[ViewVC] Diff of: OpenMD/trunk/src/math/SquareMatrix3.hpp

Comparing trunk/src/math/SquareMatrix3.hpp (file contents):
Revision 70 by tim, Wed Oct 13 06:51:09 2004 UTC vs.
Revision 123 by tim, Wed Oct 20 18:07:08 2004 UTC

+ * @date 10/11/2004
+ * @version 1.0
+ */
-<
+#ifndef MATH_SQUAREMATRIX#_HPP
-<
+#define  MATH_SQUAREMATRIX#_HPP
->
+ #ifndef MATH_SQUAREMATRIX3_HPP
->
+#define  MATH_SQUAREMATRIX3_HPP
-+
+#include "Quaternion.hpp"
+#include "SquareMatrix.hpp"
-+
+#include "Vector3.hpp"
-+
+namespace oopse {
+    template<typename Real>
+            SquareMatrix3(const SquareMatrix<Real, 3>& m)  : SquareMatrix<Real, 3>(m) {
-+
+            SquareMatrix3( const Vector3<Real>& eulerAngles) {
-+
+                setupRotMat(eulerAngles);
-+
+            }
-+
-+
+            SquareMatrix3(Real phi, Real theta, Real psi) {
-+
+                setupRotMat(phi, theta, psi);
-+
+            }
-+
-+
+            SquareMatrix3(const Quaternion<Real>& q) {
-+
+                setupRotMat(q);
-+
-+
+            }
-+
-+
+            SquareMatrix3(Real w, Real x, Real y, Real z) {
-+
+                setupRotMat(w, x, y, z);
-+
+            }
-+
+            /** copy assignment operator */
+            SquareMatrix3<Real>& operator =(const SquareMatrix<Real, 3>& m) {
+                if (this == &m)
+                    return *this;
+                 SquareMatrix<Real, 3>::operator=(m);
-+
+                 return *this;
-+
-+
+            /**
-+
+             * Sets this matrix to a rotation matrix by three euler angles
-+
+             * @ param euler
-+
+             */
-+
+            void setupRotMat(const Vector3<Real>& eulerAngles) {
-+
+                setupRotMat(eulerAngles[0], eulerAngles[1], eulerAngles[2]);
-+
+            }
-+
-+
+            /**
-+
+             * Sets this matrix to a rotation matrix by three euler angles
-+
+             * @param phi
-+
+             * @param theta
-+
+             * @psi theta
-+
+             */
-+
+            void setupRotMat(Real phi, Real theta, Real psi) {
-+
+                Real sphi, stheta, spsi;
-+
+                Real cphi, ctheta, cpsi;
-+
-+
+                sphi = sin(phi);
-+
+                stheta = sin(theta);
-+
+                spsi = sin(psi);
-+
+                cphi = cos(phi);
-+
+                ctheta = cos(theta);
-+
+                cpsi = cos(psi);
-+
-+
+                data_[0][0] = cpsi * cphi - ctheta * sphi * spsi;
-+
+                data_[0][1] = cpsi * sphi + ctheta * cphi * spsi;
-+
+                data_[0][2] = spsi * stheta;
-+
-+
+                data_[1][0] = -spsi * ctheta - ctheta * sphi * cpsi;
-+
+                data_[1][1] = -spsi * stheta + ctheta * cphi * cpsi;
-+
+                data_[1][2] = cpsi * stheta;
-+
-+
+                data_[2][0] = stheta * sphi;
-+
+                data_[2][1] = -stheta * cphi;
-+
+                data_[2][2] = ctheta;
-+
+            }
-+
-+
-+
+            /**
-+
+             * Sets this matrix to a rotation matrix by quaternion
-+
+             * @param quat
-+
+            */
-+
+            void setupRotMat(const Quaternion<Real>& quat) {
-+
+                setupRotMat(quat.w(), quat.x(), quat.y(), quat.z());
-+
+            }
-+
-+
+            /**
-+
+             * Sets this matrix to a rotation matrix by quaternion
-+
+             * @param w the first element
-+
+             * @param x the second element
-+
+             * @param y the third element
-+
+             * @param z the fourth element
-+
+            */
-+
+            void setupRotMat(Real w, Real x, Real y, Real z) {
-+
+                Quaternion<Real> q(w, x, y, z);
-+
+                *this = q.toRotationMatrix3();
-+
+            }
-+
-+
+            /**
-+
+             * Returns the quaternion from this rotation matrix
-+
+             * @return the quaternion from this rotation matrix
-+
+             * @exception invalid rotation matrix
-+
+            */
-+
+            Quaternion<Real> toQuaternion() {
-+
+                Quaternion<Real> q;
-+
+                Real t, s;
-+
+                Real ad1, ad2, ad3;
-+
+                t = data_[0][0] + data_[1][1] + data_[2][2] + 1.0;
-+
-+
+                if( t > 0.0 ){
-+
-+
+                    s = 0.5 / sqrt( t );
-+
+                    q[0] = 0.25 / s;
-+
+                    q[1] = (data_[1][2] - data_[2][1]) * s;
-+
+                    q[2] = (data_[2][0] - data_[0][2]) * s;
-+
+                    q[3] = (data_[0][1] - data_[1][0]) * s;
-+
+                } else {
-+
-+
+                    ad1 = fabs( data_[0][0] );
-+
+                    ad2 = fabs( data_[1][1] );
-+
+                    ad3 = fabs( data_[2][2] );
-+
-+
+                    if( ad1 >= ad2 && ad1 >= ad3 ){
-+
-+
+                        s = 2.0 * sqrt( 1.0 + data_[0][0] - data_[1][1] - data_[2][2] );
-+
+                        q[0] = (data_[1][2] + data_[2][1]) / s;
-+
+                        q[1] = 0.5 / s;
-+
+                        q[2] = (data_[0][1] + data_[1][0]) / s;
-+
+                        q[3] = (data_[0][2] + data_[2][0]) / s;
-+
+                    } else if ( ad2 >= ad1 && ad2 >= ad3 ) {
-+
+                        s = sqrt( 1.0 + data_[1][1] - data_[0][0] - data_[2][2] ) * 2.0;
-+
+                        q[0] = (data_[0][2] + data_[2][0]) / s;
-+
+                        q[1] = (data_[0][1] + data_[1][0]) / s;
-+
+                        q[2] = 0.5 / s;
-+
+                        q[3] = (data_[1][2] + data_[2][1]) / s;
-+
+                    } else {
-+
-+
+                        s = sqrt( 1.0 + data_[2][2] - data_[0][0] - data_[1][1] ) * 2.0;
-+
+                        q[0] = (data_[0][1] + data_[1][0]) / s;
-+
+                        q[1] = (data_[0][2] + data_[2][0]) / s;
-+
+                        q[2] = (data_[1][2] + data_[2][1]) / s;
-+
+                        q[3] = 0.5 / s;
-+
+                    }
-+
+                }
-+
-+
+                return q;
-+
-+
+            }
-+
-+
+            /**
-+
+             * Returns the euler angles from this rotation matrix
-+
+             * @return the euler angles in a vector
-+
+             * @exception invalid rotation matrix
-+
+             * We use so-called "x-convention", which is the most common definition.
-+
+             * In this convention, the rotation given by Euler angles (phi, theta, psi), where the first
-+
+             * rotation is by an angle phi about the z-axis, the second is by an angle
-+
+             * theta (0 <= theta <= 180)about the x-axis, and thethird is by an angle psi about the
-+
+             * z-axis (again).
-+
+            */
-+
+            Vector3<Real> toEulerAngles() {
-+
+                Vector3<Real> myEuler;
-+
+                Real phi,theta,psi,eps;
-+
+                Real ctheta,stheta;
-+
-+
+                // set the tolerance for Euler angles and rotation elements
-+
-+
+                theta = acos(std::min(1.0, std::max(-1.0,data_[2][2])));
-+
+                ctheta = data_[2][2];
-+
+                stheta = sqrt(1.0 - ctheta * ctheta);
-+
-+
+                // when sin(theta) is close to 0, we need to consider singularity
-+
+                // In this case, we can assign an arbitary value to phi (or psi), and then determine
-+
+                // the psi (or phi) or vice-versa. We'll assume that phi always gets the rotation, and psi is 0
-+
+                // in cases of singularity.
-+
+                // we use atan2 instead of atan, since atan2 will give us -Pi to Pi.
-+
+                // Since 0 <= theta <= 180, sin(theta) will be always non-negative. Therefore, it never
-+
+                // change the sign of both of the parameters passed to atan2.
-+
-+
+                if (fabs(stheta) <= oopse::epsilon){
-+
+                    psi = 0.0;
-+
+                    phi = atan2(-data_[1][0], data_[0][0]);
-+
+                }
-+
+                // we only have one unique solution
-+
+                else{
-+
+                    phi = atan2(data_[2][0], -data_[2][1]);
-+
+                    psi = atan2(data_[0][2], data_[1][2]);
-+
+                }
-+
-+
+                //wrap phi and psi, make sure they are in the range from 0 to 2*Pi
-+
+                if (phi < 0)
-+
+                  phi += M_PI;
-+
-+
+                if (psi < 0)
-+
+                  psi += M_PI;
-+
-+
+                myEuler[0] = phi;
-+
+                myEuler[1] = theta;
-+
+                myEuler[2] = psi;
-+
-+
+                return myEuler;
-+
+            }
-+
+            /** Returns the determinant of this matrix. */
-+
+            Real determinant() const {
-+
+                Real x,y,z;
-+
-+
+                x = data_[0][0] * (data_[1][1] * data_[2][2] - data_[1][2] * data_[2][1]);
-+
+                y = data_[0][1] * (data_[1][2] * data_[2][0] - data_[1][0] * data_[2][2]);
-+
+                z = data_[0][2] * (data_[1][0] * data_[2][1] - data_[1][1] * data_[2][0]);
-+
-+
+                return(x + y + z);
-+
+            }
-+
+            /**
+             * Sets the value of this matrix to  the inversion of itself.
+             * @note since simple algorithm can be applied to inverse the 3 by 3 matrix, we hide the
+             * implementation of inverse in SquareMatrix class
+             */
-<
+            void  inverse();
-<
->
+            SquareMatrix3<Real>  inverse() {
->
+                SquareMatrix3<Real> m;
->
+                double det = determinant();
->
+                if (fabs(det) <= oopse::epsilon) {
->
+                //"The method was called on a matrix with |determinant| <= 1e-6.",
->
+                //"This is a runtime or a programming error in your application.");
->
+                }
->
->
+                m(0, 0) = data_[1][1]*data_[2][2] - data_[1][2]*data_[2][1];
->
+                m(1, 0) = data_[1][2]*data_[2][0] - data_[1][0]*data_[2][2];
->
+                m(2, 0) = data_[1][0]*data_[2][1] - data_[1][1]*data_[2][0];
->
+                m(0, 1) = data_[2][1]*data_[0][2] - data_[2][2]*data_[0][1];
->
+                m(1, 1) = data_[2][2]*data_[0][0] - data_[2][0]*data_[0][2];
->
+                m(2, 1) = data_[2][0]*data_[0][1] - data_[2][1]*data_[0][0];
->
+                m(0, 2) = data_[0][1]*data_[1][2] - data_[0][2]*data_[1][1];
->
+                m(1, 2) = data_[0][2]*data_[1][0] - data_[0][0]*data_[1][2];
->
+                m(2, 2) = data_[0][0]*data_[1][1] - data_[0][1]*data_[1][0];
->
->
+                m /= det;
->
+                return m;
->
+            }
+            /**
-<
+             * Sets the value of this matrix to  the inversion of other matrix.
-<
+             * @ param m the source matrix
-<
+             */
-<
+            void inverse(const SquareMatrix<Real, Dim>& m);
->
+             * Extract the eigenvalues and eigenvectors from a 3x3 matrix.
->
+             * The eigenvectors (the columns of V) will be normalized.
->
+             * The eigenvectors are aligned optimally with the x, y, and z
->
+             * axes respectively.
->
+             * @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
->
+             *     overwritten
->
+             * @param w will contain the eigenvalues of the matrix On return of this function
->
+             * @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
->
+             *    normalized and mutually orthogonal.
->
+             * @warning a will be overwritten
->
+             */
->
+            static void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v);
->
+    };
->
+/*=========================================================================
-+
+  Program:   Visualization Toolkit
-+
+  Module:    $RCSfile: SquareMatrix3.hpp,v $
-+
-+
+  Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
-+
+  All rights reserved.
-+
+  See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
-+
-+
+     This software is distributed WITHOUT ANY WARRANTY; without even
-+
+     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
-+
+     PURPOSE.  See the above copyright notice for more information.
-+
-+
+=========================================================================*/
-+
+    template<typename Real>
-+
+    void SquareMatrix3<Real>::diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w,
-+
+                                                                           SquareMatrix3<Real>& v) {
-+
+        int i,j,k,maxI;
-+
+        Real tmp, maxVal;
-+
+        Vector3<Real> v_maxI, v_k, v_j;
-+
-+
+        // diagonalize using Jacobi
-+
+        jacobi(a, w, v);
-+
+        // if all the eigenvalues are the same, return identity matrix
-+
+        if (w[0] == w[1] && w[0] == w[2] ) {
-+
+              v = SquareMatrix3<Real>::identity();
-+
+              return;
-+
+        }
-+
-+
+        // transpose temporarily, it makes it easier to sort the eigenvectors
-+
+        v = v.transpose();
-+
-+
+        // if two eigenvalues are the same, re-orthogonalize to optimally line
-+
+        // up the eigenvectors with the x, y, and z axes
-+
+        for (i = 0; i < 3; i++) {
-+
+            if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same
-+
+            // find maximum element of the independant eigenvector
-+
+            maxVal = fabs(v(i, 0));
-+
+            maxI = 0;
-+
+            for (j = 1; j < 3; j++) {
-+
+                if (maxVal < (tmp = fabs(v(i, j)))){
-+
+                    maxVal = tmp;
-+
+                    maxI = j;
-+
+                }
-+
+            }
-+
-+
+            // swap the eigenvector into its proper position
-+
+            if (maxI != i) {
-+
+                tmp = w(maxI);
-+
+                w(maxI) = w(i);
-+
+                w(i) = tmp;
-+
-+
+                v.swapRow(i, maxI);
-+
+            }
-+
+            // maximum element of eigenvector should be positive
-+
+            if (v(maxI, maxI) < 0) {
-+
+                v(maxI, 0) = -v(maxI, 0);
-+
+                v(maxI, 1) = -v(maxI, 1);
-+
+                v(maxI, 2) = -v(maxI, 2);
-+
+            }
-+
-+
+            // re-orthogonalize the other two eigenvectors
-+
+            j = (maxI+1)%3;
-+
+            k = (maxI+2)%3;
-+
-+
+            v(j, 0) = 0.0;
-+
+            v(j, 1) = 0.0;
-+
+            v(j, 2) = 0.0;
-+
+            v(j, j) = 1.0;
-+
-+
+            /** @todo */
-+
+            v_maxI = v.getRow(maxI);
-+
+            v_j = v.getRow(j);
-+
+            v_k = cross(v_maxI, v_j);
-+
+            v_k.normalize();
-+
+            v_j = cross(v_k, v_maxI);
-+
+            v.setRow(j, v_j);
-+
+            v.setRow(k, v_k);
-+
-+
-+
+            // transpose vectors back to columns
-+
+            v = v.transpose();
-+
+            return;
-+
+            }
-+
+        }
-+
-+
+        // the three eigenvalues are different, just sort the eigenvectors
-+
+        // to align them with the x, y, and z axes
-+
-+
+        // find the vector with the largest x element, make that vector
-+
+        // the first vector
-+
+        maxVal = fabs(v(0, 0));
-+
+        maxI = 0;
-+
+        for (i = 1; i < 3; i++) {
-+
+            if (maxVal < (tmp = fabs(v(i, 0)))) {
-+
+                maxVal = tmp;
-+
+                maxI = i;
-+
+            }
-+
+        }
-+
-+
+        // swap eigenvalue and eigenvector
-+
+        if (maxI != 0) {
-+
+            tmp = w(maxI);
-+
+            w(maxI) = w(0);
-+
+            w(0) = tmp;
-+
+            v.swapRow(maxI, 0);
-+
+        }
-+
+        // do the same for the y element
-+
+        if (fabs(v(1, 1)) < fabs(v(2, 1))) {
-+
+            tmp = w(2);
-+
+            w(2) = w(1);
-+
+            w(1) = tmp;
-+
+            v.swapRow(2, 1);
-+
+        }
-+
-+
+        // ensure that the sign of the eigenvectors is correct
-+
+        for (i = 0; i < 2; i++) {
-+
+            if (v(i, i) < 0) {
-+
+                v(i, 0) = -v(i, 0);
-+
+                v(i, 1) = -v(i, 1);
-+
+                v(i, 2) = -v(i, 2);
-+
+            }
-+
+        }
-+
-+
+        // set sign of final eigenvector to ensure that determinant is positive
-+
+        if (v.determinant() < 0) {
-+
+            v(2, 0) = -v(2, 0);
-+
+            v(2, 1) = -v(2, 1);
-+
+            v(2, 2) = -v(2, 2);
-+
+        }
-+
-+
+        // transpose the eigenvectors back again
-+
+        v = v.transpose();
-+
+        return ;
-+
+    typedef SquareMatrix3<double> Mat3x3d;
-+
+    typedef SquareMatrix3<double> RotMat3x3d;
-<
+    };
->
+} //namespace oopse
->
+#endif // MATH_SQUAREMATRIX_HPP
-–
+}
-–
+#endif // MATH_SQUAREMATRIX#_HPP

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Comparing trunk/src/math/SquareMatrix3.hpp (file contents): Revision 70 by tim, Wed Oct 13 06:51:09 2004 UTC vs. Revision 123 by tim, Wed Oct 20 18:07:08 2004 UTC

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Comparing trunk/src/math/SquareMatrix3.hpp (file contents):
Revision 70 by tim, Wed Oct 13 06:51:09 2004 UTC vs.
Revision 123 by tim, Wed Oct 20 18:07:08 2004 UTC