--- trunk/OOPSE-2.0/src/math/SquareMatrix3.hpp 2005/03/29 21:00:54 2146 +++ trunk/OOPSE-2.0/src/math/SquareMatrix3.hpp 2005/04/15 22:04:00 2204 @@ -1,4 +1,4 @@ - /* +/* * Copyright (c) 2005 The University of Notre Dame. All Rights Reserved. * * The University of Notre Dame grants you ("Licensee") a @@ -45,7 +45,7 @@ * @date 10/11/2004 * @version 1.0 */ - #ifndef MATH_SQUAREMATRIX3_HPP +#ifndef MATH_SQUAREMATRIX3_HPP #define MATH_SQUAREMATRIX3_HPP #include "Quaternion.hpp" @@ -54,284 +54,284 @@ namespace oopse { #include "utils/NumericConstant.hpp" namespace oopse { - template - class SquareMatrix3 : public SquareMatrix { - public: + template + class SquareMatrix3 : public SquareMatrix { + public: - typedef Real ElemType; - typedef Real* ElemPoinerType; + typedef Real ElemType; + typedef Real* ElemPoinerType; - /** default constructor */ - SquareMatrix3() : SquareMatrix() { - } + /** default constructor */ + SquareMatrix3() : SquareMatrix() { + } - /** Constructs and initializes every element of this matrix to a scalar */ - SquareMatrix3(Real s) : SquareMatrix(s){ - } + /** Constructs and initializes every element of this matrix to a scalar */ + SquareMatrix3(Real s) : SquareMatrix(s){ + } - /** Constructs and initializes from an array */ - SquareMatrix3(Real* array) : SquareMatrix(array){ - } + /** Constructs and initializes from an array */ + SquareMatrix3(Real* array) : SquareMatrix(array){ + } - /** copy constructor */ - SquareMatrix3(const SquareMatrix& m) : SquareMatrix(m) { - } + /** copy constructor */ + SquareMatrix3(const SquareMatrix& m) : SquareMatrix(m) { + } - SquareMatrix3( const Vector3& eulerAngles) { - setupRotMat(eulerAngles); - } + SquareMatrix3( const Vector3& eulerAngles) { + setupRotMat(eulerAngles); + } - SquareMatrix3(Real phi, Real theta, Real psi) { - setupRotMat(phi, theta, psi); - } + SquareMatrix3(Real phi, Real theta, Real psi) { + setupRotMat(phi, theta, psi); + } - SquareMatrix3(const Quaternion& q) { - setupRotMat(q); + SquareMatrix3(const Quaternion& q) { + setupRotMat(q); - } + } - SquareMatrix3(Real w, Real x, Real y, Real z) { - setupRotMat(w, x, y, z); - } + SquareMatrix3(Real w, Real x, Real y, Real z) { + setupRotMat(w, x, y, z); + } - /** copy assignment operator */ - SquareMatrix3& operator =(const SquareMatrix& m) { - if (this == &m) - return *this; - SquareMatrix::operator=(m); - return *this; - } + /** copy assignment operator */ + SquareMatrix3& operator =(const SquareMatrix& m) { + if (this == &m) + return *this; + SquareMatrix::operator=(m); + return *this; + } - SquareMatrix3& operator =(const Quaternion& q) { - this->setupRotMat(q); - return *this; - } + SquareMatrix3& operator =(const Quaternion& q) { + this->setupRotMat(q); + return *this; + } - /** - * Sets this matrix to a rotation matrix by three euler angles - * @ param euler - */ - void setupRotMat(const Vector3& eulerAngles) { - setupRotMat(eulerAngles[0], eulerAngles[1], eulerAngles[2]); - } + /** + * Sets this matrix to a rotation matrix by three euler angles + * @ param euler + */ + void setupRotMat(const Vector3& 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; + /** + * 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); + 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_[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_[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; - } + 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& quat) { - setupRotMat(quat.w(), quat.x(), quat.y(), quat.z()); - } + /** + * Sets this matrix to a rotation matrix by quaternion + * @param quat + */ + void setupRotMat(const Quaternion& 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 q(w, x, y, z); - *this = q.toRotationMatrix3(); - } + /** + * 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 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 toQuaternion() { - Quaternion q; - Real t, s; - Real ad1, ad2, ad3; - t = this->data_[0][0] + this->data_[1][1] + this->data_[2][2] + 1.0; + /** + * Returns the quaternion from this rotation matrix + * @return the quaternion from this rotation matrix + * @exception invalid rotation matrix + */ + Quaternion toQuaternion() { + Quaternion 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 ){ + 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 { + 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 = fabs( this->data_[0][0] ); - ad2 = fabs( this->data_[1][1] ); - ad3 = fabs( this->data_[2][2] ); + ad1 = fabs( this->data_[0][0] ); + ad2 = fabs( this->data_[1][1] ); + ad3 = fabs( this->data_[2][2] ); - if( ad1 >= ad2 && ad1 >= ad3 ){ + 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_[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; - } - } + 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; + 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 toEulerAngles() { - Vector3 myEuler; - Real phi; - Real theta; - Real psi; - Real ctheta; - Real stheta; + /** + * 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 toEulerAngles() { + Vector3 myEuler; + Real phi; + Real theta; + Real psi; + Real ctheta; + Real stheta; - // set the tolerance for Euler angles and rotation elements + // 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); + 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. + // 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]); - } + 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; + //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; + if (psi < 0) + psi += M_PI; - myEuler[0] = phi; - myEuler[1] = theta; - myEuler[2] = psi; + myEuler[0] = phi; + myEuler[1] = theta; + myEuler[2] = psi; - return myEuler; - } + return myEuler; + } - /** Returns the determinant of this matrix. */ - Real determinant() const { - Real x,y,z; + /** 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]); + 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); - } + 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]; - } + /** 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 inverse() const { - SquareMatrix3 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."); - } + /** + * 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 inverse() const { + SquareMatrix3 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(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& a, Vector3& w, SquareMatrix3& v); - }; -/*========================================================================= + 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& a, Vector3& w, SquareMatrix3& v); + }; + /*========================================================================= Program: Visualization Toolkit Module: $RCSfile: SquareMatrix3.hpp,v $ @@ -340,167 +340,167 @@ namespace oopse { 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. + 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 - void SquareMatrix3::diagonalize(SquareMatrix3& a, Vector3& w, - SquareMatrix3& v) { - int i,j,k,maxI; - Real tmp, maxVal; - Vector3 v_maxI, v_k, v_j; + =========================================================================*/ + template + void SquareMatrix3::diagonalize(SquareMatrix3& a, Vector3& w, + SquareMatrix3& v) { + int i,j,k,maxI; + Real tmp, maxVal; + Vector3 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::identity(); - return; - } + // 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::identity(); + return; + } - // transpose temporarily, it makes it easier to sort the eigenvectors - v = v.transpose(); + // 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; - } - } + // 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; + // 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); - } + 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; + // 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; + 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); + /** @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; - } - } + // 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 + // 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; - } - } + // 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); - } + // 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); - } - } + // 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 ; + // 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); } - /** - * 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 - inline SquareMatrix3 operator *(const SquareMatrix3& m1, const SquareMatrix3& m2) { - SquareMatrix3 result; + // transpose the eigenvectors back again + v = v.transpose(); + return ; + } - 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 the multiplication of two matrixes (m1 * m2). + * @return the multiplication of two matrixes + * @param m1 the first matrix + * @param m2 the second matrix + */ + template + inline SquareMatrix3 operator *(const SquareMatrix3& m1, const SquareMatrix3& m2) { + SquareMatrix3 result; - return 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); - template - inline SquareMatrix3 outProduct(const Vector3& v1, const Vector3& v2) { - SquareMatrix3 result; + return 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; + template + inline SquareMatrix3 outProduct(const Vector3& v1, const Vector3& v2) { + SquareMatrix3 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 Mat3x3d; - typedef SquareMatrix3 RotMat3x3d; + typedef SquareMatrix3 Mat3x3d; + typedef SquareMatrix3 RotMat3x3d; } //namespace oopse #endif // MATH_SQUAREMATRIX_HPP