ViewVC Help
View File | Revision Log | Show Annotations | View Changeset | Root Listing
root/group/trunk/OOPSE-2.0/src/math/SquareMatrix3.hpp
(Generate patch)

Comparing trunk/OOPSE-2.0/src/math/SquareMatrix3.hpp (file contents):
Revision 2146 by tim, Tue Mar 29 21:00:54 2005 UTC vs.
Revision 2204 by gezelter, Fri Apr 15 22:04:00 2005 UTC

# Line 1 | Line 1
1 < /*
1 > /*
2   * Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3   *
4   * The University of Notre Dame grants you ("Licensee") a
# Line 45 | Line 45
45   * @date 10/11/2004
46   * @version 1.0
47   */
48 < #ifndef MATH_SQUAREMATRIX3_HPP
48 > #ifndef MATH_SQUAREMATRIX3_HPP
49   #define  MATH_SQUAREMATRIX3_HPP
50  
51   #include "Quaternion.hpp"
# Line 54 | Line 54 | namespace oopse {
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;
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 <            /** Constructs and initializes every element of this matrix to a scalar */
69 <            SquareMatrix3(Real s) : SquareMatrix<Real,3>(s){
70 <            }
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 <            }
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 <            }
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 <            }
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 <            }
85 >    SquareMatrix3(Real phi, Real theta, Real psi) {
86 >      setupRotMat(phi, theta, psi);
87 >    }
88  
89 <            SquareMatrix3(const Quaternion<Real>& q) {
90 <                setupRotMat(q);
89 >    SquareMatrix3(const Quaternion<Real>& q) {
90 >      setupRotMat(q);
91  
92 <            }
92 >    }
93  
94 <            SquareMatrix3(Real w, Real x, Real y, Real z) {
95 <                setupRotMat(w, x, y, z);
96 <            }
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 <            }
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 <            }
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 <            }
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;
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);
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;
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;
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 <            }
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 <            }
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 <            }
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;
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 ){
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 {
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( this->data_[0][0] );
192 <                    ad2 = fabs( this->data_[1][1] );
193 <                    ad3 = fabs( this->data_[2][2] );
191 >        ad1 = fabs( this->data_[0][0] );
192 >        ad2 = fabs( this->data_[1][1] );
193 >        ad3 = fabs( this->data_[2][2] );
194  
195 <                    if( ad1 >= ad2 && ad1 >= ad3 ){
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 {
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 <                }            
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 <                Vector3<Real> myEuler;
234 <                Real phi;
235 <                Real theta;
236 <                Real psi;
237 <                Real ctheta;
238 <                Real stheta;
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
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);
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(-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 <                }
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 <            /** Returns the determinant of this matrix. */
279 <            Real determinant() const {
280 <                Real x,y,z;
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]);
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 <            }            
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 <            }
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 <                }
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];
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 < /*=========================================================================
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 $
# Line 340 | Line 340 | namespace oopse {
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.
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;
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 <        }
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();
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 <            }
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;
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 <            }
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;
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;
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);
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 <        }
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
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 <        }
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 <        }
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 <        }
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 ;
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 <    /**
466 <    * Return the multiplication of two matrixes  (m1 * m2).
467 <    * @return the multiplication of two matrixes
468 <    * @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;
465 >    // transpose the eigenvectors back again
466 >    v = v.transpose();
467 >    return ;
468 >  }
469  
470 <            for (unsigned int i = 0; i < 3; i++)
471 <                for (unsigned int j = 0; j < 3; j++)
472 <                    for (unsigned int k = 0; k < 3; k++)
473 <                        result(i, j)  += m1(i, k) * m2(k, j);                
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 <        return result;
481 <    }
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 <    template<typename Real>
486 <    inline SquareMatrix3<Real> outProduct(const Vector3<Real>& v1, const Vector3<Real>& v2) {
490 <        SquareMatrix3<Real> result;
485 >    return result;
486 >  }
487  
488 <            for (unsigned int i = 0; i < 3; i++) {
489 <                for (unsigned int j = 0; j < 3; j++) {
490 <                        result(i, j)  = v1[i] * v2[j];                
491 <                }
492 <            }
493 <            
494 <        return result;        
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;
502 >  typedef SquareMatrix3<double> Mat3x3d;
503 >  typedef SquareMatrix3<double> RotMat3x3d;
504  
505   } //namespace oopse
506   #endif // MATH_SQUAREMATRIX_HPP

Diff Legend

– Removed lines
+ Added lines
< Changed lines
> Changed lines