1 |
|
/* |
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. |
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 |
< |
|
41 |
> |
|
42 |
|
/** |
43 |
|
* @file SquareMatrix3.hpp |
44 |
|
* @author Teng Lin |
45 |
|
* @date 10/11/2004 |
46 |
|
* @version 1.0 |
47 |
|
*/ |
48 |
< |
#ifndef MATH_SQUAREMATRIX_HPP |
49 |
< |
#define MATH_SQUAREMATRIX_HPP |
48 |
> |
#ifndef MATH_SQUAREMATRIX3_HPP |
49 |
> |
#define MATH_SQUAREMATRIX3_HPP |
50 |
|
|
51 |
|
#include "Quaternion.hpp" |
52 |
|
#include "SquareMatrix.hpp" |
53 |
|
#include "Vector3.hpp" |
54 |
< |
|
54 |
> |
#include "utils/NumericConstant.hpp" |
55 |
|
namespace oopse { |
56 |
|
|
57 |
< |
template<typename Real> |
58 |
< |
class SquareMatrix3 : public SquareMatrix<Real, 3> { |
59 |
< |
public: |
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 |
< |
} |
64 |
> |
/** default constructor */ |
65 |
> |
SquareMatrix3() : SquareMatrix<Real, 3>() { |
66 |
> |
} |
67 |
|
|
68 |
< |
/** copy constructor */ |
69 |
< |
SquareMatrix3(const SquareMatrix<Real, 3>& m) : SquareMatrix<Real, 3>(m) { |
70 |
< |
} |
68 |
> |
/** Constructs and initializes every element of this matrix to a scalar */ |
69 |
> |
SquareMatrix3(Real s) : SquareMatrix<Real,3>(s){ |
70 |
> |
} |
71 |
|
|
72 |
< |
SquareMatrix3( const Vector3<Real>& eulerAngles) { |
73 |
< |
setupRotMat(eulerAngles); |
74 |
< |
} |
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(Real phi, Real theta, Real psi) { |
82 |
< |
setupRotMat(phi, theta, psi); |
83 |
< |
} |
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 |
< |
*this = q.toRotationMatrix3(); |
63 |
< |
} |
89 |
> |
SquareMatrix3(const Quaternion<Real>& q) { |
90 |
> |
setupRotMat(q); |
91 |
|
|
92 |
< |
SquareMatrix3(Real w, Real x, Real y, Real z) { |
93 |
< |
Quaternion<Real> q(w, x, y, z); |
94 |
< |
*this = q.toRotationMatrix3(); |
95 |
< |
} |
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 |
< |
} |
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 |
|
|
77 |
– |
/** |
78 |
– |
* Sets this matrix to a rotation matrix by three euler angles |
79 |
– |
* @ param euler |
80 |
– |
*/ |
81 |
– |
void setupRotMat(const Vector3<Real>& eulerAngles) { |
82 |
– |
setupRotMat(eulerAngles[0], eulerAngles[1], eulerAngles[2]); |
83 |
– |
} |
106 |
|
|
107 |
< |
/** |
108 |
< |
* Sets this matrix to a rotation matrix by three euler angles |
109 |
< |
* @param phi |
110 |
< |
* @param theta |
89 |
< |
* @psi theta |
90 |
< |
*/ |
91 |
< |
void setupRotMat(Real phi, Real theta, Real psi) { |
92 |
< |
Real sphi, stheta, spsi; |
93 |
< |
Real cphi, ctheta, cpsi; |
107 |
> |
SquareMatrix3<Real>& operator =(const Quaternion<Real>& q) { |
108 |
> |
this->setupRotMat(q); |
109 |
> |
return *this; |
110 |
> |
} |
111 |
|
|
112 |
< |
sphi = sin(phi); |
113 |
< |
stheta = sin(theta); |
114 |
< |
spsi = sin(psi); |
115 |
< |
cphi = cos(phi); |
116 |
< |
ctheta = cos(theta); |
117 |
< |
cpsi = cos(psi); |
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 |
< |
data_[0][0] = cpsi * cphi - ctheta * sphi * spsi; |
121 |
< |
data_[0][1] = cpsi * sphi + ctheta * cphi * spsi; |
122 |
< |
data_[0][2] = spsi * stheta; |
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 |
< |
data_[1][0] = -spsi * ctheta - ctheta * sphi * cpsi; |
142 |
< |
data_[1][1] = -spsi * stheta + ctheta * cphi * cpsi; |
143 |
< |
data_[1][2] = cpsi * stheta; |
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 |
< |
data_[2][0] = stheta * sphi; |
146 |
< |
data_[2][1] = -stheta * cphi; |
147 |
< |
data_[2][2] = ctheta; |
148 |
< |
} |
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 |
< |
*this = quat.toRotationMatrix3(); |
157 |
< |
} |
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 |
< |
* @parma 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 |
< |
} |
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 = data_[0][0] + data_[1][1] + data_[2][2] + 1.0; |
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 > 0.0 ){ |
182 |
> |
if( t > NumericConstant::epsilon ){ |
183 |
|
|
184 |
< |
s = 0.5 / sqrt( t ); |
185 |
< |
q[0] = 0.25 / s; |
186 |
< |
q[1] = (data_[1][2] - data_[2][1]) * s; |
187 |
< |
q[2] = (data_[2][0] - data_[0][2]) * s; |
188 |
< |
q[3] = (data_[0][1] - data_[1][0]) * s; |
189 |
< |
} else { |
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 = fabs( data_[0][0] ); |
192 |
< |
ad2 = fabs( data_[1][1] ); |
193 |
< |
ad3 = fabs( data_[2][2] ); |
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 ){ |
195 |
> |
if( ad1 >= ad2 && ad1 >= ad3 ){ |
196 |
|
|
197 |
< |
s = 2.0 * sqrt( 1.0 + data_[0][0] - data_[1][1] - data_[2][2] ); |
198 |
< |
q[0] = (data_[1][2] + data_[2][1]) / s; |
199 |
< |
q[1] = 0.5 / s; |
200 |
< |
q[2] = (data_[0][1] + data_[1][0]) / s; |
201 |
< |
q[3] = (data_[0][2] + data_[2][0]) / s; |
202 |
< |
} else if ( ad2 >= ad1 && ad2 >= ad3 ) { |
203 |
< |
s = sqrt( 1.0 + data_[1][1] - data_[0][0] - data_[2][2] ) * 2.0; |
204 |
< |
q[0] = (data_[0][2] + data_[2][0]) / s; |
205 |
< |
q[1] = (data_[0][1] + data_[1][0]) / s; |
206 |
< |
q[2] = 0.5 / s; |
207 |
< |
q[3] = (data_[1][2] + data_[2][1]) / s; |
208 |
< |
} else { |
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 = sqrt( 1.0 + data_[2][2] - data_[0][0] - data_[1][1] ) * 2.0; |
211 |
< |
q[0] = (data_[0][1] + data_[1][0]) / s; |
212 |
< |
q[1] = (data_[0][2] + data_[2][0]) / s; |
213 |
< |
q[2] = (data_[1][2] + data_[2][1]) / s; |
214 |
< |
q[3] = 0.5 / s; |
215 |
< |
} |
216 |
< |
} |
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; |
218 |
> |
return q; |
219 |
|
|
220 |
< |
} |
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 |
< |
Vector<Real> myEuler; |
234 |
< |
Real phi,theta,psi,eps; |
235 |
< |
Real ctheta,stheta; |
236 |
< |
|
237 |
< |
// set the tolerance for Euler angles and rotation elements |
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(min(1.0,max(-1.0,data_[2][2]))); |
243 |
< |
ctheta = data_[2][2]; |
244 |
< |
stheta = sqrt(1.0 - ctheta * ctheta); |
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. |
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(-data_[1][0], data_[0][0]); |
257 |
< |
} |
258 |
< |
// we only have one unique solution |
259 |
< |
else{ |
260 |
< |
phi = atan2(data_[2][0], -data_[2][1]); |
261 |
< |
psi = atan2(data_[0][2], data_[1][2]); |
262 |
< |
} |
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; |
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; |
268 |
> |
if (psi < 0) |
269 |
> |
psi += M_PI; |
270 |
|
|
271 |
< |
myEuler[0] = phi; |
272 |
< |
myEuler[1] = theta; |
273 |
< |
myEuler[2] = psi; |
271 |
> |
myEuler[0] = phi; |
272 |
> |
myEuler[1] = theta; |
273 |
> |
myEuler[2] = psi; |
274 |
|
|
275 |
< |
return myEuler; |
276 |
< |
} |
275 |
> |
return myEuler; |
276 |
> |
} |
277 |
|
|
278 |
< |
/** |
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 |
243 |
< |
* implementation of inverse in SquareMatrix class |
244 |
< |
*/ |
245 |
< |
void inverse(); |
278 |
> |
/** Returns the determinant of this matrix. */ |
279 |
> |
Real determinant() const { |
280 |
> |
Real x,y,z; |
281 |
|
|
282 |
< |
void diagonalize(); |
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 |
< |
}; |
286 |
> |
return(x + y + z); |
287 |
> |
} |
288 |
|
|
289 |
< |
typedef template SquareMatrix3<double> Mat3x3d |
290 |
< |
typedef template SquareMatrix3<double> RotMat3x3d; |
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 |
+ |
SquareMatrix3<Real> transpose() const{ |
322 |
+ |
SquareMatrix3<Real> result; |
323 |
+ |
|
324 |
+ |
for (unsigned int i = 0; i < 3; i++) |
325 |
+ |
for (unsigned int j = 0; j < 3; j++) |
326 |
+ |
result(j, i) = this->data_[i][j]; |
327 |
+ |
|
328 |
+ |
return result; |
329 |
+ |
} |
330 |
+ |
/** |
331 |
+ |
* Extract the eigenvalues and eigenvectors from a 3x3 matrix. |
332 |
+ |
* The eigenvectors (the columns of V) will be normalized. |
333 |
+ |
* The eigenvectors are aligned optimally with the x, y, and z |
334 |
+ |
* axes respectively. |
335 |
+ |
* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is |
336 |
+ |
* overwritten |
337 |
+ |
* @param w will contain the eigenvalues of the matrix On return of this function |
338 |
+ |
* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are |
339 |
+ |
* normalized and mutually orthogonal. |
340 |
+ |
* @warning a will be overwritten |
341 |
+ |
*/ |
342 |
+ |
static void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v); |
343 |
+ |
}; |
344 |
+ |
/*========================================================================= |
345 |
+ |
|
346 |
+ |
Program: Visualization Toolkit |
347 |
+ |
Module: $RCSfile: SquareMatrix3.hpp,v $ |
348 |
+ |
|
349 |
+ |
Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen |
350 |
+ |
All rights reserved. |
351 |
+ |
See Copyright.txt or http://www.kitware.com/Copyright.htm for details. |
352 |
+ |
|
353 |
+ |
This software is distributed WITHOUT ANY WARRANTY; without even |
354 |
+ |
the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR |
355 |
+ |
PURPOSE. See the above copyright notice for more information. |
356 |
+ |
|
357 |
+ |
=========================================================================*/ |
358 |
+ |
template<typename Real> |
359 |
+ |
void SquareMatrix3<Real>::diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, |
360 |
+ |
SquareMatrix3<Real>& v) { |
361 |
+ |
int i,j,k,maxI; |
362 |
+ |
Real tmp, maxVal; |
363 |
+ |
Vector3<Real> v_maxI, v_k, v_j; |
364 |
+ |
|
365 |
+ |
// diagonalize using Jacobi |
366 |
+ |
jacobi(a, w, v); |
367 |
+ |
// if all the eigenvalues are the same, return identity matrix |
368 |
+ |
if (w[0] == w[1] && w[0] == w[2] ) { |
369 |
+ |
v = SquareMatrix3<Real>::identity(); |
370 |
+ |
return; |
371 |
+ |
} |
372 |
+ |
|
373 |
+ |
// transpose temporarily, it makes it easier to sort the eigenvectors |
374 |
+ |
v = v.transpose(); |
375 |
+ |
|
376 |
+ |
// if two eigenvalues are the same, re-orthogonalize to optimally line |
377 |
+ |
// up the eigenvectors with the x, y, and z axes |
378 |
+ |
for (i = 0; i < 3; i++) { |
379 |
+ |
if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same |
380 |
+ |
// find maximum element of the independant eigenvector |
381 |
+ |
maxVal = fabs(v(i, 0)); |
382 |
+ |
maxI = 0; |
383 |
+ |
for (j = 1; j < 3; j++) { |
384 |
+ |
if (maxVal < (tmp = fabs(v(i, j)))){ |
385 |
+ |
maxVal = tmp; |
386 |
+ |
maxI = j; |
387 |
+ |
} |
388 |
+ |
} |
389 |
+ |
|
390 |
+ |
// swap the eigenvector into its proper position |
391 |
+ |
if (maxI != i) { |
392 |
+ |
tmp = w(maxI); |
393 |
+ |
w(maxI) = w(i); |
394 |
+ |
w(i) = tmp; |
395 |
+ |
|
396 |
+ |
v.swapRow(i, maxI); |
397 |
+ |
} |
398 |
+ |
// maximum element of eigenvector should be positive |
399 |
+ |
if (v(maxI, maxI) < 0) { |
400 |
+ |
v(maxI, 0) = -v(maxI, 0); |
401 |
+ |
v(maxI, 1) = -v(maxI, 1); |
402 |
+ |
v(maxI, 2) = -v(maxI, 2); |
403 |
+ |
} |
404 |
+ |
|
405 |
+ |
// re-orthogonalize the other two eigenvectors |
406 |
+ |
j = (maxI+1)%3; |
407 |
+ |
k = (maxI+2)%3; |
408 |
+ |
|
409 |
+ |
v(j, 0) = 0.0; |
410 |
+ |
v(j, 1) = 0.0; |
411 |
+ |
v(j, 2) = 0.0; |
412 |
+ |
v(j, j) = 1.0; |
413 |
+ |
|
414 |
+ |
/** @todo */ |
415 |
+ |
v_maxI = v.getRow(maxI); |
416 |
+ |
v_j = v.getRow(j); |
417 |
+ |
v_k = cross(v_maxI, v_j); |
418 |
+ |
v_k.normalize(); |
419 |
+ |
v_j = cross(v_k, v_maxI); |
420 |
+ |
v.setRow(j, v_j); |
421 |
+ |
v.setRow(k, v_k); |
422 |
+ |
|
423 |
+ |
|
424 |
+ |
// transpose vectors back to columns |
425 |
+ |
v = v.transpose(); |
426 |
+ |
return; |
427 |
+ |
} |
428 |
+ |
} |
429 |
+ |
|
430 |
+ |
// the three eigenvalues are different, just sort the eigenvectors |
431 |
+ |
// to align them with the x, y, and z axes |
432 |
+ |
|
433 |
+ |
// find the vector with the largest x element, make that vector |
434 |
+ |
// the first vector |
435 |
+ |
maxVal = fabs(v(0, 0)); |
436 |
+ |
maxI = 0; |
437 |
+ |
for (i = 1; i < 3; i++) { |
438 |
+ |
if (maxVal < (tmp = fabs(v(i, 0)))) { |
439 |
+ |
maxVal = tmp; |
440 |
+ |
maxI = i; |
441 |
+ |
} |
442 |
+ |
} |
443 |
+ |
|
444 |
+ |
// swap eigenvalue and eigenvector |
445 |
+ |
if (maxI != 0) { |
446 |
+ |
tmp = w(maxI); |
447 |
+ |
w(maxI) = w(0); |
448 |
+ |
w(0) = tmp; |
449 |
+ |
v.swapRow(maxI, 0); |
450 |
+ |
} |
451 |
+ |
// do the same for the y element |
452 |
+ |
if (fabs(v(1, 1)) < fabs(v(2, 1))) { |
453 |
+ |
tmp = w(2); |
454 |
+ |
w(2) = w(1); |
455 |
+ |
w(1) = tmp; |
456 |
+ |
v.swapRow(2, 1); |
457 |
+ |
} |
458 |
+ |
|
459 |
+ |
// ensure that the sign of the eigenvectors is correct |
460 |
+ |
for (i = 0; i < 2; i++) { |
461 |
+ |
if (v(i, i) < 0) { |
462 |
+ |
v(i, 0) = -v(i, 0); |
463 |
+ |
v(i, 1) = -v(i, 1); |
464 |
+ |
v(i, 2) = -v(i, 2); |
465 |
+ |
} |
466 |
+ |
} |
467 |
+ |
|
468 |
+ |
// set sign of final eigenvector to ensure that determinant is positive |
469 |
+ |
if (v.determinant() < 0) { |
470 |
+ |
v(2, 0) = -v(2, 0); |
471 |
+ |
v(2, 1) = -v(2, 1); |
472 |
+ |
v(2, 2) = -v(2, 2); |
473 |
+ |
} |
474 |
+ |
|
475 |
+ |
// transpose the eigenvectors back again |
476 |
+ |
v = v.transpose(); |
477 |
+ |
return ; |
478 |
+ |
} |
479 |
+ |
|
480 |
+ |
/** |
481 |
+ |
* Return the multiplication of two matrixes (m1 * m2). |
482 |
+ |
* @return the multiplication of two matrixes |
483 |
+ |
* @param m1 the first matrix |
484 |
+ |
* @param m2 the second matrix |
485 |
+ |
*/ |
486 |
+ |
template<typename Real> |
487 |
+ |
inline SquareMatrix3<Real> operator *(const SquareMatrix3<Real>& m1, const SquareMatrix3<Real>& m2) { |
488 |
+ |
SquareMatrix3<Real> result; |
489 |
+ |
|
490 |
+ |
for (unsigned int i = 0; i < 3; i++) |
491 |
+ |
for (unsigned int j = 0; j < 3; j++) |
492 |
+ |
for (unsigned int k = 0; k < 3; k++) |
493 |
+ |
result(i, j) += m1(i, k) * m2(k, j); |
494 |
+ |
|
495 |
+ |
return result; |
496 |
+ |
} |
497 |
+ |
|
498 |
+ |
template<typename Real> |
499 |
+ |
inline SquareMatrix3<Real> outProduct(const Vector3<Real>& v1, const Vector3<Real>& v2) { |
500 |
+ |
SquareMatrix3<Real> result; |
501 |
+ |
|
502 |
+ |
for (unsigned int i = 0; i < 3; i++) { |
503 |
+ |
for (unsigned int j = 0; j < 3; j++) { |
504 |
+ |
result(i, j) = v1[i] * v2[j]; |
505 |
+ |
} |
506 |
+ |
} |
507 |
+ |
|
508 |
+ |
return result; |
509 |
+ |
} |
510 |
+ |
|
511 |
+ |
|
512 |
+ |
typedef SquareMatrix3<double> Mat3x3d; |
513 |
+ |
typedef SquareMatrix3<double> RotMat3x3d; |
514 |
+ |
|
515 |
|
} //namespace oopse |
516 |
|
#endif // MATH_SQUAREMATRIX_HPP |
517 |
+ |
|