspondences is a list of float[4]s, consisting of the points x |
| 36 | // and y concatenated. We will compute a homography such that y = Hx |
| 37 | matd_t *homography_compute(zarray_t *correspondences, int flags) |
| 38 | { |
| 39 | // compute centroids of both sets of points (yields a better |
| 40 | // conditioned information matrix) |
| 41 | double x_cx = 0, x_cy = 0; |
| 42 | double y_cx = 0, y_cy = 0; |
| 43 | |
| 44 | for (int i = 0; i < zarray_size(correspondences); i++) { |
| 45 | float *c; |
| 46 | zarray_get_volatile(correspondences, i, &c); |
| 47 | |
| 48 | x_cx += c[0]; |
| 49 | x_cy += c[1]; |
| 50 | y_cx += c[2]; |
| 51 | y_cy += c[3]; |
| 52 | } |
| 53 | |
| 54 | int sz = zarray_size(correspondences); |
| 55 | x_cx /= sz; |
| 56 | x_cy /= sz; |
| 57 | y_cx /= sz; |
| 58 | y_cy /= sz; |
| 59 | |
| 60 | // NB We don't normalize scale; it seems implausible that it could |
| 61 | // possibly make any difference given the dynamic range of IEEE |
| 62 | // doubles. |
| 63 | |
| 64 | matd_t *A = matd_create(9,9); |
| 65 | for (int i = 0; i < zarray_size(correspondences); i++) { |
| 66 | float *c; |
| 67 | zarray_get_volatile(correspondences, i, &c); |
| 68 | |
| 69 | // (below world is "x", and image is "y") |
| 70 | double worldx = c[0] - x_cx; |
| 71 | double worldy = c[1] - x_cy; |
| 72 | double imagex = c[2] - y_cx; |
| 73 | double imagey = c[3] - y_cy; |
| 74 | |
| 75 | double a03 = -worldx; |
| 76 | double a04 = -worldy; |
| 77 | double a05 = -1; |
| 78 | double a06 = worldx*imagey; |
| 79 | double a07 = worldy*imagey; |
| 80 | double a08 = imagey; |
| 81 | |
| 82 | MATD_EL(A, 3, 3) += a03*a03; |
| 83 | MATD_EL(A, 3, 4) += a03*a04; |
| 84 | MATD_EL(A, 3, 5) += a03*a05; |
| 85 | MATD_EL(A, 3, 6) += a03*a06; |
| 86 | MATD_EL(A, 3, 7) += a03*a07; |
| 87 | MATD_EL(A, 3, 8) += a03*a08; |
| 88 | MATD_EL(A, 4, 4) += a04*a04; |
| 89 | MATD_EL(A, 4, 5) += a04*a05; |
| 90 | MATD_EL(A, 4, 6) += a04*a06; |
| 91 | MATD_EL(A, 4, 7) += a04*a07; |
| 92 | MATD_EL(A, 4, 8) += a04*a08; |
| 93 | MATD_EL(A, 5, 5) += a05*a05; |
| 94 | MATD_EL(A, 5, 6) += a05*a06; |
| 95 | MATD_EL(A, 5, 7) += a05*a07; |
| 96 | MATD_EL(A, 5, 8) += a05*a08; |
| 97 | MATD_EL(A, 6, 6) += a06*a06; |
| 98 | MATD_EL(A, 6, 7) += a06*a07; |
| 99 | MATD_EL(A, 6, 8) += a06*a08; |
| 100 | MATD_EL(A, 7, 7) += a07*a07; |
| 101 | MATD_EL(A, 7, 8) += a07*a08; |
| 102 | MATD_EL(A, 8, 8) += a08*a08; |
| 103 | |
| 104 | double a10 = worldx; |
| 105 | double a11 = worldy; |
| 106 | double a12 = 1; |
| 107 | double a16 = -worldx*imagex; |
| 108 | double a17 = -worldy*imagex; |
| 109 | double a18 = -imagex; |
| 110 | |
| 111 | MATD_EL(A, 0, 0) += a10*a10; |
| 112 | MATD_EL(A, 0, 1) += a10*a11; |
| 113 | MATD_EL(A, 0, 2) += a10*a12; |
| 114 | MATD_EL(A, 0, 6) += a10*a16; |
| 115 | MATD_EL(A, 0, 7) += a10*a17; |
| 116 | MATD_EL(A, 0, 8) += a10*a18; |
| 117 | MATD_EL(A, 1, 1) += a11*a11; |
| 118 | MATD_EL(A, 1, 2) += a11*a12; |
| 119 | MATD_EL(A, 1, 6) += a11*a16; |
| 120 | MATD_EL(A, 1, 7) += a11*a17; |
| 121 | MATD_EL(A, 1, 8) += a11*a18; |
| 122 | MATD_EL(A, 2, 2) += a12*a12; |
| 123 | MATD_EL(A, 2, 6) += a12*a16; |
| 124 | MATD_EL(A, 2, 7) += a12*a17; |
| 125 | MATD_EL(A, 2, 8) += a12*a18; |
| 126 | MATD_EL(A, 6, 6) += a16*a16; |
| 127 | MATD_EL(A, 6, 7) += a16*a17; |
| 128 | MATD_EL(A, 6, 8) += a16*a18; |
| 129 | MATD_EL(A, 7, 7) += a17*a17; |
| 130 | MATD_EL(A, 7, 8) += a17*a18; |
| 131 | MATD_EL(A, 8, 8) += a18*a18; |
| 132 | |
| 133 | double a20 = -worldx*imagey; |
| 134 | double a21 = -worldy*imagey; |
| 135 | double a22 = -imagey; |
| 136 | double a23 = worldx*imagex; |
| 137 | double a24 = worldy*imagex; |
| 138 | double a25 = imagex; |
| 139 | |
| 140 | MATD_EL(A, 0, 0) += a20*a20; |
| 141 | MATD_EL(A, 0, 1) += a20*a21; |
| 142 | MATD_EL(A, 0, 2) += a20*a22; |
| 143 | MATD_EL(A, 0, 3) += a20*a23; |
| 144 | MATD_EL(A, 0, 4) += a20*a24; |
| 145 | MATD_EL(A, 0, 5) += a20*a25; |
| 146 | MATD_EL(A, 1, 1) += a21*a21; |
| 147 | MATD_EL(A, 1, 2) += a21*a22; |
| 148 | MATD_EL(A, 1, 3) += a21*a23; |
| 149 | MATD_EL(A, 1, 4) += a21*a24; |
| 150 | MATD_EL(A, 1, 5) += a21*a25; |
| 151 | MATD_EL(A, 2, 2) += a22*a22; |
| 152 | MATD_EL(A, 2, 3) += a22*a23; |
| 153 | MATD_EL(A, 2, 4) += a22*a24; |
| 154 | MATD_EL(A, 2, 5) += a22*a25; |
| 155 | MATD_EL(A, 3, 3) += a23*a23; |
| 156 | MATD_EL(A, 3, 4) += a23*a24; |
| 157 | MATD_EL(A, 3, 5) += a23*a25; |
| 158 | MATD_EL(A, 4, 4) += a24*a24; |
| 159 | MATD_EL(A, 4, 5) += a24*a25; |
| 160 | MATD_EL(A, 5, 5) += a25*a25; |
| 161 | } |
| 162 | |
| 163 | // make symmetric |
| 164 | for (int i = 0; i < 9; i++) |
| 165 | for (int j = i+1; j < 9; j++) |
| 166 | MATD_EL(A, j, i) = MATD_EL(A, i, j); |
| 167 | |
| 168 | matd_t *H = matd_create(3,3); |
| 169 | |
| 170 | if (flags & HOMOGRAPHY_COMPUTE_FLAG_INVERSE) { |
| 171 | // compute singular vector by (carefully) inverting the rank-deficient matrix. |
| 172 | |
| 173 | if (1) { |
| 174 | matd_t *Ainv = matd_inverse(A); |
| 175 | double scale = 0; |
| 176 | |
| 177 | for (int i = 0; i < 9; i++) |
| 178 | scale += sq(MATD_EL(Ainv, i, 0)); |
| 179 | scale = sqrt(scale); |
| 180 | |
| 181 | for (int i = 0; i < 3; i++) |
| 182 | for (int j = 0; j < 3; j++) |
| 183 | MATD_EL(H, i, j) = MATD_EL(Ainv, 3*i+j, 0) / scale; |
| 184 | |
| 185 | matd_destroy(Ainv); |
| 186 | } else { |
| 187 | |
| 188 | matd_t *b = matd_create_data(9, 1, (double[]) { 1, 0, 0, 0, 0, 0, 0, 0, 0 }); |
| 189 | matd_t *Ainv = NULL; |
| 190 | |
| 191 | if (0) { |
| 192 | matd_plu_t *lu = matd_plu(A); |
| 193 | Ainv = matd_plu_solve(lu, b); |
| 194 | matd_plu_destroy(lu); |
| 195 | } else { |
| 196 | matd_chol_t *chol = matd_chol(A); |
| 197 | Ainv = matd_chol_solve(chol, b); |
| 198 | matd_chol_destroy(chol); |
| 199 | } |
| 200 | |
| 201 | double scale = 0; |
| 202 | |
| 203 | for (int i = 0; i < 9; i++) |
| 204 | scale += sq(MATD_EL(Ainv, i, 0)); |
| 205 | scale = sqrt(scale); |
| 206 | |
| 207 | for (int i = 0; i < 3; i++) |
| 208 | for (int j = 0; j < 3; j++) |
| 209 | MATD_EL(H, i, j) = MATD_EL(Ainv, 3*i+j, 0) / scale; |
| 210 | |
| 211 | matd_destroy(b); |
| 212 | matd_destroy(Ainv); |
| 213 | } |
| 214 | |
| 215 | } else { |
| 216 | // compute singular vector using SVD. A bit slower, but more accurate. |
| 217 | matd_svd_t svd = matd_svd_flags(A, MATD_SVD_NO_WARNINGS); |
| 218 | |
| 219 | for (int i = 0; i < 3; i++) |
| 220 | for (int j = 0; j < 3; j++) |
| 221 | MATD_EL(H, i, j) = MATD_EL(svd.U, 3*i+j, 8); |
| 222 | |
| 223 | matd_destroy(svd.U); |
| 224 | matd_destroy(svd.S); |
| 225 | matd_destroy(svd.V); |
| 226 | |
| 227 | } |
| 228 | |
| 229 | matd_t *Tx = matd_identity(3); |
| 230 | MATD_EL(Tx,0,2) = -x_cx; |
| 231 | MATD_EL(Tx,1,2) = -x_cy; |
| 232 | |
| 233 | matd_t *Ty = matd_identity(3); |
| 234 | MATD_EL(Ty,0,2) = y_cx; |
| 235 | MATD_EL(Ty,1,2) = y_cy; |
| 236 | |
| 237 | matd_t *H2 = matd_op("M*M*M", Ty, H, Tx); |
| 238 | |
| 239 | matd_destroy(A); |
| 240 | matd_destroy(Tx); |
| 241 | matd_destroy(Ty); |
| 242 | matd_destroy(H); |
| 243 | |
| 244 | return H2; |
| 245 | } |
| 246 | |
| 247 | |
| 248 | // assuming that the projection matrix is: |
| 249 | // [ fx 0 cx 0 ] |
| 250 | // [ 0 fy cy 0 ] |
| 251 | // [ 0 0 1 0 ] |
| 252 | // |
| 253 | // And that the homography is equal to the projection matrix times the |
| 254 | // model matrix, recover the model matrix (which is returned). Note |
| 255 | // that the third column of the model matrix is missing in the |
| 256 | // expresison below, reflecting the fact that the homography assumes |
| 257 | // all points are at z=0 (i.e., planar) and that the element of z is |
| 258 | // thus omitted. (3x1 instead of 4x1). |
| 259 | // |
| 260 | // [ fx 0 cx 0 ] [ R00 R01 TX ] [ H00 H01 H02 ] |
| 261 | // [ 0 fy cy 0 ] [ R10 R11 TY ] = [ H10 H11 H12 ] |
| 262 | // [ 0 0 1 0 ] [ R20 R21 TZ ] = [ H20 H21 H22 ] |
| 263 | // [ 0 0 1 ] |
| 264 | // |
| 265 | // fx*R00 + cx*R20 = H00 (note, H only known up to scale; some additional adjustments required; see code.) |
| 266 | // fx*R01 + cx*R21 = H01 |
| 267 | // fx*TX + cx*TZ = H02 |
| 268 | // fy*R10 + cy*R20 = H10 |
| 269 | // fy*R11 + cy*R21 = H11 |
| 270 | // fy*TY + cy*TZ = H12 |
| 271 | // R20 = H20 |
| 272 | // R21 = H21 |
| 273 | // TZ = H22 |
| 274 | |
| 275 | matd_t *homography_to_pose(const matd_t *H, double fx, double fy, double cx, double cy) |
| 276 | { |
| 277 | // Note that every variable that we compute is proportional to the scale factor of H. |
| 278 | double R20 = MATD_EL(H, 2, 0); |
| 279 | double R21 = MATD_EL(H, 2, 1); |
| 280 | double TZ = MATD_EL(H, 2, 2); |
| 281 | double R00 = (MATD_EL(H, 0, 0) - cx*R20) / fx; |
| 282 | double R01 = (MATD_EL(H, 0, 1) - cx*R21) / fx; |
| 283 | double TX = (MATD_EL(H, 0, 2) - cx*TZ) / fx; |
| 284 | double R10 = (MATD_EL(H, 1, 0) - cy*R20) / fy; |
| 285 | double R11 = (MATD_EL(H, 1, 1) - cy*R21) / fy; |
| 286 | double TY = (MATD_EL(H, 1, 2) - cy*TZ) / fy; |
| 287 | |
| 288 | // compute the scale by requiring that the rotation columns are unit length |
| 289 | // (Use geometric average of the two length vectors we have) |
| 290 | double length1 = sqrtf(R00*R00 + R10*R10 + R20*R20); |
| 291 | double length2 = sqrtf(R01*R01 + R11*R11 + R21*R21); |
| 292 | double s = 1.0 / sqrtf(length1 * length2); |
| 293 | |
| 294 | // get sign of S by requiring the tag to be in front the camera; |
| 295 | // we assume camera looks in the -Z direction. |
| 296 | if (TZ > 0) |
| 297 | s *= -1; |
| 298 | |
| 299 | R20 *= s; |
| 300 | R21 *= s; |
| 301 | TZ *= s; |
| 302 | R00 *= s; |
| 303 | R01 *= s; |
| 304 | TX *= s; |
| 305 | R10 *= s; |
| 306 | R11 *= s; |
| 307 | TY *= s; |
| 308 | |
| 309 | // now recover [R02 R12 R22] by noting that it is the cross product of the other two columns. |
| 310 | double R02 = R10*R21 - R20*R11; |
| 311 | double R12 = R20*R01 - R00*R21; |
| 312 | double R22 = R00*R11 - R10*R01; |
| 313 | |
| 314 | // Improve rotation matrix by applying polar decomposition. |
| 315 | if (1) { |
| 316 | // do polar decomposition. This makes the rotation matrix |
| 317 | // "proper", but probably increases the reprojection error. An |
| 318 | // iterative alignment step would be superior. |
| 319 | |
| 320 | matd_t *R = matd_create_data(3, 3, (double[]) { R00, R01, R02, |
| 321 | R10, R11, R12, |
| 322 | R20, R21, R22 }); |
| 323 | |
| 324 | matd_svd_t svd = matd_svd(R); |
| 325 | matd_destroy(R); |
| 326 | |
| 327 | R = matd_op("M*M'", svd.U, svd.V); |
| 328 | |
| 329 | matd_destroy(svd.U); |
| 330 | matd_destroy(svd.S); |
| 331 | matd_destroy(svd.V); |
| 332 | |
| 333 | R00 = MATD_EL(R, 0, 0); |
| 334 | R01 = MATD_EL(R, 0, 1); |
| 335 | R02 = MATD_EL(R, 0, 2); |
| 336 | R10 = MATD_EL(R, 1, 0); |
| 337 | R11 = MATD_EL(R, 1, 1); |
| 338 | R12 = MATD_EL(R, 1, 2); |
| 339 | R20 = MATD_EL(R, 2, 0); |
| 340 | R21 = MATD_EL(R, 2, 1); |
| 341 | R22 = MATD_EL(R, 2, 2); |
| 342 | |
| 343 | matd_destroy(R); |
| 344 | } |
| 345 | |
| 346 | return matd_create_data(4, 4, (double[]) { R00, R01, R02, TX, |
| 347 | R10, R11, R12, TY, |
| 348 | R20, R21, R22, TZ, |
| 349 | 0, 0, 0, 1 }); |
| 350 | } |
| 351 | |
| 352 | // Similar to above |
| 353 | // Recover the model view matrix assuming that the projection matrix is: |
| 354 | // |
| 355 | // [ F 0 A 0 ] (see glFrustrum) |
| 356 | // [ 0 G B 0 ] |
| 357 | // [ 0 0 C D ] |
| 358 | // [ 0 0 -1 0 ] |
| 359 | |
| 360 | matd_t *homography_to_model_view(const matd_t *H, double F, double G, double A, double B, double C, double D) |
| 361 | { |
| 362 | // Note that every variable that we compute is proportional to the scale factor of H. |
| 363 | double R20 = -MATD_EL(H, 2, 0); |
| 364 | double R21 = -MATD_EL(H, 2, 1); |
| 365 | double TZ = -MATD_EL(H, 2, 2); |
| 366 | double R00 = (MATD_EL(H, 0, 0) - A*R20) / F; |
| 367 | double R01 = (MATD_EL(H, 0, 1) - A*R21) / F; |
| 368 | double TX = (MATD_EL(H, 0, 2) - A*TZ) / F; |
| 369 | double R10 = (MATD_EL(H, 1, 0) - B*R20) / G; |
| 370 | double R11 = (MATD_EL(H, 1, 1) - B*R21) / G; |
| 371 | double TY = (MATD_EL(H, 1, 2) - B*TZ) / G; |
| 372 | |
| 373 | // compute the scale by requiring that the rotation columns are unit length |
| 374 | // (Use geometric average of the two length vectors we have) |
| 375 | double length1 = sqrtf(R00*R00 + R10*R10 + R20*R20); |
| 376 | double length2 = sqrtf(R01*R01 + R11*R11 + R21*R21); |
| 377 | double s = 1.0 / sqrtf(length1 * length2); |
| 378 | |
| 379 | // get sign of S by requiring the tag to be in front of the camera |
| 380 | // (which is Z < 0) for our conventions. |
| 381 | if (TZ > 0) |
| 382 | s *= -1; |
| 383 | |
| 384 | R20 *= s; |
| 385 | R21 *= s; |
| 386 | TZ *= s; |
| 387 | R00 *= s; |
| 388 | R01 *= s; |
| 389 | TX *= s; |
| 390 | R10 *= s; |
| 391 | R11 *= s; |
| 392 | TY *= s; |
| 393 | |
| 394 | // now recover [R02 R12 R22] by noting that it is the cross product of the other two columns. |
| 395 | double R02 = R10*R21 - R20*R11; |
| 396 | double R12 = R20*R01 - R00*R21; |
| 397 | double R22 = R00*R11 - R10*R01; |
| 398 | |
| 399 | // TODO XXX: Improve rotation matrix by applying polar decomposition. |
| 400 | |
| 401 | return matd_create_data(4, 4, (double[]) { R00, R01, R02, TX, |
| 402 | R10, R11, R12, TY, |
| 403 | R20, R21, R22, TZ, |
| 404 | 0, 0, 0, 1 }); |
| 405 | } |
| 406 | |
| 407 | // Only uses the upper 3x3 matrix. |
| 408 | /* |
| 409 | static void matrix_to_quat(const matd_t *R, double q[4]) |
| 410 | { |
| 411 | // see: "from quaternion to matrix and back" |
| 412 | |
| 413 | // trace: get the same result if R is 4x4 or 3x3: |
| 414 | double T = MATD_EL(R, 0, 0) + MATD_EL(R, 1, 1) + MATD_EL(R, 2, 2) + 1; |
| 415 | double S = 0; |
| 416 | |
| 417 | double m0 = MATD_EL(R, 0, 0); |
| 418 | double m1 = MATD_EL(R, 1, 0); |
| 419 | double m2 = MATD_EL(R, 2, 0); |
| 420 | double m4 = MATD_EL(R, 0, 1); |
| 421 | double m5 = MATD_EL(R, 1, 1); |
| 422 | double m6 = MATD_EL(R, 2, 1); |
| 423 | double m8 = MATD_EL(R, 0, 2); |
| 424 | double m9 = MATD_EL(R, 1, 2); |
| 425 | double m10 = MATD_EL(R, 2, 2); |
| 426 | |
| 427 | if (T > 0.0000001) { |
| 428 | S = sqrtf(T) * 2; |
| 429 | q[1] = -( m9 - m6 ) / S; |
| 430 | q[2] = -( m2 - m8 ) / S; |
| 431 | q[3] = -( m4 - m1 ) / S; |
| 432 | q[0] = 0.25 * S; |
| 433 | } else if ( m0 > m5 && m0 > m10 ) { // Column 0: |
| 434 | S = sqrtf( 1.0 + m0 - m5 - m10 ) * 2; |
| 435 | q[1] = -0.25 * S; |
| 436 | q[2] = -(m4 + m1 ) / S; |
| 437 | q[3] = -(m2 + m8 ) / S; |
| 438 | q[0] = (m9 - m6 ) / S; |
| 439 | } else if ( m5 > m10 ) { // Column 1: |
| 440 | S = sqrtf( 1.0 + m5 - m0 - m10 ) * 2; |
| 441 | q[1] = -(m4 + m1 ) / S; |
| 442 | q[2] = -0.25 * S; |
| 443 | q[3] = -(m9 + m6 ) / S; |
| 444 | q[0] = (m2 - m8 ) / S; |
| 445 | } else { |
| 446 | // Column 2: |
| 447 | S = sqrtf( 1.0 + m10 - m0 - m5 ) * 2; |
| 448 | q[1] = -(m2 + m8 ) / S; |
| 449 | q[2] = -(m9 + m6 ) / S; |
| 450 | q[3] = -0.25 * S; |
| 451 | q[0] = (m4 - m1 ) / S; |
| 452 | } |
| 453 | |
| 454 | double mag2 = 0; |
| 455 | for (int i = 0; i < 4; i++) |
| 456 | mag2 += q[i]*q[i]; |
| 457 | double norm = 1.0 / sqrtf(mag2); |
| 458 | for (int i = 0; i < 4; i++) |
| 459 | q[i] *= norm; |
| 460 | } |
| 461 | */ |
| 462 | |
| 463 | // overwrites upper 3x3 area of matrix M. Doesn't touch any other elements of M. |
| 464 | void quat_to_matrix(const double q[4], matd_t *M) |
| 465 | { |
| 466 | double w = q[0], x = q[1], y = q[2], z = q[3]; |
| 467 | |
| 468 | MATD_EL(M, 0, 0) = w*w + x*x - y*y - z*z; |
| 469 | MATD_EL(M, 0, 1) = 2*x*y - 2*w*z; |
| 470 | MATD_EL(M, 0, 2) = 2*x*z + 2*w*y; |
| 471 | |
| 472 | MATD_EL(M, 1, 0) = 2*x*y + 2*w*z; |
| 473 | MATD_EL(M, 1, 1) = w*w - x*x + y*y - z*z; |
| 474 | MATD_EL(M, 1, 2) = 2*y*z - 2*w*x; |
| 475 | |
| 476 | MATD_EL(M, 2, 0) = 2*x*z - 2*w*y; |
| 477 | MATD_EL(M, 2, 1) = 2*y*z + 2*w*x; |
| 478 | MATD_EL(M, 2, 2) = w*w - x*x - y*y + z*z; |
| 479 | } |