| 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" |
| 41 |
|
template<typename Real> |
| 42 |
|
class SquareMatrix3 : public SquareMatrix<Real, 3> { |
| 43 |
|
public: |
| 44 |
+ |
|
| 45 |
+ |
typedef Real ElemType; |
| 46 |
+ |
typedef Real* ElemPoinerType; |
| 47 |
|
|
| 48 |
|
/** default constructor */ |
| 49 |
|
SquareMatrix3() : SquareMatrix<Real, 3>() { |
| 278 |
|
m /= det; |
| 279 |
|
return m; |
| 280 |
|
} |
| 281 |
< |
|
| 282 |
< |
void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v) { |
| 283 |
< |
int i,j,k,maxI; |
| 284 |
< |
Real tmp, maxVal; |
| 285 |
< |
Vector3<Real> v_maxI, v_k, v_j; |
| 286 |
< |
|
| 287 |
< |
// diagonalize using Jacobi |
| 288 |
< |
jacobi(a, w, v); |
| 281 |
> |
/** |
| 282 |
> |
* Extract the eigenvalues and eigenvectors from a 3x3 matrix. |
| 283 |
> |
* The eigenvectors (the columns of V) will be normalized. |
| 284 |
> |
* The eigenvectors are aligned optimally with the x, y, and z |
| 285 |
> |
* axes respectively. |
| 286 |
> |
* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is |
| 287 |
> |
* overwritten |
| 288 |
> |
* @param w will contain the eigenvalues of the matrix On return of this function |
| 289 |
> |
* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are |
| 290 |
> |
* normalized and mutually orthogonal. |
| 291 |
> |
* @warning a will be overwritten |
| 292 |
> |
*/ |
| 293 |
> |
static void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v); |
| 294 |
> |
}; |
| 295 |
> |
/*========================================================================= |
| 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 |
< |
} |
| 297 |
> |
Program: Visualization Toolkit |
| 298 |
> |
Module: $RCSfile: SquareMatrix3.hpp,v $ |
| 299 |
> |
|
| 300 |
> |
Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen |
| 301 |
> |
All rights reserved. |
| 302 |
> |
See Copyright.txt or http://www.kitware.com/Copyright.htm for details. |
| 303 |
|
|
| 304 |
< |
// transpose temporarily, it makes it easier to sort the eigenvectors |
| 305 |
< |
v = v.transpose(); |
| 306 |
< |
|
| 307 |
< |
// if two eigenvalues are the same, re-orthogonalize to optimally line |
| 308 |
< |
// up the eigenvectors with the x, y, and z axes |
| 309 |
< |
for (i = 0; i < 3; i++) { |
| 310 |
< |
if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same |
| 311 |
< |
// find maximum element of the independant eigenvector |
| 312 |
< |
maxVal = fabs(v(i, 0)); |
| 313 |
< |
maxI = 0; |
| 314 |
< |
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; |
| 304 |
> |
This software is distributed WITHOUT ANY WARRANTY; without even |
| 305 |
> |
the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR |
| 306 |
> |
PURPOSE. See the above copyright notice for more information. |
| 307 |
> |
|
| 308 |
> |
=========================================================================*/ |
| 309 |
> |
template<typename Real> |
| 310 |
> |
void SquareMatrix3<Real>::diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, |
| 311 |
> |
SquareMatrix3<Real>& v) { |
| 312 |
> |
int i,j,k,maxI; |
| 313 |
> |
Real tmp, maxVal; |
| 314 |
> |
Vector3<Real> v_maxI, v_k, v_j; |
| 315 |
|
|
| 316 |
< |
v.swapRow(i, maxI); |
| 317 |
< |
} |
| 318 |
< |
// maximum element of eigenvector should be positive |
| 319 |
< |
if (v(maxI, maxI) < 0) { |
| 320 |
< |
v(maxI, 0) = -v(maxI, 0); |
| 321 |
< |
v(maxI, 1) = -v(maxI, 1); |
| 322 |
< |
v(maxI, 2) = -v(maxI, 2); |
| 323 |
< |
} |
| 316 |
> |
// diagonalize using Jacobi |
| 317 |
> |
jacobi(a, w, v); |
| 318 |
> |
// if all the eigenvalues are the same, return identity matrix |
| 319 |
> |
if (w[0] == w[1] && w[0] == w[2] ) { |
| 320 |
> |
v = SquareMatrix3<Real>::identity(); |
| 321 |
> |
return; |
| 322 |
> |
} |
| 323 |
|
|
| 324 |
< |
// re-orthogonalize the other two eigenvectors |
| 325 |
< |
j = (maxI+1)%3; |
| 326 |
< |
k = (maxI+2)%3; |
| 324 |
> |
// transpose temporarily, it makes it easier to sort the eigenvectors |
| 325 |
> |
v = v.transpose(); |
| 326 |
> |
|
| 327 |
> |
// if two eigenvalues are the same, re-orthogonalize to optimally line |
| 328 |
> |
// up the eigenvectors with the x, y, and z axes |
| 329 |
> |
for (i = 0; i < 3; i++) { |
| 330 |
> |
if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same |
| 331 |
> |
// find maximum element of the independant eigenvector |
| 332 |
> |
maxVal = fabs(v(i, 0)); |
| 333 |
> |
maxI = 0; |
| 334 |
> |
for (j = 1; j < 3; j++) { |
| 335 |
> |
if (maxVal < (tmp = fabs(v(i, j)))){ |
| 336 |
> |
maxVal = tmp; |
| 337 |
> |
maxI = j; |
| 338 |
> |
} |
| 339 |
> |
} |
| 340 |
> |
|
| 341 |
> |
// swap the eigenvector into its proper position |
| 342 |
> |
if (maxI != i) { |
| 343 |
> |
tmp = w(maxI); |
| 344 |
> |
w(maxI) = w(i); |
| 345 |
> |
w(i) = tmp; |
| 346 |
|
|
| 347 |
< |
v(j, 0) = 0.0; |
| 348 |
< |
v(j, 1) = 0.0; |
| 349 |
< |
v(j, 2) = 0.0; |
| 350 |
< |
v(j, j) = 1.0; |
| 347 |
> |
v.swapRow(i, maxI); |
| 348 |
> |
} |
| 349 |
> |
// maximum element of eigenvector should be positive |
| 350 |
> |
if (v(maxI, maxI) < 0) { |
| 351 |
> |
v(maxI, 0) = -v(maxI, 0); |
| 352 |
> |
v(maxI, 1) = -v(maxI, 1); |
| 353 |
> |
v(maxI, 2) = -v(maxI, 2); |
| 354 |
> |
} |
| 355 |
|
|
| 356 |
< |
/** @todo */ |
| 357 |
< |
v_maxI = v.getRow(maxI); |
| 358 |
< |
v_j = v.getRow(j); |
| 337 |
< |
v_k = cross(v_maxI, v_j); |
| 338 |
< |
v_k.normalize(); |
| 339 |
< |
v_j = cross(v_k, v_maxI); |
| 340 |
< |
v.setRow(j, v_j); |
| 341 |
< |
v.setRow(k, v_k); |
| 356 |
> |
// re-orthogonalize the other two eigenvectors |
| 357 |
> |
j = (maxI+1)%3; |
| 358 |
> |
k = (maxI+2)%3; |
| 359 |
|
|
| 360 |
+ |
v(j, 0) = 0.0; |
| 361 |
+ |
v(j, 1) = 0.0; |
| 362 |
+ |
v(j, 2) = 0.0; |
| 363 |
+ |
v(j, j) = 1.0; |
| 364 |
|
|
| 365 |
< |
// transpose vectors back to columns |
| 366 |
< |
v = v.transpose(); |
| 367 |
< |
return; |
| 368 |
< |
} |
| 369 |
< |
} |
| 365 |
> |
/** @todo */ |
| 366 |
> |
v_maxI = v.getRow(maxI); |
| 367 |
> |
v_j = v.getRow(j); |
| 368 |
> |
v_k = cross(v_maxI, v_j); |
| 369 |
> |
v_k.normalize(); |
| 370 |
> |
v_j = cross(v_k, v_maxI); |
| 371 |
> |
v.setRow(j, v_j); |
| 372 |
> |
v.setRow(k, v_k); |
| 373 |
|
|
| 350 |
– |
// the three eigenvalues are different, just sort the eigenvectors |
| 351 |
– |
// to align them with the x, y, and z axes |
| 374 |
|
|
| 375 |
< |
// find the vector with the largest x element, make that vector |
| 376 |
< |
// the first vector |
| 377 |
< |
maxVal = fabs(v(0, 0)); |
| 378 |
< |
maxI = 0; |
| 379 |
< |
for (i = 1; i < 3; i++) { |
| 358 |
< |
if (maxVal < (tmp = fabs(v(i, 0)))) { |
| 359 |
< |
maxVal = tmp; |
| 360 |
< |
maxI = i; |
| 361 |
< |
} |
| 362 |
< |
} |
| 375 |
> |
// transpose vectors back to columns |
| 376 |
> |
v = v.transpose(); |
| 377 |
> |
return; |
| 378 |
> |
} |
| 379 |
> |
} |
| 380 |
|
|
| 381 |
< |
// swap eigenvalue and eigenvector |
| 382 |
< |
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 |
< |
} |
| 381 |
> |
// the three eigenvalues are different, just sort the eigenvectors |
| 382 |
> |
// to align them with the x, y, and z axes |
| 383 |
|
|
| 384 |
< |
// ensure that the sign of the eigenvectors is correct |
| 385 |
< |
for (i = 0; i < 2; i++) { |
| 386 |
< |
if (v(i, i) < 0) { |
| 387 |
< |
v(i, 0) = -v(i, 0); |
| 388 |
< |
v(i, 1) = -v(i, 1); |
| 389 |
< |
v(i, 2) = -v(i, 2); |
| 390 |
< |
} |
| 391 |
< |
} |
| 384 |
> |
// find the vector with the largest x element, make that vector |
| 385 |
> |
// the first vector |
| 386 |
> |
maxVal = fabs(v(0, 0)); |
| 387 |
> |
maxI = 0; |
| 388 |
> |
for (i = 1; i < 3; i++) { |
| 389 |
> |
if (maxVal < (tmp = fabs(v(i, 0)))) { |
| 390 |
> |
maxVal = tmp; |
| 391 |
> |
maxI = i; |
| 392 |
> |
} |
| 393 |
> |
} |
| 394 |
|
|
| 395 |
< |
// set sign of final eigenvector to ensure that determinant is positive |
| 396 |
< |
if (v.determinant() < 0) { |
| 397 |
< |
v(2, 0) = -v(2, 0); |
| 398 |
< |
v(2, 1) = -v(2, 1); |
| 399 |
< |
v(2, 2) = -v(2, 2); |
| 400 |
< |
} |
| 395 |
> |
// swap eigenvalue and eigenvector |
| 396 |
> |
if (maxI != 0) { |
| 397 |
> |
tmp = w(maxI); |
| 398 |
> |
w(maxI) = w(0); |
| 399 |
> |
w(0) = tmp; |
| 400 |
> |
v.swapRow(maxI, 0); |
| 401 |
> |
} |
| 402 |
> |
// do the same for the y element |
| 403 |
> |
if (fabs(v(1, 1)) < fabs(v(2, 1))) { |
| 404 |
> |
tmp = w(2); |
| 405 |
> |
w(2) = w(1); |
| 406 |
> |
w(1) = tmp; |
| 407 |
> |
v.swapRow(2, 1); |
| 408 |
> |
} |
| 409 |
|
|
| 410 |
< |
// transpose the eigenvectors back again |
| 411 |
< |
v = v.transpose(); |
| 412 |
< |
return ; |
| 410 |
> |
// ensure that the sign of the eigenvectors is correct |
| 411 |
> |
for (i = 0; i < 2; i++) { |
| 412 |
> |
if (v(i, i) < 0) { |
| 413 |
> |
v(i, 0) = -v(i, 0); |
| 414 |
> |
v(i, 1) = -v(i, 1); |
| 415 |
> |
v(i, 2) = -v(i, 2); |
| 416 |
|
} |
| 417 |
< |
}; |
| 417 |
> |
} |
| 418 |
|
|
| 419 |
+ |
// set sign of final eigenvector to ensure that determinant is positive |
| 420 |
+ |
if (v.determinant() < 0) { |
| 421 |
+ |
v(2, 0) = -v(2, 0); |
| 422 |
+ |
v(2, 1) = -v(2, 1); |
| 423 |
+ |
v(2, 2) = -v(2, 2); |
| 424 |
+ |
} |
| 425 |
+ |
|
| 426 |
+ |
// transpose the eigenvectors back again |
| 427 |
+ |
v = v.transpose(); |
| 428 |
+ |
return ; |
| 429 |
+ |
} |
| 430 |
|
typedef SquareMatrix3<double> Mat3x3d; |
| 431 |
|
typedef SquareMatrix3<double> RotMat3x3d; |
| 432 |
|
|
| 433 |
|
} //namespace oopse |
| 434 |
|
#endif // MATH_SQUAREMATRIX_HPP |
| 435 |
+ |
|
