72 |
|
if (this == &m) |
73 |
|
return *this; |
74 |
|
SquareMatrix<Real, 3>::operator=(m); |
75 |
+ |
return *this; |
76 |
|
} |
77 |
|
|
78 |
|
/** |
127 |
|
* @param w the first element |
128 |
|
* @param x the second element |
129 |
|
* @param y the third element |
130 |
< |
* @parma z the fourth element |
130 |
> |
* @param z the fourth element |
131 |
|
*/ |
132 |
|
void setupRotMat(Real w, Real x, Real y, Real z) { |
133 |
|
Quaternion<Real> q(w, x, y, z); |
238 |
|
return myEuler; |
239 |
|
} |
240 |
|
|
241 |
+ |
/** Returns the determinant of this matrix. */ |
242 |
+ |
Real determinant() const { |
243 |
+ |
Real x,y,z; |
244 |
+ |
|
245 |
+ |
x = data_[0][0] * (data_[1][1] * data_[2][2] - data_[1][2] * data_[2][1]); |
246 |
+ |
y = data_[0][1] * (data_[1][2] * data_[2][0] - data_[1][0] * data_[2][2]); |
247 |
+ |
z = data_[0][2] * (data_[1][0] * data_[2][1] - data_[1][1] * data_[2][0]); |
248 |
+ |
|
249 |
+ |
return(x + y + z); |
250 |
+ |
} |
251 |
+ |
|
252 |
|
/** |
253 |
|
* Sets the value of this matrix to the inversion of itself. |
254 |
|
* @note since simple algorithm can be applied to inverse the 3 by 3 matrix, we hide the |
255 |
|
* implementation of inverse in SquareMatrix class |
256 |
|
*/ |
257 |
< |
void inverse() { |
257 |
> |
SquareMatrix3<Real> inverse() { |
258 |
> |
SquareMatrix3<Real> m; |
259 |
> |
double det = determinant(); |
260 |
> |
if (fabs(det) <= oopse::epsilon) { |
261 |
> |
//"The method was called on a matrix with |determinant| <= 1e-6.", |
262 |
> |
//"This is a runtime or a programming error in your application."); |
263 |
> |
} |
264 |
|
|
265 |
+ |
m(0, 0) = data_[1][1]*data_[2][2] - data_[1][2]*data_[2][1]; |
266 |
+ |
m(1, 0) = data_[1][2]*data_[2][0] - data_[1][0]*data_[2][2]; |
267 |
+ |
m(2, 0) = data_[1][0]*data_[2][1] - data_[1][1]*data_[2][0]; |
268 |
+ |
m(0, 1) = data_[2][1]*data_[0][2] - data_[2][2]*data_[0][1]; |
269 |
+ |
m(1, 1) = data_[2][2]*data_[0][0] - data_[2][0]*data_[0][2]; |
270 |
+ |
m(2, 1) = data_[2][0]*data_[0][1] - data_[2][1]*data_[0][0]; |
271 |
+ |
m(0, 2) = data_[0][1]*data_[1][2] - data_[0][2]*data_[1][1]; |
272 |
+ |
m(1, 2) = data_[0][2]*data_[1][0] - data_[0][0]*data_[1][2]; |
273 |
+ |
m(2, 2) = data_[0][0]*data_[1][1] - data_[0][1]*data_[1][0]; |
274 |
+ |
|
275 |
+ |
m /= det; |
276 |
+ |
return m; |
277 |
|
} |
278 |
|
|
279 |
< |
void diagonalize() { |
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; |
283 |
|
|
284 |
+ |
// diagonalize using Jacobi |
285 |
+ |
jacobi(a, w, v); |
286 |
+ |
|
287 |
+ |
// if all the eigenvalues are the same, return identity matrix |
288 |
+ |
if (w[0] == w[1] && w[0] == w[2] ){ |
289 |
+ |
v = SquareMatrix3<Real>::identity(); |
290 |
+ |
return |
291 |
+ |
} |
292 |
+ |
|
293 |
+ |
// transpose temporarily, it makes it easier to sort the eigenvectors |
294 |
+ |
v = v.tanspose(); |
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; |
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 |
+ |
} |
324 |
+ |
|
325 |
+ |
// re-orthogonalize the other two eigenvectors |
326 |
+ |
j = (maxI+1)%3; |
327 |
+ |
k = (maxI+2)%3; |
328 |
+ |
|
329 |
+ |
v(j, 0) = 0.0; |
330 |
+ |
v(j, 1) = 0.0; |
331 |
+ |
v(j, 2) = 0.0; |
332 |
+ |
v(j, j) = 1.0; |
333 |
+ |
|
334 |
+ |
/** @todo */ |
335 |
+ |
v_maxI = v.getRow(maxI); |
336 |
+ |
v_j = v.getRow(j); |
337 |
+ |
v_k = cross(v_maxI, v_j); |
338 |
+ |
v_k.normailze(); |
339 |
+ |
v_j = cross(v_k, v_maxI); |
340 |
+ |
v.setRow(j, v_j); |
341 |
+ |
v.setRow(k, v_k); |
342 |
+ |
|
343 |
+ |
|
344 |
+ |
// transpose vectors back to columns |
345 |
+ |
v = v.transpose(); |
346 |
+ |
return; |
347 |
+ |
} |
348 |
+ |
} |
349 |
+ |
|
350 |
+ |
// the three eigenvalues are different, just sort the eigenvectors |
351 |
+ |
// to align them with the x, y, and z axes |
352 |
+ |
|
353 |
+ |
// find the vector with the largest x element, make that vector |
354 |
+ |
// the first vector |
355 |
+ |
maxVal = fabs(v(0, 0)); |
356 |
+ |
maxI = 0; |
357 |
+ |
for (i = 1; i < 3; i++) { |
358 |
+ |
if (maxVal < (tmp = fabs(v(i, 0)))) { |
359 |
+ |
maxVal = tmp; |
360 |
+ |
maxI = i; |
361 |
+ |
} |
362 |
+ |
} |
363 |
+ |
|
364 |
+ |
// swap eigenvalue and eigenvector |
365 |
+ |
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 |
+ |
|
379 |
+ |
// ensure that the sign of the eigenvectors is correct |
380 |
+ |
for (i = 0; i < 2; i++) { |
381 |
+ |
if (v(i, i) < 0) { |
382 |
+ |
v(i, 0) = -v(i, 0); |
383 |
+ |
v(i, 1) = -v(i, 1); |
384 |
+ |
v(i, 2) = -v(i, 2); |
385 |
+ |
} |
386 |
+ |
} |
387 |
+ |
|
388 |
+ |
// set sign of final eigenvector to ensure that determinant is positive |
389 |
+ |
if (determinant(v) < 0) { |
390 |
+ |
v(2, 0) = -v(2, 0); |
391 |
+ |
v(2, 1) = -v(2, 1); |
392 |
+ |
v(2, 2) = -v(2, 2); |
393 |
+ |
} |
394 |
+ |
|
395 |
+ |
// transpose the eigenvectors back again |
396 |
+ |
v = v.transpose(); |
397 |
+ |
return ; |
398 |
|
} |
399 |
|
}; |
400 |
|
|