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root/group/trunk/OOPSE-2.0/src/math/SquareMatrix3.hpp
Revision: 2336
Committed: Wed Sep 28 16:55:57 2005 UTC (18 years, 9 months ago) by tim
File size: 16379 byte(s)
Log Message: 
using epsilon instead of 0.0 to avoid divergence in rotation matrix to quaternion transformation

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# Content
1 /*
2 * Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3 *
4 * The University of Notre Dame grants you ("Licensee") a
5 * non-exclusive, royalty free, license to use, modify and
6 * redistribute this software in source and binary code form, provided
7 * that the following conditions are met:
8 *
9 * 1. Acknowledgement of the program authors must be made in any
10 * publication of scientific results based in part on use of the
11 * program. An acceptable form of acknowledgement is citation of
12 * the article in which the program was described (Matthew
13 * A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
14 * J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
15 * Parallel Simulation Engine for Molecular Dynamics,"
16 * J. Comput. Chem. 26, pp. 252-271 (2005))
17 *
18 * 2. Redistributions of source code must retain the above copyright
19 * notice, this list of conditions and the following disclaimer.
20 *
21 * 3. Redistributions in binary form must reproduce the above copyright
22 * notice, this list of conditions and the following disclaimer in the
23 * documentation and/or other materials provided with the
24 * distribution.
25 *
26 * This software is provided "AS IS," without a warranty of any
27 * kind. All express or implied conditions, representations and
28 * warranties, including any implied warranty of merchantability,
29 * fitness for a particular purpose or non-infringement, are hereby
30 * excluded. The University of Notre Dame and its licensors shall not
31 * be liable for any damages suffered by licensee as a result of
32 * using, modifying or distributing the software or its
33 * derivatives. In no event will the University of Notre Dame or its
34 * licensors be liable for any lost revenue, profit or data, or for
35 * direct, indirect, special, consequential, incidental or punitive
36 * damages, however caused and regardless of the theory of liability,
37 * arising out of the use of or inability to use software, even if the
38 * University of Notre Dame has been advised of the possibility of
39 * such damages.
40 */
41
42 /**
43 * @file SquareMatrix3.hpp
44 * @author Teng Lin
45 * @date 10/11/2004
46 * @version 1.0
47 */
48 #ifndef MATH_SQUAREMATRIX3_HPP
49 #define MATH_SQUAREMATRIX3_HPP
50
51 #include "Quaternion.hpp"
52 #include "SquareMatrix.hpp"
53 #include "Vector3.hpp"
54 #include "utils/NumericConstant.hpp"
55 namespace oopse {
56
57 template<typename Real>
58 class SquareMatrix3 : public SquareMatrix<Real, 3> {
59 public:
60
61 typedef Real ElemType;
62 typedef Real* ElemPoinerType;
63
64 /** default constructor */
65 SquareMatrix3() : SquareMatrix<Real, 3>() {
66 }
67
68 /** Constructs and initializes every element of this matrix to a scalar */
69 SquareMatrix3(Real s) : SquareMatrix<Real,3>(s){
70 }
71
72 /** Constructs and initializes from an array */
73 SquareMatrix3(Real* array) : SquareMatrix<Real,3>(array){
74 }
75
76
77 /** copy constructor */
78 SquareMatrix3(const SquareMatrix<Real, 3>& m) : SquareMatrix<Real, 3>(m) {
79 }
80
81 SquareMatrix3( const Vector3<Real>& eulerAngles) {
82 setupRotMat(eulerAngles);
83 }
84
85 SquareMatrix3(Real phi, Real theta, Real psi) {
86 setupRotMat(phi, theta, psi);
87 }
88
89 SquareMatrix3(const Quaternion<Real>& q) {
90 setupRotMat(q);
91
92 }
93
94 SquareMatrix3(Real w, Real x, Real y, Real z) {
95 setupRotMat(w, x, y, z);
96 }
97
98 /** copy assignment operator */
99 SquareMatrix3<Real>& operator =(const SquareMatrix<Real, 3>& m) {
100 if (this == &m)
101 return *this;
102 SquareMatrix<Real, 3>::operator=(m);
103 return *this;
104 }
105
106
107 SquareMatrix3<Real>& operator =(const Quaternion<Real>& q) {
108 this->setupRotMat(q);
109 return *this;
110 }
111
112 /**
113 * Sets this matrix to a rotation matrix by three euler angles
114 * @ param euler
115 */
116 void setupRotMat(const Vector3<Real>& eulerAngles) {
117 setupRotMat(eulerAngles[0], eulerAngles[1], eulerAngles[2]);
118 }
119
120 /**
121 * Sets this matrix to a rotation matrix by three euler angles
122 * @param phi
123 * @param theta
124 * @psi theta
125 */
126 void setupRotMat(Real phi, Real theta, Real psi) {
127 Real sphi, stheta, spsi;
128 Real cphi, ctheta, cpsi;
129
130 sphi = sin(phi);
131 stheta = sin(theta);
132 spsi = sin(psi);
133 cphi = cos(phi);
134 ctheta = cos(theta);
135 cpsi = cos(psi);
136
137 this->data_[0][0] = cpsi * cphi - ctheta * sphi * spsi;
138 this->data_[0][1] = cpsi * sphi + ctheta * cphi * spsi;
139 this->data_[0][2] = spsi * stheta;
140
141 this->data_[1][0] = -spsi * ctheta - ctheta * sphi * cpsi;
142 this->data_[1][1] = -spsi * stheta + ctheta * cphi * cpsi;
143 this->data_[1][2] = cpsi * stheta;
144
145 this->data_[2][0] = stheta * sphi;
146 this->data_[2][1] = -stheta * cphi;
147 this->data_[2][2] = ctheta;
148 }
149
150
151 /**
152 * Sets this matrix to a rotation matrix by quaternion
153 * @param quat
154 */
155 void setupRotMat(const Quaternion<Real>& quat) {
156 setupRotMat(quat.w(), quat.x(), quat.y(), quat.z());
157 }
158
159 /**
160 * Sets this matrix to a rotation matrix by quaternion
161 * @param w the first element
162 * @param x the second element
163 * @param y the third element
164 * @param z the fourth element
165 */
166 void setupRotMat(Real w, Real x, Real y, Real z) {
167 Quaternion<Real> q(w, x, y, z);
168 *this = q.toRotationMatrix3();
169 }
170
171 /**
172 * Returns the quaternion from this rotation matrix
173 * @return the quaternion from this rotation matrix
174 * @exception invalid rotation matrix
175 */
176 Quaternion<Real> toQuaternion() {
177 Quaternion<Real> q;
178 Real t, s;
179 Real ad1, ad2, ad3;
180 t = this->data_[0][0] + this->data_[1][1] + this->data_[2][2] + 1.0;
181
182 if( t > NumericConstant::epsilon ){
183
184 s = 0.5 / sqrt( t );
185 q[0] = 0.25 / s;
186 q[1] = (this->data_[1][2] - this->data_[2][1]) * s;
187 q[2] = (this->data_[2][0] - this->data_[0][2]) * s;
188 q[3] = (this->data_[0][1] - this->data_[1][0]) * s;
189 } else {
190
191 ad1 = this->data_[0][0];
192 ad2 = this->data_[1][1];
193 ad3 = this->data_[2][2];
194
195 if( ad1 >= ad2 && ad1 >= ad3 ){
196
197 s = 0.5 / sqrt( 1.0 + this->data_[0][0] - this->data_[1][1] - this->data_[2][2] );
198 q[0] = (this->data_[1][2] - this->data_[2][1]) * s;
199 q[1] = 0.25 / s;
200 q[2] = (this->data_[0][1] + this->data_[1][0]) * s;
201 q[3] = (this->data_[0][2] + this->data_[2][0]) * s;
202 } else if ( ad2 >= ad1 && ad2 >= ad3 ) {
203 s = 0.5 / sqrt( 1.0 + this->data_[1][1] - this->data_[0][0] - this->data_[2][2] );
204 q[0] = (this->data_[2][0] - this->data_[0][2] ) * s;
205 q[1] = (this->data_[0][1] + this->data_[1][0]) * s;
206 q[2] = 0.25 / s;
207 q[3] = (this->data_[1][2] + this->data_[2][1]) * s;
208 } else {
209
210 s = 0.5 / sqrt( 1.0 + this->data_[2][2] - this->data_[0][0] - this->data_[1][1] );
211 q[0] = (this->data_[0][1] - this->data_[1][0]) * s;
212 q[1] = (this->data_[0][2] + this->data_[2][0]) * s;
213 q[2] = (this->data_[1][2] + this->data_[2][1]) * s;
214 q[3] = 0.25 / s;
215 }
216 }
217
218 return q;
219
220 }
221
222 /**
223 * Returns the euler angles from this rotation matrix
224 * @return the euler angles in a vector
225 * @exception invalid rotation matrix
226 * We use so-called "x-convention", which is the most common definition.
227 * In this convention, the rotation given by Euler angles (phi, theta, psi), where the first
228 * rotation is by an angle phi about the z-axis, the second is by an angle
229 * theta (0 <= theta <= 180)about the x-axis, and thethird is by an angle psi about the
230 * z-axis (again).
231 */
232 Vector3<Real> toEulerAngles() {
233 Vector3<Real> myEuler;
234 Real phi;
235 Real theta;
236 Real psi;
237 Real ctheta;
238 Real stheta;
239
240 // set the tolerance for Euler angles and rotation elements
241
242 theta = acos(std::min(1.0, std::max(-1.0,this->data_[2][2])));
243 ctheta = this->data_[2][2];
244 stheta = sqrt(1.0 - ctheta * ctheta);
245
246 // when sin(theta) is close to 0, we need to consider singularity
247 // In this case, we can assign an arbitary value to phi (or psi), and then determine
248 // the psi (or phi) or vice-versa. We'll assume that phi always gets the rotation, and psi is 0
249 // in cases of singularity.
250 // we use atan2 instead of atan, since atan2 will give us -Pi to Pi.
251 // Since 0 <= theta <= 180, sin(theta) will be always non-negative. Therefore, it never
252 // change the sign of both of the parameters passed to atan2.
253
254 if (fabs(stheta) <= oopse::epsilon){
255 psi = 0.0;
256 phi = atan2(-this->data_[1][0], this->data_[0][0]);
257 }
258 // we only have one unique solution
259 else{
260 phi = atan2(this->data_[2][0], -this->data_[2][1]);
261 psi = atan2(this->data_[0][2], this->data_[1][2]);
262 }
263
264 //wrap phi and psi, make sure they are in the range from 0 to 2*Pi
265 if (phi < 0)
266 phi += M_PI;
267
268 if (psi < 0)
269 psi += M_PI;
270
271 myEuler[0] = phi;
272 myEuler[1] = theta;
273 myEuler[2] = psi;
274
275 return myEuler;
276 }
277
278 /** Returns the determinant of this matrix. */
279 Real determinant() const {
280 Real x,y,z;
281
282 x = this->data_[0][0] * (this->data_[1][1] * this->data_[2][2] - this->data_[1][2] * this->data_[2][1]);
283 y = this->data_[0][1] * (this->data_[1][2] * this->data_[2][0] - this->data_[1][0] * this->data_[2][2]);
284 z = this->data_[0][2] * (this->data_[1][0] * this->data_[2][1] - this->data_[1][1] * this->data_[2][0]);
285
286 return(x + y + z);
287 }
288
289 /** Returns the trace of this matrix. */
290 Real trace() const {
291 return this->data_[0][0] + this->data_[1][1] + this->data_[2][2];
292 }
293
294 /**
295 * Sets the value of this matrix to the inversion of itself.
296 * @note since simple algorithm can be applied to inverse the 3 by 3 matrix, we hide the
297 * implementation of inverse in SquareMatrix class
298 */
299 SquareMatrix3<Real> inverse() const {
300 SquareMatrix3<Real> m;
301 double det = determinant();
302 if (fabs(det) <= oopse::epsilon) {
303 //"The method was called on a matrix with |determinant| <= 1e-6.",
304 //"This is a runtime or a programming error in your application.");
305 }
306
307 m(0, 0) = this->data_[1][1]*this->data_[2][2] - this->data_[1][2]*this->data_[2][1];
308 m(1, 0) = this->data_[1][2]*this->data_[2][0] - this->data_[1][0]*this->data_[2][2];
309 m(2, 0) = this->data_[1][0]*this->data_[2][1] - this->data_[1][1]*this->data_[2][0];
310 m(0, 1) = this->data_[2][1]*this->data_[0][2] - this->data_[2][2]*this->data_[0][1];
311 m(1, 1) = this->data_[2][2]*this->data_[0][0] - this->data_[2][0]*this->data_[0][2];
312 m(2, 1) = this->data_[2][0]*this->data_[0][1] - this->data_[2][1]*this->data_[0][0];
313 m(0, 2) = this->data_[0][1]*this->data_[1][2] - this->data_[0][2]*this->data_[1][1];
314 m(1, 2) = this->data_[0][2]*this->data_[1][0] - this->data_[0][0]*this->data_[1][2];
315 m(2, 2) = this->data_[0][0]*this->data_[1][1] - this->data_[0][1]*this->data_[1][0];
316
317 m /= det;
318 return m;
319 }
320 /**
321 * Extract the eigenvalues and eigenvectors from a 3x3 matrix.
322 * The eigenvectors (the columns of V) will be normalized.
323 * The eigenvectors are aligned optimally with the x, y, and z
324 * axes respectively.
325 * @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
326 * overwritten
327 * @param w will contain the eigenvalues of the matrix On return of this function
328 * @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
329 * normalized and mutually orthogonal.
330 * @warning a will be overwritten
331 */
332 static void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v);
333 };
334 /*=========================================================================
335
336 Program: Visualization Toolkit
337 Module: $RCSfile: SquareMatrix3.hpp,v $
338
339 Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
340 All rights reserved.
341 See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
342
343 This software is distributed WITHOUT ANY WARRANTY; without even
344 the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
345 PURPOSE. See the above copyright notice for more information.
346
347 =========================================================================*/
348 template<typename Real>
349 void SquareMatrix3<Real>::diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w,
350 SquareMatrix3<Real>& v) {
351 int i,j,k,maxI;
352 Real tmp, maxVal;
353 Vector3<Real> v_maxI, v_k, v_j;
354
355 // diagonalize using Jacobi
356 jacobi(a, w, v);
357 // if all the eigenvalues are the same, return identity matrix
358 if (w[0] == w[1] && w[0] == w[2] ) {
359 v = SquareMatrix3<Real>::identity();
360 return;
361 }
362
363 // transpose temporarily, it makes it easier to sort the eigenvectors
364 v = v.transpose();
365
366 // if two eigenvalues are the same, re-orthogonalize to optimally line
367 // up the eigenvectors with the x, y, and z axes
368 for (i = 0; i < 3; i++) {
369 if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same
370 // find maximum element of the independant eigenvector
371 maxVal = fabs(v(i, 0));
372 maxI = 0;
373 for (j = 1; j < 3; j++) {
374 if (maxVal < (tmp = fabs(v(i, j)))){
375 maxVal = tmp;
376 maxI = j;
377 }
378 }
379
380 // swap the eigenvector into its proper position
381 if (maxI != i) {
382 tmp = w(maxI);
383 w(maxI) = w(i);
384 w(i) = tmp;
385
386 v.swapRow(i, maxI);
387 }
388 // maximum element of eigenvector should be positive
389 if (v(maxI, maxI) < 0) {
390 v(maxI, 0) = -v(maxI, 0);
391 v(maxI, 1) = -v(maxI, 1);
392 v(maxI, 2) = -v(maxI, 2);
393 }
394
395 // re-orthogonalize the other two eigenvectors
396 j = (maxI+1)%3;
397 k = (maxI+2)%3;
398
399 v(j, 0) = 0.0;
400 v(j, 1) = 0.0;
401 v(j, 2) = 0.0;
402 v(j, j) = 1.0;
403
404 /** @todo */
405 v_maxI = v.getRow(maxI);
406 v_j = v.getRow(j);
407 v_k = cross(v_maxI, v_j);
408 v_k.normalize();
409 v_j = cross(v_k, v_maxI);
410 v.setRow(j, v_j);
411 v.setRow(k, v_k);
412
413
414 // transpose vectors back to columns
415 v = v.transpose();
416 return;
417 }
418 }
419
420 // the three eigenvalues are different, just sort the eigenvectors
421 // to align them with the x, y, and z axes
422
423 // find the vector with the largest x element, make that vector
424 // the first vector
425 maxVal = fabs(v(0, 0));
426 maxI = 0;
427 for (i = 1; i < 3; i++) {
428 if (maxVal < (tmp = fabs(v(i, 0)))) {
429 maxVal = tmp;
430 maxI = i;
431 }
432 }
433
434 // swap eigenvalue and eigenvector
435 if (maxI != 0) {
436 tmp = w(maxI);
437 w(maxI) = w(0);
438 w(0) = tmp;
439 v.swapRow(maxI, 0);
440 }
441 // do the same for the y element
442 if (fabs(v(1, 1)) < fabs(v(2, 1))) {
443 tmp = w(2);
444 w(2) = w(1);
445 w(1) = tmp;
446 v.swapRow(2, 1);
447 }
448
449 // ensure that the sign of the eigenvectors is correct
450 for (i = 0; i < 2; i++) {
451 if (v(i, i) < 0) {
452 v(i, 0) = -v(i, 0);
453 v(i, 1) = -v(i, 1);
454 v(i, 2) = -v(i, 2);
455 }
456 }
457
458 // set sign of final eigenvector to ensure that determinant is positive
459 if (v.determinant() < 0) {
460 v(2, 0) = -v(2, 0);
461 v(2, 1) = -v(2, 1);
462 v(2, 2) = -v(2, 2);
463 }
464
465 // transpose the eigenvectors back again
466 v = v.transpose();
467 return ;
468 }
469
470 /**
471 * Return the multiplication of two matrixes (m1 * m2).
472 * @return the multiplication of two matrixes
473 * @param m1 the first matrix
474 * @param m2 the second matrix
475 */
476 template<typename Real>
477 inline SquareMatrix3<Real> operator *(const SquareMatrix3<Real>& m1, const SquareMatrix3<Real>& m2) {
478 SquareMatrix3<Real> result;
479
480 for (unsigned int i = 0; i < 3; i++)
481 for (unsigned int j = 0; j < 3; j++)
482 for (unsigned int k = 0; k < 3; k++)
483 result(i, j) += m1(i, k) * m2(k, j);
484
485 return result;
486 }
487
488 template<typename Real>
489 inline SquareMatrix3<Real> outProduct(const Vector3<Real>& v1, const Vector3<Real>& v2) {
490 SquareMatrix3<Real> result;
491
492 for (unsigned int i = 0; i < 3; i++) {
493 for (unsigned int j = 0; j < 3; j++) {
494 result(i, j) = v1[i] * v2[j];
495 }
496 }
497
498 return result;
499 }
500
501
502 typedef SquareMatrix3<double> Mat3x3d;
503 typedef SquareMatrix3<double> RotMat3x3d;
504
505 } //namespace oopse
506 #endif // MATH_SQUAREMATRIX_HPP
507