# | Line 29 | Line 29 | |
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29 | * @date 10/11/2004 | |
30 | * @version 1.0 | |
31 | */ | |
32 | < | #ifndef MATH_SQUAREMATRIX3_HPP |
32 | > | #ifndef MATH_SQUAREMATRIX3_HPP |
33 | #define MATH_SQUAREMATRIX3_HPP | |
34 | ||
35 | #include "Quaternion.hpp" | |
# | Line 275 | Line 275 | namespace oopse { | |
275 | m /= det; | |
276 | return m; | |
277 | } | |
278 | < | |
279 | < | void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v) { |
280 | < | int i,j,k,maxI; |
281 | < | Real tmp, maxVal; |
282 | < | Vector3<Real> v_maxI, v_k, v_j; |
278 | > | /** |
279 | > | * Extract the eigenvalues and eigenvectors from a 3x3 matrix. |
280 | > | * The eigenvectors (the columns of V) will be normalized. |
281 | > | * The eigenvectors are aligned optimally with the x, y, and z |
282 | > | * axes respectively. |
283 | > | * @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is |
284 | > | * overwritten |
285 | > | * @param w will contain the eigenvalues of the matrix On return of this function |
286 | > | * @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are |
287 | > | * normalized and mutually orthogonal. |
288 | > | * @warning a will be overwritten |
289 | > | */ |
290 | > | static void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v); |
291 | > | }; |
292 | > | /*========================================================================= |
293 | ||
294 | < | // diagonalize using Jacobi |
295 | < | jacobi(a, w, v); |
294 | > | Program: Visualization Toolkit |
295 | > | Module: $RCSfile: SquareMatrix3.hpp,v $ |
296 | ||
297 | < | // if all the eigenvalues are the same, return identity matrix |
298 | < | if (w[0] == w[1] && w[0] == w[2] ) { |
299 | < | v = SquareMatrix3<Real>::identity(); |
300 | < | return; |
301 | < | } |
302 | < | |
303 | < | // transpose temporarily, it makes it easier to sort the eigenvectors |
294 | < | v = v.transpose(); |
295 | < | |
296 | < | // if two eigenvalues are the same, re-orthogonalize to optimally line |
297 | < | // up the eigenvectors with the x, y, and z axes |
298 | < | for (i = 0; i < 3; i++) { |
299 | < | if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same |
300 | < | // find maximum element of the independant eigenvector |
301 | < | maxVal = fabs(v(i, 0)); |
302 | < | maxI = 0; |
303 | < | for (j = 1; j < 3; j++) { |
304 | < | if (maxVal < (tmp = fabs(v(i, j)))){ |
305 | < | maxVal = tmp; |
306 | < | maxI = j; |
307 | < | } |
308 | < | } |
309 | < | |
310 | < | // swap the eigenvector into its proper position |
311 | < | if (maxI != i) { |
312 | < | tmp = w(maxI); |
313 | < | w(maxI) = w(i); |
314 | < | w(i) = tmp; |
297 | > | Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen |
298 | > | All rights reserved. |
299 | > | See Copyright.txt or http://www.kitware.com/Copyright.htm for details. |
300 | > | |
301 | > | This software is distributed WITHOUT ANY WARRANTY; without even |
302 | > | the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR |
303 | > | PURPOSE. See the above copyright notice for more information. |
304 | ||
305 | < | v.swapRow(i, maxI); |
306 | < | } |
307 | < | // maximum element of eigenvector should be positive |
308 | < | if (v(maxI, maxI) < 0) { |
309 | < | v(maxI, 0) = -v(maxI, 0); |
310 | < | v(maxI, 1) = -v(maxI, 1); |
311 | < | v(maxI, 2) = -v(maxI, 2); |
323 | < | } |
305 | > | =========================================================================*/ |
306 | > | template<typename Real> |
307 | > | void SquareMatrix3<Real>::diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, |
308 | > | SquareMatrix3<Real>& v) { |
309 | > | int i,j,k,maxI; |
310 | > | Real tmp, maxVal; |
311 | > | Vector3<Real> v_maxI, v_k, v_j; |
312 | ||
313 | < | // re-orthogonalize the other two eigenvectors |
314 | < | j = (maxI+1)%3; |
315 | < | k = (maxI+2)%3; |
313 | > | // diagonalize using Jacobi |
314 | > | jacobi(a, w, v); |
315 | > | // if all the eigenvalues are the same, return identity matrix |
316 | > | if (w[0] == w[1] && w[0] == w[2] ) { |
317 | > | v = SquareMatrix3<Real>::identity(); |
318 | > | return; |
319 | > | } |
320 | ||
321 | < | v(j, 0) = 0.0; |
322 | < | v(j, 1) = 0.0; |
323 | < | v(j, 2) = 0.0; |
324 | < | v(j, j) = 1.0; |
321 | > | // transpose temporarily, it makes it easier to sort the eigenvectors |
322 | > | v = v.transpose(); |
323 | > | |
324 | > | // if two eigenvalues are the same, re-orthogonalize to optimally line |
325 | > | // up the eigenvectors with the x, y, and z axes |
326 | > | for (i = 0; i < 3; i++) { |
327 | > | if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same |
328 | > | // find maximum element of the independant eigenvector |
329 | > | maxVal = fabs(v(i, 0)); |
330 | > | maxI = 0; |
331 | > | for (j = 1; j < 3; j++) { |
332 | > | if (maxVal < (tmp = fabs(v(i, j)))){ |
333 | > | maxVal = tmp; |
334 | > | maxI = j; |
335 | > | } |
336 | > | } |
337 | > | |
338 | > | // swap the eigenvector into its proper position |
339 | > | if (maxI != i) { |
340 | > | tmp = w(maxI); |
341 | > | w(maxI) = w(i); |
342 | > | w(i) = tmp; |
343 | ||
344 | < | /** @todo */ |
345 | < | v_maxI = v.getRow(maxI); |
346 | < | v_j = v.getRow(j); |
347 | < | v_k = cross(v_maxI, v_j); |
348 | < | v_k.normalize(); |
349 | < | v_j = cross(v_k, v_maxI); |
350 | < | v.setRow(j, v_j); |
351 | < | v.setRow(k, v_k); |
344 | > | v.swapRow(i, maxI); |
345 | > | } |
346 | > | // maximum element of eigenvector should be positive |
347 | > | if (v(maxI, maxI) < 0) { |
348 | > | v(maxI, 0) = -v(maxI, 0); |
349 | > | v(maxI, 1) = -v(maxI, 1); |
350 | > | v(maxI, 2) = -v(maxI, 2); |
351 | > | } |
352 | > | |
353 | > | // re-orthogonalize the other two eigenvectors |
354 | > | j = (maxI+1)%3; |
355 | > | k = (maxI+2)%3; |
356 | ||
357 | + | v(j, 0) = 0.0; |
358 | + | v(j, 1) = 0.0; |
359 | + | v(j, 2) = 0.0; |
360 | + | v(j, j) = 1.0; |
361 | ||
362 | < | // transpose vectors back to columns |
363 | < | v = v.transpose(); |
364 | < | return; |
365 | < | } |
366 | < | } |
362 | > | /** @todo */ |
363 | > | v_maxI = v.getRow(maxI); |
364 | > | v_j = v.getRow(j); |
365 | > | v_k = cross(v_maxI, v_j); |
366 | > | v_k.normalize(); |
367 | > | v_j = cross(v_k, v_maxI); |
368 | > | v.setRow(j, v_j); |
369 | > | v.setRow(k, v_k); |
370 | ||
350 | – | // the three eigenvalues are different, just sort the eigenvectors |
351 | – | // to align them with the x, y, and z axes |
371 | ||
372 | < | // find the vector with the largest x element, make that vector |
373 | < | // the first vector |
374 | < | maxVal = fabs(v(0, 0)); |
375 | < | maxI = 0; |
376 | < | for (i = 1; i < 3; i++) { |
358 | < | if (maxVal < (tmp = fabs(v(i, 0)))) { |
359 | < | maxVal = tmp; |
360 | < | maxI = i; |
361 | < | } |
362 | < | } |
372 | > | // transpose vectors back to columns |
373 | > | v = v.transpose(); |
374 | > | return; |
375 | > | } |
376 | > | } |
377 | ||
378 | < | // swap eigenvalue and eigenvector |
379 | < | if (maxI != 0) { |
366 | < | tmp = w(maxI); |
367 | < | w(maxI) = w(0); |
368 | < | w(0) = tmp; |
369 | < | v.swapRow(maxI, 0); |
370 | < | } |
371 | < | // do the same for the y element |
372 | < | if (fabs(v(1, 1)) < fabs(v(2, 1))) { |
373 | < | tmp = w(2); |
374 | < | w(2) = w(1); |
375 | < | w(1) = tmp; |
376 | < | v.swapRow(2, 1); |
377 | < | } |
378 | > | // the three eigenvalues are different, just sort the eigenvectors |
379 | > | // to align them with the x, y, and z axes |
380 | ||
381 | < | // ensure that the sign of the eigenvectors is correct |
382 | < | for (i = 0; i < 2; i++) { |
383 | < | if (v(i, i) < 0) { |
384 | < | v(i, 0) = -v(i, 0); |
385 | < | v(i, 1) = -v(i, 1); |
386 | < | v(i, 2) = -v(i, 2); |
387 | < | } |
388 | < | } |
381 | > | // find the vector with the largest x element, make that vector |
382 | > | // the first vector |
383 | > | maxVal = fabs(v(0, 0)); |
384 | > | maxI = 0; |
385 | > | for (i = 1; i < 3; i++) { |
386 | > | if (maxVal < (tmp = fabs(v(i, 0)))) { |
387 | > | maxVal = tmp; |
388 | > | maxI = i; |
389 | > | } |
390 | > | } |
391 | ||
392 | < | // set sign of final eigenvector to ensure that determinant is positive |
393 | < | if (v.determinant() < 0) { |
394 | < | v(2, 0) = -v(2, 0); |
395 | < | v(2, 1) = -v(2, 1); |
396 | < | v(2, 2) = -v(2, 2); |
397 | < | } |
392 | > | // swap eigenvalue and eigenvector |
393 | > | if (maxI != 0) { |
394 | > | tmp = w(maxI); |
395 | > | w(maxI) = w(0); |
396 | > | w(0) = tmp; |
397 | > | v.swapRow(maxI, 0); |
398 | > | } |
399 | > | // do the same for the y element |
400 | > | if (fabs(v(1, 1)) < fabs(v(2, 1))) { |
401 | > | tmp = w(2); |
402 | > | w(2) = w(1); |
403 | > | w(1) = tmp; |
404 | > | v.swapRow(2, 1); |
405 | > | } |
406 | ||
407 | < | // transpose the eigenvectors back again |
408 | < | v = v.transpose(); |
409 | < | return ; |
407 | > | // ensure that the sign of the eigenvectors is correct |
408 | > | for (i = 0; i < 2; i++) { |
409 | > | if (v(i, i) < 0) { |
410 | > | v(i, 0) = -v(i, 0); |
411 | > | v(i, 1) = -v(i, 1); |
412 | > | v(i, 2) = -v(i, 2); |
413 | } | |
414 | < | }; |
414 | > | } |
415 | ||
416 | + | // set sign of final eigenvector to ensure that determinant is positive |
417 | + | if (v.determinant() < 0) { |
418 | + | v(2, 0) = -v(2, 0); |
419 | + | v(2, 1) = -v(2, 1); |
420 | + | v(2, 2) = -v(2, 2); |
421 | + | } |
422 | + | |
423 | + | // transpose the eigenvectors back again |
424 | + | v = v.transpose(); |
425 | + | return ; |
426 | + | } |
427 | typedef SquareMatrix3<double> Mat3x3d; | |
428 | typedef SquareMatrix3<double> RotMat3x3d; | |
429 | ||
430 | } //namespace oopse | |
431 | #endif // MATH_SQUAREMATRIX_HPP | |
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