src/math/SquareMatrix3.hpp

/*
 * Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
 *
 * The University of Notre Dame grants you ("Licensee") a
 * non-exclusive, royalty free, license to use, modify and
 * redistribute this software in source and binary code form, provided
 * that the following conditions are met:
 *
 * 1. Acknowledgement of the program authors must be made in any
 *    publication of scientific results based in part on use of the
 *    program.  An acceptable form of acknowledgement is citation of
 *    the article in which the program was described (Matthew
 *    A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
 *    J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
 *    Parallel Simulation Engine for Molecular Dynamics,"
 *    J. Comput. Chem. 26, pp. 252-271 (2005))
 *
 * 2. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 3. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the
 *    distribution.
 *
 * This software is provided "AS IS," without a warranty of any
 * kind. All express or implied conditions, representations and
 * warranties, including any implied warranty of merchantability,
 * fitness for a particular purpose or non-infringement, are hereby
 * excluded.  The University of Notre Dame and its licensors shall not
 * be liable for any damages suffered by licensee as a result of
 * using, modifying or distributing the software or its
 * derivatives. In no event will the University of Notre Dame or its
 * licensors be liable for any lost revenue, profit or data, or for
 * direct, indirect, special, consequential, incidental or punitive
 * damages, however caused and regardless of the theory of liability,
 * arising out of the use of or inability to use software, even if the
 * University of Notre Dame has been advised of the possibility of
 * such damages.
 */
 
/**
 * @file SquareMatrix3.hpp
 * @author Teng Lin
 * @date 10/11/2004
 * @version 1.0
 */
#ifndef MATH_SQUAREMATRIX3_HPP
#define  MATH_SQUAREMATRIX3_HPP

#include "Quaternion.hpp"
#include "SquareMatrix.hpp"
#include "Vector3.hpp"
#include "utils/NumericConstant.hpp"
namespace oopse {

  template<typename Real>
  class SquareMatrix3 : public SquareMatrix<Real, 3> {
  public:

    typedef Real ElemType;
    typedef Real* ElemPoinerType;
            
    /** default constructor */
    SquareMatrix3() : SquareMatrix<Real, 3>() {
    }

    /** Constructs and initializes every element of this matrix to a scalar */ 
    SquareMatrix3(Real s) : SquareMatrix<Real,3>(s){
    }

    /** Constructs and initializes from an array */ 
    SquareMatrix3(Real* array) : SquareMatrix<Real,3>(array){
    }


    /** copy  constructor */
    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;
    }


    SquareMatrix3<Real>& operator =(const Quaternion<Real>& q) {
      this->setupRotMat(q);
      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);

      this->data_[0][0] = cpsi * cphi - ctheta * sphi * spsi;
      this->data_[0][1] = cpsi * sphi + ctheta * cphi * spsi;
      this->data_[0][2] = spsi * stheta;
                
      this->data_[1][0] = -spsi * ctheta - ctheta * sphi * cpsi;
      this->data_[1][1] = -spsi * stheta + ctheta * cphi * cpsi;
      this->data_[1][2] = cpsi * stheta;

      this->data_[2][0] = stheta * sphi;
      this->data_[2][1] = -stheta * cphi;
      this->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 = this->data_[0][0] + this->data_[1][1] + this->data_[2][2] + 1.0;

      if( t > NumericConstant::epsilon ){

        s = 0.5 / sqrt( t );
        q[0] = 0.25 / s;
        q[1] = (this->data_[1][2] - this->data_[2][1]) * s;
        q[2] = (this->data_[2][0] - this->data_[0][2]) * s;
        q[3] = (this->data_[0][1] - this->data_[1][0]) * s;
      } else {

        ad1 = this->data_[0][0];
        ad2 = this->data_[1][1];
        ad3 = this->data_[2][2];

        if( ad1 >= ad2 && ad1 >= ad3 ){

          s = 0.5 / sqrt( 1.0 + this->data_[0][0] - this->data_[1][1] - this->data_[2][2] );
          q[0] = (this->data_[1][2] - this->data_[2][1]) * s;
          q[1] = 0.25 / s;
          q[2] = (this->data_[0][1] + this->data_[1][0]) * s;
          q[3] = (this->data_[0][2] + this->data_[2][0]) * s;
        } else if ( ad2 >= ad1 && ad2 >= ad3 ) {
          s = 0.5 / sqrt( 1.0 + this->data_[1][1] - this->data_[0][0] - this->data_[2][2] );
          q[0] = (this->data_[2][0] - this->data_[0][2] ) * s;
          q[1] = (this->data_[0][1] + this->data_[1][0]) * s;
          q[2] = 0.25 / s;
          q[3] = (this->data_[1][2] + this->data_[2][1]) * s;
        } else {

          s = 0.5 / sqrt( 1.0 + this->data_[2][2] - this->data_[0][0] - this->data_[1][1] );
          q[0] = (this->data_[0][1] - this->data_[1][0]) * s;
          q[1] = (this->data_[0][2] + this->data_[2][0]) * s;
          q[2] = (this->data_[1][2] + this->data_[2][1]) * s;
          q[3] = 0.25 / 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;
      Real theta;
      Real psi;
      Real ctheta;
      Real stheta;
                
      // set the tolerance for Euler angles and rotation elements

      theta = acos(std::min(1.0, std::max(-1.0,this->data_[2][2])));
      ctheta = this->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(-this->data_[1][0], this->data_[0][0]);  
      }
      // we only have one unique solution
      else{    
        phi = atan2(this->data_[2][0], -this->data_[2][1]);
        psi = atan2(this->data_[0][2], this->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 = this->data_[0][0] * (this->data_[1][1] * this->data_[2][2] - this->data_[1][2] * this->data_[2][1]);
      y = this->data_[0][1] * (this->data_[1][2] * this->data_[2][0] - this->data_[1][0] * this->data_[2][2]);
      z = this->data_[0][2] * (this->data_[1][0] * this->data_[2][1] - this->data_[1][1] * this->data_[2][0]);

      return(x + y + z);
    }            

    /** Returns the trace of this matrix. */
    Real trace() const {
      return this->data_[0][0] + this->data_[1][1] + this->data_[2][2];
    }
            
    /**
     * 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
     */
    SquareMatrix3<Real>  inverse() const {
      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) = this->data_[1][1]*this->data_[2][2] - this->data_[1][2]*this->data_[2][1];
      m(1, 0) = this->data_[1][2]*this->data_[2][0] - this->data_[1][0]*this->data_[2][2];
      m(2, 0) = this->data_[1][0]*this->data_[2][1] - this->data_[1][1]*this->data_[2][0];
      m(0, 1) = this->data_[2][1]*this->data_[0][2] - this->data_[2][2]*this->data_[0][1];
      m(1, 1) = this->data_[2][2]*this->data_[0][0] - this->data_[2][0]*this->data_[0][2];
      m(2, 1) = this->data_[2][0]*this->data_[0][1] - this->data_[2][1]*this->data_[0][0];
      m(0, 2) = this->data_[0][1]*this->data_[1][2] - this->data_[0][2]*this->data_[1][1];
      m(1, 2) = this->data_[0][2]*this->data_[1][0] - this->data_[0][0]*this->data_[1][2];
      m(2, 2) = this->data_[0][0]*this->data_[1][1] - this->data_[0][1]*this->data_[1][0];

      m /= det;
      return 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 ;
  }

  /**
   * Return the multiplication of two matrixes  (m1 * m2). 
   * @return the multiplication of two matrixes
   * @param m1 the first matrix
   * @param m2 the second matrix
   */
  template<typename Real> 
  inline SquareMatrix3<Real> operator *(const SquareMatrix3<Real>& m1, const SquareMatrix3<Real>& m2) {
    SquareMatrix3<Real> result;

    for (unsigned int i = 0; i < 3; i++)
      for (unsigned int j = 0; j < 3; j++)
        for (unsigned int k = 0; k < 3; k++)
          result(i, j)  += m1(i, k) * m2(k, j);                

    return result;
  }

  template<typename Real> 
  inline SquareMatrix3<Real> outProduct(const Vector3<Real>& v1, const Vector3<Real>& v2) {
    SquareMatrix3<Real> result;

    for (unsigned int i = 0; i < 3; i++) {
      for (unsigned int j = 0; j < 3; j++) {
        result(i, j)  = v1[i] * v2[j];                
      }
    }
            
    return result;        
  }

    
  typedef SquareMatrix3<double> Mat3x3d;
  typedef SquareMatrix3<double> RotMat3x3d;

} //namespace oopse
#endif // MATH_SQUAREMATRIX_HPP

Revision:	2336
Committed:	Wed Sep 28 16:55:57 2005 UTC (18 years, 9 months ago) by tim
File size:	16379 byte(s)
Log Message:	using epsilon instead of 0.0 to avoid divergence in rotation matrix to quaternion transformation
#	User	Rev	Content
1	gezelter	2204	/*
2	gezelter	1930	* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3	tim	1563	*
4	gezelter	1930	* 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	tim	1563	*/
41	gezelter	1930
42	tim	1563	/**
43			* @file SquareMatrix3.hpp
44			* @author Teng Lin
45			* @date 10/11/2004
46			* @version 1.0
47			*/
48	gezelter	2204	#ifndef MATH_SQUAREMATRIX3_HPP
49	tim	1592	#define MATH_SQUAREMATRIX3_HPP
50	tim	1563
51	tim	1586	#include "Quaternion.hpp"
52	tim	1563	#include "SquareMatrix.hpp"
53	tim	1586	#include "Vector3.hpp"
54	tim	2146	#include "utils/NumericConstant.hpp"
55	tim	1563	namespace oopse {
56
57	gezelter	2204	template<typename Real>
58			class SquareMatrix3 : public SquareMatrix<Real, 3> {
59			public:
60	tim	1630
61	gezelter	2204	typedef Real ElemType;
62			typedef Real* ElemPoinerType;
63	tim	1563
64	gezelter	2204	/** default constructor */
65			SquareMatrix3() : SquareMatrix<Real, 3>() {
66			}
67	tim	1563
68	gezelter	2204	/** Constructs and initializes every element of this matrix to a scalar */
69			SquareMatrix3(Real s) : SquareMatrix<Real,3>(s){
70			}
71	tim	1644
72	gezelter	2204	/** Constructs and initializes from an array */
73			SquareMatrix3(Real* array) : SquareMatrix<Real,3>(array){
74			}
75	tim	1644
76
77	gezelter	2204	/** copy constructor */
78			SquareMatrix3(const SquareMatrix<Real, 3>& m) : SquareMatrix<Real, 3>(m) {
79			}
80	gezelter	1930
81	gezelter	2204	SquareMatrix3( const Vector3<Real>& eulerAngles) {
82			setupRotMat(eulerAngles);
83			}
84	tim	1586
85	gezelter	2204	SquareMatrix3(Real phi, Real theta, Real psi) {
86			setupRotMat(phi, theta, psi);
87			}
88	tim	1586
89	gezelter	2204	SquareMatrix3(const Quaternion<Real>& q) {
90			setupRotMat(q);
91	tim	1606
92	gezelter	2204	}
93	tim	1586
94	gezelter	2204	SquareMatrix3(Real w, Real x, Real y, Real z) {
95			setupRotMat(w, x, y, z);
96			}
97	tim	1586
98	gezelter	2204	/** 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	tim	1569
106	gezelter	1930
107	gezelter	2204	SquareMatrix3<Real>& operator =(const Quaternion<Real>& q) {
108			this->setupRotMat(q);
109			return *this;
110			}
111	gezelter	1930
112	gezelter	2204	/**
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	tim	1569
120	gezelter	2204	/**
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	tim	1569
130	gezelter	2204	sphi = sin(phi);
131			stheta = sin(theta);
132			spsi = sin(psi);
133			cphi = cos(phi);
134			ctheta = cos(theta);
135			cpsi = cos(psi);
136	tim	1569
137	gezelter	2204	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	tim	1586
141	gezelter	2204	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	tim	1586
145	gezelter	2204	this->data_[2][0] = stheta * sphi;
146			this->data_[2][1] = -stheta * cphi;
147			this->data_[2][2] = ctheta;
148			}
149	tim	1586
150
151	gezelter	2204	/**
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	tim	1569
159	gezelter	2204	/**
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	tim	1569
171	gezelter	2204	/**
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	tim	1569
182	tim	2336	if( t > NumericConstant::epsilon ){
183	tim	1586
184	gezelter	2204	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	tim	1586
191	tim	2332	ad1 = this->data_[0][0];
192			ad2 = this->data_[1][1];
193			ad3 = this->data_[2][2];
194	tim	1586
195	gezelter	2204	if( ad1 >= ad2 && ad1 >= ad3 ){
196	tim	1586
197	gezelter	2204	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	tim	1586
210	gezelter	2204	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	tim	1586
218	gezelter	2204	return q;
219	tim	1586
220	gezelter	2204	}
221	tim	1586
222	gezelter	2204	/**
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	tim	1586
240	gezelter	2204	// set the tolerance for Euler angles and rotation elements
241	tim	1586
242	gezelter	2204	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	tim	1586
246	gezelter	2204	// 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	tim	1586
254	gezelter	2204	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	tim	1586
264	gezelter	2204	//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	tim	1586
268	gezelter	2204	if (psi < 0)
269			psi += M_PI;
270	tim	1586
271	gezelter	2204	myEuler[0] = phi;
272			myEuler[1] = theta;
273			myEuler[2] = psi;
274	tim	1586
275	gezelter	2204	return myEuler;
276			}
277	tim	1563
278	gezelter	2204	/** Returns the determinant of this matrix. */
279			Real determinant() const {
280			Real x,y,z;
281	tim	1594
282	gezelter	2204	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	tim	1594
286	gezelter	2204	return(x + y + z);
287			}
288	gezelter	1930
289	gezelter	2204	/** 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	tim	1594
294	gezelter	2204	/**
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	tim	1563
307	gezelter	2204	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	tim	1594
317	gezelter	2204	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	tim	1569
336	tim	1616	Program: Visualization Toolkit
337			Module: $RCSfile: SquareMatrix3.hpp,v $
338	tim	1592
339	tim	1616	Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
340			All rights reserved.
341			See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
342	tim	1594
343	gezelter	2204	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	tim	1594
347	gezelter	2204	=========================================================================*/
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	tim	1594
355	gezelter	2204	// 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	tim	1594
363	gezelter	2204	// transpose temporarily, it makes it easier to sort the eigenvectors
364			v = v.transpose();
365	tim	1616
366	gezelter	2204	// 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	tim	1616
380	gezelter	2204	// 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	tim	1594
386	gezelter	2204	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	tim	1594
395	gezelter	2204	// re-orthogonalize the other two eigenvectors
396			j = (maxI+1)%3;
397			k = (maxI+2)%3;
398	tim	1594
399	gezelter	2204	v(j, 0) = 0.0;
400			v(j, 1) = 0.0;
401			v(j, 2) = 0.0;
402			v(j, j) = 1.0;
403	tim	1594
404	gezelter	2204	/** @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	tim	1594
413
414	gezelter	2204	// transpose vectors back to columns
415			v = v.transpose();
416			return;
417			}
418			}
419	tim	1594
420	gezelter	2204	// the three eigenvalues are different, just sort the eigenvectors
421			// to align them with the x, y, and z axes
422	tim	1594
423	gezelter	2204	// 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	tim	1594
434	gezelter	2204	// 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	tim	1594
449	gezelter	2204	// 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	tim	1563
458	gezelter	2204	// 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	tim	1616	}
464	gezelter	1930
465	gezelter	2204	// transpose the eigenvectors back again
466			v = v.transpose();
467			return ;
468			}
469	gezelter	1930
470	gezelter	2204	/**
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	gezelter	1930
480	gezelter	2204	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	gezelter	1930
485	gezelter	2204	return result;
486			}
487	gezelter	1930
488	gezelter	2204	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	gezelter	1930
498	gezelter	2204	return result;
499			}
500	gezelter	1930
501
502	gezelter	2204	typedef SquareMatrix3<double> Mat3x3d;
503			typedef SquareMatrix3<double> RotMat3x3d;
504	tim	1586
505			} //namespace oopse
506			#endif // MATH_SQUAREMATRIX_HPP
507	tim	1616