1 |
tim |
1563 |
/* |
2 |
|
|
* Copyright (C) 2000-2004 Object Oriented Parallel Simulation Engine (OOPSE) project |
3 |
|
|
* |
4 |
|
|
* Contact: oopse@oopse.org |
5 |
|
|
* |
6 |
|
|
* This program is free software; you can redistribute it and/or |
7 |
|
|
* modify it under the terms of the GNU Lesser General Public License |
8 |
|
|
* as published by the Free Software Foundation; either version 2.1 |
9 |
|
|
* of the License, or (at your option) any later version. |
10 |
|
|
* All we ask is that proper credit is given for our work, which includes |
11 |
|
|
* - but is not limited to - adding the above copyright notice to the beginning |
12 |
|
|
* of your source code files, and to any copyright notice that you may distribute |
13 |
|
|
* with programs based on this work. |
14 |
|
|
* |
15 |
|
|
* This program is distributed in the hope that it will be useful, |
16 |
|
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of |
17 |
|
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
18 |
|
|
* GNU Lesser General Public License for more details. |
19 |
|
|
* |
20 |
|
|
* You should have received a copy of the GNU Lesser General Public License |
21 |
|
|
* along with this program; if not, write to the Free Software |
22 |
|
|
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
23 |
|
|
* |
24 |
|
|
*/ |
25 |
|
|
|
26 |
|
|
/** |
27 |
|
|
* @file SquareMatrix3.hpp |
28 |
|
|
* @author Teng Lin |
29 |
|
|
* @date 10/11/2004 |
30 |
|
|
* @version 1.0 |
31 |
|
|
*/ |
32 |
tim |
1616 |
#ifndef MATH_SQUAREMATRIX3_HPP |
33 |
tim |
1592 |
#define MATH_SQUAREMATRIX3_HPP |
34 |
tim |
1563 |
|
35 |
tim |
1586 |
#include "Quaternion.hpp" |
36 |
tim |
1563 |
#include "SquareMatrix.hpp" |
37 |
tim |
1586 |
#include "Vector3.hpp" |
38 |
|
|
|
39 |
tim |
1563 |
namespace oopse { |
40 |
|
|
|
41 |
|
|
template<typename Real> |
42 |
|
|
class SquareMatrix3 : public SquareMatrix<Real, 3> { |
43 |
|
|
public: |
44 |
tim |
1630 |
|
45 |
|
|
typedef Real ElemType; |
46 |
|
|
typedef Real* ElemPoinerType; |
47 |
tim |
1563 |
|
48 |
|
|
/** default constructor */ |
49 |
|
|
SquareMatrix3() : SquareMatrix<Real, 3>() { |
50 |
|
|
} |
51 |
|
|
|
52 |
tim |
1644 |
/** Constructs and initializes every element of this matrix to a scalar */ |
53 |
|
|
SquareMatrix3(Real s) : SquareMatrix<Real,3>(s){ |
54 |
|
|
} |
55 |
|
|
|
56 |
|
|
/** Constructs and initializes from an array */ |
57 |
|
|
SquareMatrix3(Real* array) : SquareMatrix<Real,3>(array){ |
58 |
|
|
} |
59 |
|
|
|
60 |
|
|
|
61 |
tim |
1563 |
/** copy constructor */ |
62 |
|
|
SquareMatrix3(const SquareMatrix<Real, 3>& m) : SquareMatrix<Real, 3>(m) { |
63 |
|
|
} |
64 |
tim |
1695 |
|
65 |
tim |
1586 |
SquareMatrix3( const Vector3<Real>& eulerAngles) { |
66 |
|
|
setupRotMat(eulerAngles); |
67 |
|
|
} |
68 |
|
|
|
69 |
|
|
SquareMatrix3(Real phi, Real theta, Real psi) { |
70 |
|
|
setupRotMat(phi, theta, psi); |
71 |
|
|
} |
72 |
|
|
|
73 |
|
|
SquareMatrix3(const Quaternion<Real>& q) { |
74 |
tim |
1606 |
setupRotMat(q); |
75 |
|
|
|
76 |
tim |
1586 |
} |
77 |
|
|
|
78 |
|
|
SquareMatrix3(Real w, Real x, Real y, Real z) { |
79 |
tim |
1606 |
setupRotMat(w, x, y, z); |
80 |
tim |
1586 |
} |
81 |
|
|
|
82 |
tim |
1563 |
/** copy assignment operator */ |
83 |
|
|
SquareMatrix3<Real>& operator =(const SquareMatrix<Real, 3>& m) { |
84 |
|
|
if (this == &m) |
85 |
|
|
return *this; |
86 |
|
|
SquareMatrix<Real, 3>::operator=(m); |
87 |
tim |
1594 |
return *this; |
88 |
tim |
1563 |
} |
89 |
tim |
1569 |
|
90 |
tim |
1870 |
|
91 |
|
|
SquareMatrix3<Real>& operator =(const Quaternion<Real>& q) { |
92 |
|
|
this->setupRotMat(q); |
93 |
|
|
return *this; |
94 |
|
|
} |
95 |
|
|
|
96 |
tim |
1569 |
/** |
97 |
|
|
* Sets this matrix to a rotation matrix by three euler angles |
98 |
|
|
* @ param euler |
99 |
|
|
*/ |
100 |
tim |
1586 |
void setupRotMat(const Vector3<Real>& eulerAngles) { |
101 |
|
|
setupRotMat(eulerAngles[0], eulerAngles[1], eulerAngles[2]); |
102 |
|
|
} |
103 |
tim |
1569 |
|
104 |
|
|
/** |
105 |
|
|
* Sets this matrix to a rotation matrix by three euler angles |
106 |
|
|
* @param phi |
107 |
|
|
* @param theta |
108 |
|
|
* @psi theta |
109 |
|
|
*/ |
110 |
tim |
1586 |
void setupRotMat(Real phi, Real theta, Real psi) { |
111 |
|
|
Real sphi, stheta, spsi; |
112 |
|
|
Real cphi, ctheta, cpsi; |
113 |
tim |
1569 |
|
114 |
tim |
1586 |
sphi = sin(phi); |
115 |
|
|
stheta = sin(theta); |
116 |
|
|
spsi = sin(psi); |
117 |
|
|
cphi = cos(phi); |
118 |
|
|
ctheta = cos(theta); |
119 |
|
|
cpsi = cos(psi); |
120 |
tim |
1569 |
|
121 |
tim |
1586 |
data_[0][0] = cpsi * cphi - ctheta * sphi * spsi; |
122 |
|
|
data_[0][1] = cpsi * sphi + ctheta * cphi * spsi; |
123 |
|
|
data_[0][2] = spsi * stheta; |
124 |
|
|
|
125 |
|
|
data_[1][0] = -spsi * ctheta - ctheta * sphi * cpsi; |
126 |
|
|
data_[1][1] = -spsi * stheta + ctheta * cphi * cpsi; |
127 |
|
|
data_[1][2] = cpsi * stheta; |
128 |
|
|
|
129 |
|
|
data_[2][0] = stheta * sphi; |
130 |
|
|
data_[2][1] = -stheta * cphi; |
131 |
|
|
data_[2][2] = ctheta; |
132 |
|
|
} |
133 |
|
|
|
134 |
|
|
|
135 |
tim |
1569 |
/** |
136 |
|
|
* Sets this matrix to a rotation matrix by quaternion |
137 |
|
|
* @param quat |
138 |
|
|
*/ |
139 |
tim |
1586 |
void setupRotMat(const Quaternion<Real>& quat) { |
140 |
tim |
1606 |
setupRotMat(quat.w(), quat.x(), quat.y(), quat.z()); |
141 |
tim |
1586 |
} |
142 |
tim |
1569 |
|
143 |
|
|
/** |
144 |
|
|
* Sets this matrix to a rotation matrix by quaternion |
145 |
tim |
1586 |
* @param w the first element |
146 |
|
|
* @param x the second element |
147 |
|
|
* @param y the third element |
148 |
tim |
1594 |
* @param z the fourth element |
149 |
tim |
1569 |
*/ |
150 |
tim |
1586 |
void setupRotMat(Real w, Real x, Real y, Real z) { |
151 |
|
|
Quaternion<Real> q(w, x, y, z); |
152 |
|
|
*this = q.toRotationMatrix3(); |
153 |
|
|
} |
154 |
tim |
1569 |
|
155 |
|
|
/** |
156 |
|
|
* Returns the quaternion from this rotation matrix |
157 |
|
|
* @return the quaternion from this rotation matrix |
158 |
|
|
* @exception invalid rotation matrix |
159 |
|
|
*/ |
160 |
tim |
1586 |
Quaternion<Real> toQuaternion() { |
161 |
|
|
Quaternion<Real> q; |
162 |
|
|
Real t, s; |
163 |
|
|
Real ad1, ad2, ad3; |
164 |
|
|
t = data_[0][0] + data_[1][1] + data_[2][2] + 1.0; |
165 |
tim |
1569 |
|
166 |
tim |
1586 |
if( t > 0.0 ){ |
167 |
|
|
|
168 |
|
|
s = 0.5 / sqrt( t ); |
169 |
|
|
q[0] = 0.25 / s; |
170 |
|
|
q[1] = (data_[1][2] - data_[2][1]) * s; |
171 |
|
|
q[2] = (data_[2][0] - data_[0][2]) * s; |
172 |
|
|
q[3] = (data_[0][1] - data_[1][0]) * s; |
173 |
|
|
} else { |
174 |
|
|
|
175 |
|
|
ad1 = fabs( data_[0][0] ); |
176 |
|
|
ad2 = fabs( data_[1][1] ); |
177 |
|
|
ad3 = fabs( data_[2][2] ); |
178 |
|
|
|
179 |
|
|
if( ad1 >= ad2 && ad1 >= ad3 ){ |
180 |
|
|
|
181 |
|
|
s = 2.0 * sqrt( 1.0 + data_[0][0] - data_[1][1] - data_[2][2] ); |
182 |
|
|
q[0] = (data_[1][2] + data_[2][1]) / s; |
183 |
|
|
q[1] = 0.5 / s; |
184 |
|
|
q[2] = (data_[0][1] + data_[1][0]) / s; |
185 |
|
|
q[3] = (data_[0][2] + data_[2][0]) / s; |
186 |
|
|
} else if ( ad2 >= ad1 && ad2 >= ad3 ) { |
187 |
|
|
s = sqrt( 1.0 + data_[1][1] - data_[0][0] - data_[2][2] ) * 2.0; |
188 |
|
|
q[0] = (data_[0][2] + data_[2][0]) / s; |
189 |
|
|
q[1] = (data_[0][1] + data_[1][0]) / s; |
190 |
|
|
q[2] = 0.5 / s; |
191 |
|
|
q[3] = (data_[1][2] + data_[2][1]) / s; |
192 |
|
|
} else { |
193 |
|
|
|
194 |
|
|
s = sqrt( 1.0 + data_[2][2] - data_[0][0] - data_[1][1] ) * 2.0; |
195 |
|
|
q[0] = (data_[0][1] + data_[1][0]) / s; |
196 |
|
|
q[1] = (data_[0][2] + data_[2][0]) / s; |
197 |
|
|
q[2] = (data_[1][2] + data_[2][1]) / s; |
198 |
|
|
q[3] = 0.5 / s; |
199 |
|
|
} |
200 |
|
|
} |
201 |
|
|
|
202 |
|
|
return q; |
203 |
|
|
|
204 |
|
|
} |
205 |
|
|
|
206 |
tim |
1569 |
/** |
207 |
|
|
* Returns the euler angles from this rotation matrix |
208 |
tim |
1586 |
* @return the euler angles in a vector |
209 |
tim |
1569 |
* @exception invalid rotation matrix |
210 |
tim |
1586 |
* We use so-called "x-convention", which is the most common definition. |
211 |
|
|
* In this convention, the rotation given by Euler angles (phi, theta, psi), where the first |
212 |
|
|
* rotation is by an angle phi about the z-axis, the second is by an angle |
213 |
|
|
* theta (0 <= theta <= 180)about the x-axis, and thethird is by an angle psi about the |
214 |
|
|
* z-axis (again). |
215 |
tim |
1569 |
*/ |
216 |
tim |
1586 |
Vector3<Real> toEulerAngles() { |
217 |
tim |
1606 |
Vector3<Real> myEuler; |
218 |
tim |
1883 |
Real phi; |
219 |
|
|
Real theta; |
220 |
|
|
Real psi; |
221 |
|
|
Real ctheta; |
222 |
|
|
Real stheta; |
223 |
tim |
1586 |
|
224 |
|
|
// set the tolerance for Euler angles and rotation elements |
225 |
|
|
|
226 |
tim |
1606 |
theta = acos(std::min(1.0, std::max(-1.0,data_[2][2]))); |
227 |
tim |
1586 |
ctheta = data_[2][2]; |
228 |
|
|
stheta = sqrt(1.0 - ctheta * ctheta); |
229 |
|
|
|
230 |
|
|
// when sin(theta) is close to 0, we need to consider singularity |
231 |
|
|
// In this case, we can assign an arbitary value to phi (or psi), and then determine |
232 |
|
|
// the psi (or phi) or vice-versa. We'll assume that phi always gets the rotation, and psi is 0 |
233 |
|
|
// in cases of singularity. |
234 |
|
|
// we use atan2 instead of atan, since atan2 will give us -Pi to Pi. |
235 |
|
|
// Since 0 <= theta <= 180, sin(theta) will be always non-negative. Therefore, it never |
236 |
|
|
// change the sign of both of the parameters passed to atan2. |
237 |
|
|
|
238 |
|
|
if (fabs(stheta) <= oopse::epsilon){ |
239 |
|
|
psi = 0.0; |
240 |
|
|
phi = atan2(-data_[1][0], data_[0][0]); |
241 |
|
|
} |
242 |
|
|
// we only have one unique solution |
243 |
|
|
else{ |
244 |
|
|
phi = atan2(data_[2][0], -data_[2][1]); |
245 |
|
|
psi = atan2(data_[0][2], data_[1][2]); |
246 |
|
|
} |
247 |
|
|
|
248 |
|
|
//wrap phi and psi, make sure they are in the range from 0 to 2*Pi |
249 |
|
|
if (phi < 0) |
250 |
|
|
phi += M_PI; |
251 |
|
|
|
252 |
|
|
if (psi < 0) |
253 |
|
|
psi += M_PI; |
254 |
|
|
|
255 |
|
|
myEuler[0] = phi; |
256 |
|
|
myEuler[1] = theta; |
257 |
|
|
myEuler[2] = psi; |
258 |
|
|
|
259 |
|
|
return myEuler; |
260 |
|
|
} |
261 |
tim |
1563 |
|
262 |
tim |
1594 |
/** Returns the determinant of this matrix. */ |
263 |
|
|
Real determinant() const { |
264 |
|
|
Real x,y,z; |
265 |
|
|
|
266 |
|
|
x = data_[0][0] * (data_[1][1] * data_[2][2] - data_[1][2] * data_[2][1]); |
267 |
|
|
y = data_[0][1] * (data_[1][2] * data_[2][0] - data_[1][0] * data_[2][2]); |
268 |
|
|
z = data_[0][2] * (data_[1][0] * data_[2][1] - data_[1][1] * data_[2][0]); |
269 |
|
|
|
270 |
|
|
return(x + y + z); |
271 |
|
|
} |
272 |
tim |
1822 |
|
273 |
|
|
/** Returns the trace of this matrix. */ |
274 |
|
|
Real trace() const { |
275 |
|
|
return data_[0][0] + data_[1][1] + data_[2][2]; |
276 |
|
|
} |
277 |
tim |
1594 |
|
278 |
tim |
1563 |
/** |
279 |
|
|
* Sets the value of this matrix to the inversion of itself. |
280 |
|
|
* @note since simple algorithm can be applied to inverse the 3 by 3 matrix, we hide the |
281 |
|
|
* implementation of inverse in SquareMatrix class |
282 |
|
|
*/ |
283 |
tim |
1695 |
SquareMatrix3<Real> inverse() const { |
284 |
tim |
1594 |
SquareMatrix3<Real> m; |
285 |
|
|
double det = determinant(); |
286 |
|
|
if (fabs(det) <= oopse::epsilon) { |
287 |
|
|
//"The method was called on a matrix with |determinant| <= 1e-6.", |
288 |
|
|
//"This is a runtime or a programming error in your application."); |
289 |
|
|
} |
290 |
tim |
1563 |
|
291 |
tim |
1594 |
m(0, 0) = data_[1][1]*data_[2][2] - data_[1][2]*data_[2][1]; |
292 |
|
|
m(1, 0) = data_[1][2]*data_[2][0] - data_[1][0]*data_[2][2]; |
293 |
|
|
m(2, 0) = data_[1][0]*data_[2][1] - data_[1][1]*data_[2][0]; |
294 |
|
|
m(0, 1) = data_[2][1]*data_[0][2] - data_[2][2]*data_[0][1]; |
295 |
|
|
m(1, 1) = data_[2][2]*data_[0][0] - data_[2][0]*data_[0][2]; |
296 |
|
|
m(2, 1) = data_[2][0]*data_[0][1] - data_[2][1]*data_[0][0]; |
297 |
|
|
m(0, 2) = data_[0][1]*data_[1][2] - data_[0][2]*data_[1][1]; |
298 |
|
|
m(1, 2) = data_[0][2]*data_[1][0] - data_[0][0]*data_[1][2]; |
299 |
|
|
m(2, 2) = data_[0][0]*data_[1][1] - data_[0][1]*data_[1][0]; |
300 |
|
|
|
301 |
|
|
m /= det; |
302 |
|
|
return m; |
303 |
tim |
1592 |
} |
304 |
tim |
1616 |
/** |
305 |
|
|
* Extract the eigenvalues and eigenvectors from a 3x3 matrix. |
306 |
|
|
* The eigenvectors (the columns of V) will be normalized. |
307 |
|
|
* The eigenvectors are aligned optimally with the x, y, and z |
308 |
|
|
* axes respectively. |
309 |
|
|
* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is |
310 |
|
|
* overwritten |
311 |
|
|
* @param w will contain the eigenvalues of the matrix On return of this function |
312 |
|
|
* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are |
313 |
|
|
* normalized and mutually orthogonal. |
314 |
|
|
* @warning a will be overwritten |
315 |
|
|
*/ |
316 |
|
|
static void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v); |
317 |
|
|
}; |
318 |
|
|
/*========================================================================= |
319 |
tim |
1569 |
|
320 |
tim |
1616 |
Program: Visualization Toolkit |
321 |
|
|
Module: $RCSfile: SquareMatrix3.hpp,v $ |
322 |
tim |
1592 |
|
323 |
tim |
1616 |
Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen |
324 |
|
|
All rights reserved. |
325 |
|
|
See Copyright.txt or http://www.kitware.com/Copyright.htm for details. |
326 |
tim |
1594 |
|
327 |
tim |
1616 |
This software is distributed WITHOUT ANY WARRANTY; without even |
328 |
|
|
the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR |
329 |
|
|
PURPOSE. See the above copyright notice for more information. |
330 |
tim |
1594 |
|
331 |
tim |
1616 |
=========================================================================*/ |
332 |
|
|
template<typename Real> |
333 |
|
|
void SquareMatrix3<Real>::diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, |
334 |
|
|
SquareMatrix3<Real>& v) { |
335 |
|
|
int i,j,k,maxI; |
336 |
|
|
Real tmp, maxVal; |
337 |
|
|
Vector3<Real> v_maxI, v_k, v_j; |
338 |
tim |
1594 |
|
339 |
tim |
1616 |
// diagonalize using Jacobi |
340 |
|
|
jacobi(a, w, v); |
341 |
|
|
// if all the eigenvalues are the same, return identity matrix |
342 |
|
|
if (w[0] == w[1] && w[0] == w[2] ) { |
343 |
|
|
v = SquareMatrix3<Real>::identity(); |
344 |
|
|
return; |
345 |
|
|
} |
346 |
tim |
1594 |
|
347 |
tim |
1616 |
// transpose temporarily, it makes it easier to sort the eigenvectors |
348 |
|
|
v = v.transpose(); |
349 |
|
|
|
350 |
|
|
// if two eigenvalues are the same, re-orthogonalize to optimally line |
351 |
|
|
// up the eigenvectors with the x, y, and z axes |
352 |
|
|
for (i = 0; i < 3; i++) { |
353 |
|
|
if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same |
354 |
|
|
// find maximum element of the independant eigenvector |
355 |
|
|
maxVal = fabs(v(i, 0)); |
356 |
|
|
maxI = 0; |
357 |
|
|
for (j = 1; j < 3; j++) { |
358 |
|
|
if (maxVal < (tmp = fabs(v(i, j)))){ |
359 |
|
|
maxVal = tmp; |
360 |
|
|
maxI = j; |
361 |
|
|
} |
362 |
|
|
} |
363 |
|
|
|
364 |
|
|
// swap the eigenvector into its proper position |
365 |
|
|
if (maxI != i) { |
366 |
|
|
tmp = w(maxI); |
367 |
|
|
w(maxI) = w(i); |
368 |
|
|
w(i) = tmp; |
369 |
tim |
1594 |
|
370 |
tim |
1616 |
v.swapRow(i, maxI); |
371 |
|
|
} |
372 |
|
|
// maximum element of eigenvector should be positive |
373 |
|
|
if (v(maxI, maxI) < 0) { |
374 |
|
|
v(maxI, 0) = -v(maxI, 0); |
375 |
|
|
v(maxI, 1) = -v(maxI, 1); |
376 |
|
|
v(maxI, 2) = -v(maxI, 2); |
377 |
|
|
} |
378 |
tim |
1594 |
|
379 |
tim |
1616 |
// re-orthogonalize the other two eigenvectors |
380 |
|
|
j = (maxI+1)%3; |
381 |
|
|
k = (maxI+2)%3; |
382 |
tim |
1594 |
|
383 |
tim |
1616 |
v(j, 0) = 0.0; |
384 |
|
|
v(j, 1) = 0.0; |
385 |
|
|
v(j, 2) = 0.0; |
386 |
|
|
v(j, j) = 1.0; |
387 |
tim |
1594 |
|
388 |
tim |
1616 |
/** @todo */ |
389 |
|
|
v_maxI = v.getRow(maxI); |
390 |
|
|
v_j = v.getRow(j); |
391 |
|
|
v_k = cross(v_maxI, v_j); |
392 |
|
|
v_k.normalize(); |
393 |
|
|
v_j = cross(v_k, v_maxI); |
394 |
|
|
v.setRow(j, v_j); |
395 |
|
|
v.setRow(k, v_k); |
396 |
tim |
1594 |
|
397 |
|
|
|
398 |
tim |
1616 |
// transpose vectors back to columns |
399 |
|
|
v = v.transpose(); |
400 |
|
|
return; |
401 |
|
|
} |
402 |
|
|
} |
403 |
tim |
1594 |
|
404 |
tim |
1616 |
// the three eigenvalues are different, just sort the eigenvectors |
405 |
|
|
// to align them with the x, y, and z axes |
406 |
tim |
1594 |
|
407 |
tim |
1616 |
// find the vector with the largest x element, make that vector |
408 |
|
|
// the first vector |
409 |
|
|
maxVal = fabs(v(0, 0)); |
410 |
|
|
maxI = 0; |
411 |
|
|
for (i = 1; i < 3; i++) { |
412 |
|
|
if (maxVal < (tmp = fabs(v(i, 0)))) { |
413 |
|
|
maxVal = tmp; |
414 |
|
|
maxI = i; |
415 |
|
|
} |
416 |
|
|
} |
417 |
tim |
1594 |
|
418 |
tim |
1616 |
// swap eigenvalue and eigenvector |
419 |
|
|
if (maxI != 0) { |
420 |
|
|
tmp = w(maxI); |
421 |
|
|
w(maxI) = w(0); |
422 |
|
|
w(0) = tmp; |
423 |
|
|
v.swapRow(maxI, 0); |
424 |
|
|
} |
425 |
|
|
// do the same for the y element |
426 |
|
|
if (fabs(v(1, 1)) < fabs(v(2, 1))) { |
427 |
|
|
tmp = w(2); |
428 |
|
|
w(2) = w(1); |
429 |
|
|
w(1) = tmp; |
430 |
|
|
v.swapRow(2, 1); |
431 |
|
|
} |
432 |
tim |
1594 |
|
433 |
tim |
1616 |
// ensure that the sign of the eigenvectors is correct |
434 |
|
|
for (i = 0; i < 2; i++) { |
435 |
|
|
if (v(i, i) < 0) { |
436 |
|
|
v(i, 0) = -v(i, 0); |
437 |
|
|
v(i, 1) = -v(i, 1); |
438 |
|
|
v(i, 2) = -v(i, 2); |
439 |
tim |
1592 |
} |
440 |
tim |
1616 |
} |
441 |
tim |
1563 |
|
442 |
tim |
1616 |
// set sign of final eigenvector to ensure that determinant is positive |
443 |
|
|
if (v.determinant() < 0) { |
444 |
|
|
v(2, 0) = -v(2, 0); |
445 |
|
|
v(2, 1) = -v(2, 1); |
446 |
|
|
v(2, 2) = -v(2, 2); |
447 |
|
|
} |
448 |
|
|
|
449 |
|
|
// transpose the eigenvectors back again |
450 |
|
|
v = v.transpose(); |
451 |
|
|
return ; |
452 |
|
|
} |
453 |
tim |
1695 |
|
454 |
|
|
/** |
455 |
|
|
* Return the multiplication of two matrixes (m1 * m2). |
456 |
|
|
* @return the multiplication of two matrixes |
457 |
|
|
* @param m1 the first matrix |
458 |
|
|
* @param m2 the second matrix |
459 |
|
|
*/ |
460 |
|
|
template<typename Real> |
461 |
|
|
inline SquareMatrix3<Real> operator *(const SquareMatrix3<Real>& m1, const SquareMatrix3<Real>& m2) { |
462 |
|
|
SquareMatrix3<Real> result; |
463 |
|
|
|
464 |
|
|
for (unsigned int i = 0; i < 3; i++) |
465 |
|
|
for (unsigned int j = 0; j < 3; j++) |
466 |
|
|
for (unsigned int k = 0; k < 3; k++) |
467 |
|
|
result(i, j) += m1(i, k) * m2(k, j); |
468 |
|
|
|
469 |
|
|
return result; |
470 |
|
|
} |
471 |
|
|
|
472 |
tim |
1804 |
template<typename Real> |
473 |
|
|
inline SquareMatrix3<Real> outProduct(const Vector3<Real>& v1, const Vector3<Real>& v2) { |
474 |
|
|
SquareMatrix3<Real> result; |
475 |
|
|
|
476 |
|
|
for (unsigned int i = 0; i < 3; i++) { |
477 |
|
|
for (unsigned int j = 0; j < 3; j++) { |
478 |
|
|
result(i, j) = v1[i] * v2[j]; |
479 |
|
|
} |
480 |
|
|
} |
481 |
|
|
|
482 |
|
|
return result; |
483 |
|
|
} |
484 |
|
|
|
485 |
|
|
|
486 |
tim |
1592 |
typedef SquareMatrix3<double> Mat3x3d; |
487 |
|
|
typedef SquareMatrix3<double> RotMat3x3d; |
488 |
tim |
1586 |
|
489 |
|
|
} //namespace oopse |
490 |
|
|
#endif // MATH_SQUAREMATRIX_HPP |
491 |
tim |
1616 |
|