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/* |
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/* |
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* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved. |
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* |
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* The University of Notre Dame grants you ("Licensee") a |
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* @date 10/11/2004 |
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* @version 1.0 |
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*/ |
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#ifndef MATH_SQUAREMATRIX3_HPP |
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#ifndef MATH_SQUAREMATRIX3_HPP |
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#define MATH_SQUAREMATRIX3_HPP |
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|
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#include <vector> |
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#include "Quaternion.hpp" |
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#include "SquareMatrix.hpp" |
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#include "Vector3.hpp" |
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#include "utils/NumericConstant.hpp" |
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namespace oopse { |
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|
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template<typename Real> |
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class SquareMatrix3 : public SquareMatrix<Real, 3> { |
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public: |
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template<typename Real> |
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class SquareMatrix3 : public SquareMatrix<Real, 3> { |
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public: |
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|
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typedef Real ElemType; |
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typedef Real* ElemPoinerType; |
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typedef Real ElemType; |
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typedef Real* ElemPoinerType; |
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|
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/** default constructor */ |
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SquareMatrix3() : SquareMatrix<Real, 3>() { |
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} |
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/** default constructor */ |
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SquareMatrix3() : SquareMatrix<Real, 3>() { |
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} |
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|
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/** Constructs and initializes every element of this matrix to a scalar */ |
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SquareMatrix3(Real s) : SquareMatrix<Real,3>(s){ |
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} |
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/** Constructs and initializes every element of this matrix to a scalar */ |
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SquareMatrix3(Real s) : SquareMatrix<Real,3>(s){ |
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} |
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|
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/** Constructs and initializes from an array */ |
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SquareMatrix3(Real* array) : SquareMatrix<Real,3>(array){ |
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} |
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/** Constructs and initializes from an array */ |
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SquareMatrix3(Real* array) : SquareMatrix<Real,3>(array){ |
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} |
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|
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|
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/** copy constructor */ |
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SquareMatrix3(const SquareMatrix<Real, 3>& m) : SquareMatrix<Real, 3>(m) { |
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} |
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/** copy constructor */ |
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SquareMatrix3(const SquareMatrix<Real, 3>& m) : SquareMatrix<Real, 3>(m) { |
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} |
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|
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SquareMatrix3( const Vector3<Real>& eulerAngles) { |
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setupRotMat(eulerAngles); |
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} |
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SquareMatrix3( const Vector3<Real>& eulerAngles) { |
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setupRotMat(eulerAngles); |
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} |
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|
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SquareMatrix3(Real phi, Real theta, Real psi) { |
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setupRotMat(phi, theta, psi); |
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} |
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SquareMatrix3(Real phi, Real theta, Real psi) { |
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setupRotMat(phi, theta, psi); |
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} |
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|
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SquareMatrix3(const Quaternion<Real>& q) { |
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setupRotMat(q); |
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SquareMatrix3(const Quaternion<Real>& q) { |
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setupRotMat(q); |
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|
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} |
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} |
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SquareMatrix3(Real w, Real x, Real y, Real z) { |
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setupRotMat(w, x, y, z); |
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} |
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SquareMatrix3(Real w, Real x, Real y, Real z) { |
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setupRotMat(w, x, y, z); |
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} |
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|
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/** copy assignment operator */ |
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SquareMatrix3<Real>& operator =(const SquareMatrix<Real, 3>& m) { |
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if (this == &m) |
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return *this; |
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SquareMatrix<Real, 3>::operator=(m); |
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return *this; |
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} |
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/** copy assignment operator */ |
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SquareMatrix3<Real>& operator =(const SquareMatrix<Real, 3>& m) { |
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if (this == &m) |
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return *this; |
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SquareMatrix<Real, 3>::operator=(m); |
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return *this; |
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} |
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SquareMatrix3<Real>& operator =(const Quaternion<Real>& q) { |
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this->setupRotMat(q); |
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return *this; |
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} |
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SquareMatrix3<Real>& operator =(const Quaternion<Real>& q) { |
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this->setupRotMat(q); |
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return *this; |
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} |
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|
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/** |
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* Sets this matrix to a rotation matrix by three euler angles |
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* @ param euler |
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*/ |
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void setupRotMat(const Vector3<Real>& eulerAngles) { |
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setupRotMat(eulerAngles[0], eulerAngles[1], eulerAngles[2]); |
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} |
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/** |
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* Sets this matrix to a rotation matrix by three euler angles |
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* @ param euler |
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*/ |
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void setupRotMat(const Vector3<Real>& eulerAngles) { |
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setupRotMat(eulerAngles[0], eulerAngles[1], eulerAngles[2]); |
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} |
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|
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/** |
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* Sets this matrix to a rotation matrix by three euler angles |
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* @param phi |
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* @param theta |
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* @psi theta |
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*/ |
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void setupRotMat(Real phi, Real theta, Real psi) { |
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Real sphi, stheta, spsi; |
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Real cphi, ctheta, cpsi; |
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/** |
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* Sets this matrix to a rotation matrix by three euler angles |
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* @param phi |
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* @param theta |
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* @psi theta |
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*/ |
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void setupRotMat(Real phi, Real theta, Real psi) { |
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Real sphi, stheta, spsi; |
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Real cphi, ctheta, cpsi; |
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sphi = sin(phi); |
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stheta = sin(theta); |
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spsi = sin(psi); |
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cphi = cos(phi); |
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ctheta = cos(theta); |
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cpsi = cos(psi); |
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sphi = sin(phi); |
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stheta = sin(theta); |
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spsi = sin(psi); |
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cphi = cos(phi); |
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ctheta = cos(theta); |
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cpsi = cos(psi); |
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|
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this->data_[0][0] = cpsi * cphi - ctheta * sphi * spsi; |
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this->data_[0][1] = cpsi * sphi + ctheta * cphi * spsi; |
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this->data_[0][2] = spsi * stheta; |
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this->data_[0][0] = cpsi * cphi - ctheta * sphi * spsi; |
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this->data_[0][1] = cpsi * sphi + ctheta * cphi * spsi; |
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this->data_[0][2] = spsi * stheta; |
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this->data_[1][0] = -spsi * ctheta - ctheta * sphi * cpsi; |
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this->data_[1][1] = -spsi * stheta + ctheta * cphi * cpsi; |
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this->data_[1][2] = cpsi * stheta; |
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this->data_[1][0] = -spsi * ctheta - ctheta * sphi * cpsi; |
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this->data_[1][1] = -spsi * stheta + ctheta * cphi * cpsi; |
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this->data_[1][2] = cpsi * stheta; |
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this->data_[2][0] = stheta * sphi; |
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this->data_[2][1] = -stheta * cphi; |
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this->data_[2][2] = ctheta; |
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} |
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this->data_[2][0] = stheta * sphi; |
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this->data_[2][1] = -stheta * cphi; |
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this->data_[2][2] = ctheta; |
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} |
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|
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/** |
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* Sets this matrix to a rotation matrix by quaternion |
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* @param quat |
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*/ |
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void setupRotMat(const Quaternion<Real>& quat) { |
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setupRotMat(quat.w(), quat.x(), quat.y(), quat.z()); |
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} |
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/** |
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* Sets this matrix to a rotation matrix by quaternion |
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* @param quat |
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*/ |
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void setupRotMat(const Quaternion<Real>& quat) { |
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setupRotMat(quat.w(), quat.x(), quat.y(), quat.z()); |
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} |
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|
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/** |
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* Sets this matrix to a rotation matrix by quaternion |
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* @param w the first element |
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* @param x the second element |
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* @param y the third element |
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* @param z the fourth element |
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*/ |
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void setupRotMat(Real w, Real x, Real y, Real z) { |
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Quaternion<Real> q(w, x, y, z); |
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*this = q.toRotationMatrix3(); |
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} |
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/** |
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* Sets this matrix to a rotation matrix by quaternion |
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* @param w the first element |
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* @param x the second element |
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* @param y the third element |
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* @param z the fourth element |
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*/ |
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void setupRotMat(Real w, Real x, Real y, Real z) { |
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Quaternion<Real> q(w, x, y, z); |
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*this = q.toRotationMatrix3(); |
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} |
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/** |
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* Returns the quaternion from this rotation matrix |
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* @return the quaternion from this rotation matrix |
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* @exception invalid rotation matrix |
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*/ |
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Quaternion<Real> toQuaternion() { |
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Quaternion<Real> q; |
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Real t, s; |
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Real ad1, ad2, ad3; |
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t = this->data_[0][0] + this->data_[1][1] + this->data_[2][2] + 1.0; |
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void setupSkewMat(Vector3<Real> v) { |
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setupSkewMat(v[0], v[1], v[2]); |
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} |
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if( t > NumericConstant::epsilon ){ |
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void setupSkewMat(Real v1, Real v2, Real v3) { |
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this->data_[0][0] = 0; |
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this->data_[0][1] = -v3; |
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this->data_[0][2] = v2; |
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this->data_[1][0] = v3; |
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this->data_[1][1] = 0; |
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this->data_[1][2] = -v1; |
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this->data_[2][0] = -v2; |
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this->data_[2][1] = v1; |
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this->data_[2][2] = 0; |
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|
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|
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} |
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s = 0.5 / sqrt( t ); |
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q[0] = 0.25 / s; |
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q[1] = (this->data_[1][2] - this->data_[2][1]) * s; |
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q[2] = (this->data_[2][0] - this->data_[0][2]) * s; |
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q[3] = (this->data_[0][1] - this->data_[1][0]) * s; |
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} else { |
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ad1 = fabs( this->data_[0][0] ); |
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ad2 = fabs( this->data_[1][1] ); |
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ad3 = fabs( this->data_[2][2] ); |
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if( ad1 >= ad2 && ad1 >= ad3 ){ |
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/** |
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* Returns the quaternion from this rotation matrix |
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* @return the quaternion from this rotation matrix |
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* @exception invalid rotation matrix |
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*/ |
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Quaternion<Real> toQuaternion() { |
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Quaternion<Real> q; |
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Real t, s; |
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Real ad1, ad2, ad3; |
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t = this->data_[0][0] + this->data_[1][1] + this->data_[2][2] + 1.0; |
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s = 0.5 / sqrt( 1.0 + this->data_[0][0] - this->data_[1][1] - this->data_[2][2] ); |
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q[0] = (this->data_[1][2] - this->data_[2][1]) * s; |
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q[1] = 0.25 / s; |
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q[2] = (this->data_[0][1] + this->data_[1][0]) * s; |
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q[3] = (this->data_[0][2] + this->data_[2][0]) * s; |
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} else if ( ad2 >= ad1 && ad2 >= ad3 ) { |
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s = 0.5 / sqrt( 1.0 + this->data_[1][1] - this->data_[0][0] - this->data_[2][2] ); |
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q[0] = (this->data_[2][0] - this->data_[0][2] ) * s; |
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q[1] = (this->data_[0][1] + this->data_[1][0]) * s; |
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q[2] = 0.25 / s; |
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q[3] = (this->data_[1][2] + this->data_[2][1]) * s; |
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} else { |
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if( t > NumericConstant::epsilon ){ |
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|
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s = 0.5 / sqrt( 1.0 + this->data_[2][2] - this->data_[0][0] - this->data_[1][1] ); |
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q[0] = (this->data_[0][1] - this->data_[1][0]) * s; |
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q[1] = (this->data_[0][2] + this->data_[2][0]) * s; |
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q[2] = (this->data_[1][2] + this->data_[2][1]) * s; |
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q[3] = 0.25 / s; |
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} |
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} |
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s = 0.5 / sqrt( t ); |
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q[0] = 0.25 / s; |
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q[1] = (this->data_[1][2] - this->data_[2][1]) * s; |
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q[2] = (this->data_[2][0] - this->data_[0][2]) * s; |
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q[3] = (this->data_[0][1] - this->data_[1][0]) * s; |
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} else { |
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return q; |
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ad1 = this->data_[0][0]; |
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ad2 = this->data_[1][1]; |
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ad3 = this->data_[2][2]; |
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|
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if( ad1 >= ad2 && ad1 >= ad3 ){ |
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|
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s = 0.5 / sqrt( 1.0 + this->data_[0][0] - this->data_[1][1] - this->data_[2][2] ); |
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q[0] = (this->data_[1][2] - this->data_[2][1]) * s; |
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q[1] = 0.25 / s; |
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q[2] = (this->data_[0][1] + this->data_[1][0]) * s; |
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q[3] = (this->data_[0][2] + this->data_[2][0]) * s; |
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} else if ( ad2 >= ad1 && ad2 >= ad3 ) { |
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s = 0.5 / sqrt( 1.0 + this->data_[1][1] - this->data_[0][0] - this->data_[2][2] ); |
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q[0] = (this->data_[2][0] - this->data_[0][2] ) * s; |
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q[1] = (this->data_[0][1] + this->data_[1][0]) * s; |
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q[2] = 0.25 / s; |
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q[3] = (this->data_[1][2] + this->data_[2][1]) * s; |
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} else { |
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|
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s = 0.5 / sqrt( 1.0 + this->data_[2][2] - this->data_[0][0] - this->data_[1][1] ); |
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q[0] = (this->data_[0][1] - this->data_[1][0]) * s; |
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q[1] = (this->data_[0][2] + this->data_[2][0]) * s; |
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q[2] = (this->data_[1][2] + this->data_[2][1]) * s; |
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q[3] = 0.25 / s; |
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} |
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} |
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|
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return q; |
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|
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} |
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} |
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|
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/** |
243 |
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* Returns the euler angles from this rotation matrix |
244 |
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* @return the euler angles in a vector |
245 |
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* @exception invalid rotation matrix |
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* We use so-called "x-convention", which is the most common definition. |
247 |
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* In this convention, the rotation given by Euler angles (phi, theta, psi), where the first |
248 |
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* rotation is by an angle phi about the z-axis, the second is by an angle |
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* theta (0 <= theta <= 180)about the x-axis, and thethird is by an angle psi about the |
250 |
< |
* z-axis (again). |
251 |
< |
*/ |
252 |
< |
Vector3<Real> toEulerAngles() { |
253 |
< |
Vector3<Real> myEuler; |
254 |
< |
Real phi; |
255 |
< |
Real theta; |
256 |
< |
Real psi; |
257 |
< |
Real ctheta; |
258 |
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Real stheta; |
242 |
> |
/** |
243 |
> |
* Returns the euler angles from this rotation matrix |
244 |
> |
* @return the euler angles in a vector |
245 |
> |
* @exception invalid rotation matrix |
246 |
> |
* We use so-called "x-convention", which is the most common definition. |
247 |
> |
* In this convention, the rotation given by Euler angles (phi, theta, psi), where the first |
248 |
> |
* rotation is by an angle phi about the z-axis, the second is by an angle |
249 |
> |
* theta (0 <= theta <= 180)about the x-axis, and thethird is by an angle psi about the |
250 |
> |
* z-axis (again). |
251 |
> |
*/ |
252 |
> |
Vector3<Real> toEulerAngles() { |
253 |
> |
Vector3<Real> myEuler; |
254 |
> |
Real phi; |
255 |
> |
Real theta; |
256 |
> |
Real psi; |
257 |
> |
Real ctheta; |
258 |
> |
Real stheta; |
259 |
|
|
260 |
< |
// set the tolerance for Euler angles and rotation elements |
260 |
> |
// set the tolerance for Euler angles and rotation elements |
261 |
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|
262 |
< |
theta = acos(std::min(1.0, std::max(-1.0,this->data_[2][2]))); |
263 |
< |
ctheta = this->data_[2][2]; |
264 |
< |
stheta = sqrt(1.0 - ctheta * ctheta); |
262 |
> |
theta = acos(std::min(1.0, std::max(-1.0,this->data_[2][2]))); |
263 |
> |
ctheta = this->data_[2][2]; |
264 |
> |
stheta = sqrt(1.0 - ctheta * ctheta); |
265 |
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|
266 |
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// when sin(theta) is close to 0, we need to consider singularity |
267 |
< |
// In this case, we can assign an arbitary value to phi (or psi), and then determine |
268 |
< |
// the psi (or phi) or vice-versa. We'll assume that phi always gets the rotation, and psi is 0 |
269 |
< |
// in cases of singularity. |
270 |
< |
// we use atan2 instead of atan, since atan2 will give us -Pi to Pi. |
271 |
< |
// Since 0 <= theta <= 180, sin(theta) will be always non-negative. Therefore, it never |
272 |
< |
// change the sign of both of the parameters passed to atan2. |
266 |
> |
// when sin(theta) is close to 0, we need to consider singularity |
267 |
> |
// In this case, we can assign an arbitary value to phi (or psi), and then determine |
268 |
> |
// the psi (or phi) or vice-versa. We'll assume that phi always gets the rotation, and psi is 0 |
269 |
> |
// in cases of singularity. |
270 |
> |
// we use atan2 instead of atan, since atan2 will give us -Pi to Pi. |
271 |
> |
// Since 0 <= theta <= 180, sin(theta) will be always non-negative. Therefore, it never |
272 |
> |
// change the sign of both of the parameters passed to atan2. |
273 |
|
|
274 |
< |
if (fabs(stheta) <= oopse::epsilon){ |
275 |
< |
psi = 0.0; |
276 |
< |
phi = atan2(-this->data_[1][0], this->data_[0][0]); |
277 |
< |
} |
278 |
< |
// we only have one unique solution |
279 |
< |
else{ |
280 |
< |
phi = atan2(this->data_[2][0], -this->data_[2][1]); |
281 |
< |
psi = atan2(this->data_[0][2], this->data_[1][2]); |
282 |
< |
} |
274 |
> |
if (fabs(stheta) <= oopse::epsilon){ |
275 |
> |
psi = 0.0; |
276 |
> |
phi = atan2(-this->data_[1][0], this->data_[0][0]); |
277 |
> |
} |
278 |
> |
// we only have one unique solution |
279 |
> |
else{ |
280 |
> |
phi = atan2(this->data_[2][0], -this->data_[2][1]); |
281 |
> |
psi = atan2(this->data_[0][2], this->data_[1][2]); |
282 |
> |
} |
283 |
|
|
284 |
< |
//wrap phi and psi, make sure they are in the range from 0 to 2*Pi |
285 |
< |
if (phi < 0) |
286 |
< |
phi += M_PI; |
284 |
> |
//wrap phi and psi, make sure they are in the range from 0 to 2*Pi |
285 |
> |
if (phi < 0) |
286 |
> |
phi += M_PI; |
287 |
|
|
288 |
< |
if (psi < 0) |
289 |
< |
psi += M_PI; |
288 |
> |
if (psi < 0) |
289 |
> |
psi += M_PI; |
290 |
|
|
291 |
< |
myEuler[0] = phi; |
292 |
< |
myEuler[1] = theta; |
293 |
< |
myEuler[2] = psi; |
291 |
> |
myEuler[0] = phi; |
292 |
> |
myEuler[1] = theta; |
293 |
> |
myEuler[2] = psi; |
294 |
|
|
295 |
< |
return myEuler; |
296 |
< |
} |
295 |
> |
return myEuler; |
296 |
> |
} |
297 |
|
|
298 |
< |
/** Returns the determinant of this matrix. */ |
299 |
< |
Real determinant() const { |
300 |
< |
Real x,y,z; |
298 |
> |
/** Returns the determinant of this matrix. */ |
299 |
> |
Real determinant() const { |
300 |
> |
Real x,y,z; |
301 |
|
|
302 |
< |
x = this->data_[0][0] * (this->data_[1][1] * this->data_[2][2] - this->data_[1][2] * this->data_[2][1]); |
303 |
< |
y = this->data_[0][1] * (this->data_[1][2] * this->data_[2][0] - this->data_[1][0] * this->data_[2][2]); |
304 |
< |
z = this->data_[0][2] * (this->data_[1][0] * this->data_[2][1] - this->data_[1][1] * this->data_[2][0]); |
302 |
> |
x = this->data_[0][0] * (this->data_[1][1] * this->data_[2][2] - this->data_[1][2] * this->data_[2][1]); |
303 |
> |
y = this->data_[0][1] * (this->data_[1][2] * this->data_[2][0] - this->data_[1][0] * this->data_[2][2]); |
304 |
> |
z = this->data_[0][2] * (this->data_[1][0] * this->data_[2][1] - this->data_[1][1] * this->data_[2][0]); |
305 |
|
|
306 |
< |
return(x + y + z); |
307 |
< |
} |
306 |
> |
return(x + y + z); |
307 |
> |
} |
308 |
|
|
309 |
< |
/** Returns the trace of this matrix. */ |
310 |
< |
Real trace() const { |
311 |
< |
return this->data_[0][0] + this->data_[1][1] + this->data_[2][2]; |
312 |
< |
} |
309 |
> |
/** Returns the trace of this matrix. */ |
310 |
> |
Real trace() const { |
311 |
> |
return this->data_[0][0] + this->data_[1][1] + this->data_[2][2]; |
312 |
> |
} |
313 |
|
|
314 |
< |
/** |
315 |
< |
* Sets the value of this matrix to the inversion of itself. |
316 |
< |
* @note since simple algorithm can be applied to inverse the 3 by 3 matrix, we hide the |
317 |
< |
* implementation of inverse in SquareMatrix class |
318 |
< |
*/ |
319 |
< |
SquareMatrix3<Real> inverse() const { |
320 |
< |
SquareMatrix3<Real> m; |
321 |
< |
double det = determinant(); |
322 |
< |
if (fabs(det) <= oopse::epsilon) { |
323 |
< |
//"The method was called on a matrix with |determinant| <= 1e-6.", |
324 |
< |
//"This is a runtime or a programming error in your application."); |
325 |
< |
} |
314 |
> |
/** |
315 |
> |
* Sets the value of this matrix to the inversion of itself. |
316 |
> |
* @note since simple algorithm can be applied to inverse the 3 by 3 matrix, we hide the |
317 |
> |
* implementation of inverse in SquareMatrix class |
318 |
> |
*/ |
319 |
> |
SquareMatrix3<Real> inverse() const { |
320 |
> |
SquareMatrix3<Real> m; |
321 |
> |
double det = determinant(); |
322 |
> |
if (fabs(det) <= oopse::epsilon) { |
323 |
> |
//"The method was called on a matrix with |determinant| <= 1e-6.", |
324 |
> |
//"This is a runtime or a programming error in your application."); |
325 |
> |
std::vector<int> zeroDiagElementIndex; |
326 |
> |
for (int i =0; i < 3; ++i) { |
327 |
> |
if (fabs(this->data_[i][i]) <= oopse::epsilon) { |
328 |
> |
zeroDiagElementIndex.push_back(i); |
329 |
> |
} |
330 |
> |
} |
331 |
|
|
332 |
< |
m(0, 0) = this->data_[1][1]*this->data_[2][2] - this->data_[1][2]*this->data_[2][1]; |
333 |
< |
m(1, 0) = this->data_[1][2]*this->data_[2][0] - this->data_[1][0]*this->data_[2][2]; |
334 |
< |
m(2, 0) = this->data_[1][0]*this->data_[2][1] - this->data_[1][1]*this->data_[2][0]; |
335 |
< |
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]; |
332 |
> |
if (zeroDiagElementIndex.size() == 2) { |
333 |
> |
int index = zeroDiagElementIndex[0]; |
334 |
> |
m(index, index) = 1.0 / this->data_[index][index]; |
335 |
> |
}else if (zeroDiagElementIndex.size() == 1) { |
336 |
|
|
337 |
< |
m /= det; |
338 |
< |
return m; |
337 |
> |
int a = (zeroDiagElementIndex[0] + 1) % 3; |
338 |
> |
int b = (zeroDiagElementIndex[0] + 2) %3; |
339 |
> |
double denom = this->data_[a][a] * this->data_[b][b] - this->data_[b][a]*this->data_[a][b]; |
340 |
> |
m(a, a) = this->data_[b][b] /denom; |
341 |
> |
m(b, a) = -this->data_[b][a]/denom; |
342 |
> |
|
343 |
> |
m(a,b) = -this->data_[a][b]/denom; |
344 |
> |
m(b, b) = this->data_[a][a]/denom; |
345 |
> |
|
346 |
> |
} |
347 |
> |
|
348 |
> |
/* |
349 |
> |
for(std::vector<int>::iterator iter = zeroDiagElementIndex.begin(); iter != zeroDiagElementIndex.end() ++iter) { |
350 |
> |
if (this->data_[*iter][0] > oopse::epsilon || this->data_[*iter][1] ||this->data_[*iter][2] || |
351 |
> |
this->data_[0][*iter] > oopse::epsilon || this->data_[1][*iter] ||this->data_[2][*iter] ) { |
352 |
> |
std::cout << "can not inverse matrix" << std::endl; |
353 |
|
} |
354 |
< |
/** |
355 |
< |
* Extract the eigenvalues and eigenvectors from a 3x3 matrix. |
356 |
< |
* 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 |
< |
/*========================================================================= |
354 |
> |
} |
355 |
> |
*/ |
356 |
> |
} else { |
357 |
|
|
358 |
+ |
m(0, 0) = this->data_[1][1]*this->data_[2][2] - this->data_[1][2]*this->data_[2][1]; |
359 |
+ |
m(1, 0) = this->data_[1][2]*this->data_[2][0] - this->data_[1][0]*this->data_[2][2]; |
360 |
+ |
m(2, 0) = this->data_[1][0]*this->data_[2][1] - this->data_[1][1]*this->data_[2][0]; |
361 |
+ |
m(0, 1) = this->data_[2][1]*this->data_[0][2] - this->data_[2][2]*this->data_[0][1]; |
362 |
+ |
m(1, 1) = this->data_[2][2]*this->data_[0][0] - this->data_[2][0]*this->data_[0][2]; |
363 |
+ |
m(2, 1) = this->data_[2][0]*this->data_[0][1] - this->data_[2][1]*this->data_[0][0]; |
364 |
+ |
m(0, 2) = this->data_[0][1]*this->data_[1][2] - this->data_[0][2]*this->data_[1][1]; |
365 |
+ |
m(1, 2) = this->data_[0][2]*this->data_[1][0] - this->data_[0][0]*this->data_[1][2]; |
366 |
+ |
m(2, 2) = this->data_[0][0]*this->data_[1][1] - this->data_[0][1]*this->data_[1][0]; |
367 |
+ |
|
368 |
+ |
m /= det; |
369 |
+ |
} |
370 |
+ |
return m; |
371 |
+ |
} |
372 |
+ |
|
373 |
+ |
SquareMatrix3<Real> transpose() const{ |
374 |
+ |
SquareMatrix3<Real> result; |
375 |
+ |
|
376 |
+ |
for (unsigned int i = 0; i < 3; i++) |
377 |
+ |
for (unsigned int j = 0; j < 3; j++) |
378 |
+ |
result(j, i) = this->data_[i][j]; |
379 |
+ |
|
380 |
+ |
return result; |
381 |
+ |
} |
382 |
+ |
/** |
383 |
+ |
* Extract the eigenvalues and eigenvectors from a 3x3 matrix. |
384 |
+ |
* The eigenvectors (the columns of V) will be normalized. |
385 |
+ |
* The eigenvectors are aligned optimally with the x, y, and z |
386 |
+ |
* axes respectively. |
387 |
+ |
* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is |
388 |
+ |
* overwritten |
389 |
+ |
* @param w will contain the eigenvalues of the matrix On return of this function |
390 |
+ |
* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are |
391 |
+ |
* normalized and mutually orthogonal. |
392 |
+ |
* @warning a will be overwritten |
393 |
+ |
*/ |
394 |
+ |
static void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v); |
395 |
+ |
}; |
396 |
+ |
/*========================================================================= |
397 |
+ |
|
398 |
|
Program: Visualization Toolkit |
399 |
|
Module: $RCSfile: SquareMatrix3.hpp,v $ |
400 |
|
|
402 |
|
All rights reserved. |
403 |
|
See Copyright.txt or http://www.kitware.com/Copyright.htm for details. |
404 |
|
|
405 |
< |
This software is distributed WITHOUT ANY WARRANTY; without even |
406 |
< |
the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR |
407 |
< |
PURPOSE. See the above copyright notice for more information. |
405 |
> |
This software is distributed WITHOUT ANY WARRANTY; without even |
406 |
> |
the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR |
407 |
> |
PURPOSE. See the above copyright notice for more information. |
408 |
|
|
409 |
< |
=========================================================================*/ |
410 |
< |
template<typename Real> |
411 |
< |
void SquareMatrix3<Real>::diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, |
412 |
< |
SquareMatrix3<Real>& v) { |
413 |
< |
int i,j,k,maxI; |
414 |
< |
Real tmp, maxVal; |
415 |
< |
Vector3<Real> v_maxI, v_k, v_j; |
409 |
> |
=========================================================================*/ |
410 |
> |
template<typename Real> |
411 |
> |
void SquareMatrix3<Real>::diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, |
412 |
> |
SquareMatrix3<Real>& v) { |
413 |
> |
int i,j,k,maxI; |
414 |
> |
Real tmp, maxVal; |
415 |
> |
Vector3<Real> v_maxI, v_k, v_j; |
416 |
|
|
417 |
< |
// diagonalize using Jacobi |
418 |
< |
jacobi(a, w, v); |
419 |
< |
// if all the eigenvalues are the same, return identity matrix |
420 |
< |
if (w[0] == w[1] && w[0] == w[2] ) { |
421 |
< |
v = SquareMatrix3<Real>::identity(); |
422 |
< |
return; |
423 |
< |
} |
417 |
> |
// diagonalize using Jacobi |
418 |
> |
jacobi(a, w, v); |
419 |
> |
// if all the eigenvalues are the same, return identity matrix |
420 |
> |
if (w[0] == w[1] && w[0] == w[2] ) { |
421 |
> |
v = SquareMatrix3<Real>::identity(); |
422 |
> |
return; |
423 |
> |
} |
424 |
|
|
425 |
< |
// transpose temporarily, it makes it easier to sort the eigenvectors |
426 |
< |
v = v.transpose(); |
425 |
> |
// transpose temporarily, it makes it easier to sort the eigenvectors |
426 |
> |
v = v.transpose(); |
427 |
|
|
428 |
< |
// if two eigenvalues are the same, re-orthogonalize to optimally line |
429 |
< |
// up the eigenvectors with the x, y, and z axes |
430 |
< |
for (i = 0; i < 3; i++) { |
431 |
< |
if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same |
432 |
< |
// find maximum element of the independant eigenvector |
433 |
< |
maxVal = fabs(v(i, 0)); |
434 |
< |
maxI = 0; |
435 |
< |
for (j = 1; j < 3; j++) { |
436 |
< |
if (maxVal < (tmp = fabs(v(i, j)))){ |
437 |
< |
maxVal = tmp; |
438 |
< |
maxI = j; |
439 |
< |
} |
440 |
< |
} |
428 |
> |
// if two eigenvalues are the same, re-orthogonalize to optimally line |
429 |
> |
// up the eigenvectors with the x, y, and z axes |
430 |
> |
for (i = 0; i < 3; i++) { |
431 |
> |
if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same |
432 |
> |
// find maximum element of the independant eigenvector |
433 |
> |
maxVal = fabs(v(i, 0)); |
434 |
> |
maxI = 0; |
435 |
> |
for (j = 1; j < 3; j++) { |
436 |
> |
if (maxVal < (tmp = fabs(v(i, j)))){ |
437 |
> |
maxVal = tmp; |
438 |
> |
maxI = j; |
439 |
> |
} |
440 |
> |
} |
441 |
|
|
442 |
< |
// swap the eigenvector into its proper position |
443 |
< |
if (maxI != i) { |
444 |
< |
tmp = w(maxI); |
445 |
< |
w(maxI) = w(i); |
446 |
< |
w(i) = tmp; |
442 |
> |
// swap the eigenvector into its proper position |
443 |
> |
if (maxI != i) { |
444 |
> |
tmp = w(maxI); |
445 |
> |
w(maxI) = w(i); |
446 |
> |
w(i) = tmp; |
447 |
|
|
448 |
< |
v.swapRow(i, maxI); |
449 |
< |
} |
450 |
< |
// maximum element of eigenvector should be positive |
451 |
< |
if (v(maxI, maxI) < 0) { |
452 |
< |
v(maxI, 0) = -v(maxI, 0); |
453 |
< |
v(maxI, 1) = -v(maxI, 1); |
454 |
< |
v(maxI, 2) = -v(maxI, 2); |
455 |
< |
} |
448 |
> |
v.swapRow(i, maxI); |
449 |
> |
} |
450 |
> |
// maximum element of eigenvector should be positive |
451 |
> |
if (v(maxI, maxI) < 0) { |
452 |
> |
v(maxI, 0) = -v(maxI, 0); |
453 |
> |
v(maxI, 1) = -v(maxI, 1); |
454 |
> |
v(maxI, 2) = -v(maxI, 2); |
455 |
> |
} |
456 |
|
|
457 |
< |
// re-orthogonalize the other two eigenvectors |
458 |
< |
j = (maxI+1)%3; |
459 |
< |
k = (maxI+2)%3; |
457 |
> |
// re-orthogonalize the other two eigenvectors |
458 |
> |
j = (maxI+1)%3; |
459 |
> |
k = (maxI+2)%3; |
460 |
|
|
461 |
< |
v(j, 0) = 0.0; |
462 |
< |
v(j, 1) = 0.0; |
463 |
< |
v(j, 2) = 0.0; |
464 |
< |
v(j, j) = 1.0; |
461 |
> |
v(j, 0) = 0.0; |
462 |
> |
v(j, 1) = 0.0; |
463 |
> |
v(j, 2) = 0.0; |
464 |
> |
v(j, j) = 1.0; |
465 |
|
|
466 |
< |
/** @todo */ |
467 |
< |
v_maxI = v.getRow(maxI); |
468 |
< |
v_j = v.getRow(j); |
469 |
< |
v_k = cross(v_maxI, v_j); |
470 |
< |
v_k.normalize(); |
471 |
< |
v_j = cross(v_k, v_maxI); |
472 |
< |
v.setRow(j, v_j); |
473 |
< |
v.setRow(k, v_k); |
466 |
> |
/** @todo */ |
467 |
> |
v_maxI = v.getRow(maxI); |
468 |
> |
v_j = v.getRow(j); |
469 |
> |
v_k = cross(v_maxI, v_j); |
470 |
> |
v_k.normalize(); |
471 |
> |
v_j = cross(v_k, v_maxI); |
472 |
> |
v.setRow(j, v_j); |
473 |
> |
v.setRow(k, v_k); |
474 |
|
|
475 |
|
|
476 |
< |
// transpose vectors back to columns |
477 |
< |
v = v.transpose(); |
478 |
< |
return; |
479 |
< |
} |
480 |
< |
} |
476 |
> |
// transpose vectors back to columns |
477 |
> |
v = v.transpose(); |
478 |
> |
return; |
479 |
> |
} |
480 |
> |
} |
481 |
|
|
482 |
< |
// the three eigenvalues are different, just sort the eigenvectors |
483 |
< |
// to align them with the x, y, and z axes |
482 |
> |
// the three eigenvalues are different, just sort the eigenvectors |
483 |
> |
// to align them with the x, y, and z axes |
484 |
|
|
485 |
< |
// find the vector with the largest x element, make that vector |
486 |
< |
// the first vector |
487 |
< |
maxVal = fabs(v(0, 0)); |
488 |
< |
maxI = 0; |
489 |
< |
for (i = 1; i < 3; i++) { |
490 |
< |
if (maxVal < (tmp = fabs(v(i, 0)))) { |
491 |
< |
maxVal = tmp; |
492 |
< |
maxI = i; |
493 |
< |
} |
494 |
< |
} |
485 |
> |
// find the vector with the largest x element, make that vector |
486 |
> |
// the first vector |
487 |
> |
maxVal = fabs(v(0, 0)); |
488 |
> |
maxI = 0; |
489 |
> |
for (i = 1; i < 3; i++) { |
490 |
> |
if (maxVal < (tmp = fabs(v(i, 0)))) { |
491 |
> |
maxVal = tmp; |
492 |
> |
maxI = i; |
493 |
> |
} |
494 |
> |
} |
495 |
|
|
496 |
< |
// swap eigenvalue and eigenvector |
497 |
< |
if (maxI != 0) { |
498 |
< |
tmp = w(maxI); |
499 |
< |
w(maxI) = w(0); |
500 |
< |
w(0) = tmp; |
501 |
< |
v.swapRow(maxI, 0); |
502 |
< |
} |
503 |
< |
// do the same for the y element |
504 |
< |
if (fabs(v(1, 1)) < fabs(v(2, 1))) { |
505 |
< |
tmp = w(2); |
506 |
< |
w(2) = w(1); |
507 |
< |
w(1) = tmp; |
508 |
< |
v.swapRow(2, 1); |
509 |
< |
} |
496 |
> |
// swap eigenvalue and eigenvector |
497 |
> |
if (maxI != 0) { |
498 |
> |
tmp = w(maxI); |
499 |
> |
w(maxI) = w(0); |
500 |
> |
w(0) = tmp; |
501 |
> |
v.swapRow(maxI, 0); |
502 |
> |
} |
503 |
> |
// do the same for the y element |
504 |
> |
if (fabs(v(1, 1)) < fabs(v(2, 1))) { |
505 |
> |
tmp = w(2); |
506 |
> |
w(2) = w(1); |
507 |
> |
w(1) = tmp; |
508 |
> |
v.swapRow(2, 1); |
509 |
> |
} |
510 |
|
|
511 |
< |
// ensure that the sign of the eigenvectors is correct |
512 |
< |
for (i = 0; i < 2; i++) { |
513 |
< |
if (v(i, i) < 0) { |
514 |
< |
v(i, 0) = -v(i, 0); |
515 |
< |
v(i, 1) = -v(i, 1); |
516 |
< |
v(i, 2) = -v(i, 2); |
517 |
< |
} |
518 |
< |
} |
511 |
> |
// ensure that the sign of the eigenvectors is correct |
512 |
> |
for (i = 0; i < 2; i++) { |
513 |
> |
if (v(i, i) < 0) { |
514 |
> |
v(i, 0) = -v(i, 0); |
515 |
> |
v(i, 1) = -v(i, 1); |
516 |
> |
v(i, 2) = -v(i, 2); |
517 |
> |
} |
518 |
> |
} |
519 |
|
|
520 |
< |
// set sign of final eigenvector to ensure that determinant is positive |
521 |
< |
if (v.determinant() < 0) { |
522 |
< |
v(2, 0) = -v(2, 0); |
523 |
< |
v(2, 1) = -v(2, 1); |
524 |
< |
v(2, 2) = -v(2, 2); |
463 |
< |
} |
464 |
< |
|
465 |
< |
// transpose the eigenvectors back again |
466 |
< |
v = v.transpose(); |
467 |
< |
return ; |
520 |
> |
// set sign of final eigenvector to ensure that determinant is positive |
521 |
> |
if (v.determinant() < 0) { |
522 |
> |
v(2, 0) = -v(2, 0); |
523 |
> |
v(2, 1) = -v(2, 1); |
524 |
> |
v(2, 2) = -v(2, 2); |
525 |
|
} |
526 |
|
|
527 |
< |
/** |
528 |
< |
* Return the multiplication of two matrixes (m1 * m2). |
529 |
< |
* @return the multiplication of two matrixes |
530 |
< |
* @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; |
527 |
> |
// transpose the eigenvectors back again |
528 |
> |
v = v.transpose(); |
529 |
> |
return ; |
530 |
> |
} |
531 |
|
|
532 |
< |
for (unsigned int i = 0; i < 3; i++) |
533 |
< |
for (unsigned int j = 0; j < 3; j++) |
534 |
< |
for (unsigned int k = 0; k < 3; k++) |
535 |
< |
result(i, j) += m1(i, k) * m2(k, j); |
532 |
> |
/** |
533 |
> |
* Return the multiplication of two matrixes (m1 * m2). |
534 |
> |
* @return the multiplication of two matrixes |
535 |
> |
* @param m1 the first matrix |
536 |
> |
* @param m2 the second matrix |
537 |
> |
*/ |
538 |
> |
template<typename Real> |
539 |
> |
inline SquareMatrix3<Real> operator *(const SquareMatrix3<Real>& m1, const SquareMatrix3<Real>& m2) { |
540 |
> |
SquareMatrix3<Real> result; |
541 |
|
|
542 |
< |
return result; |
543 |
< |
} |
542 |
> |
for (unsigned int i = 0; i < 3; i++) |
543 |
> |
for (unsigned int j = 0; j < 3; j++) |
544 |
> |
for (unsigned int k = 0; k < 3; k++) |
545 |
> |
result(i, j) += m1(i, k) * m2(k, j); |
546 |
|
|
547 |
< |
template<typename Real> |
548 |
< |
inline SquareMatrix3<Real> outProduct(const Vector3<Real>& v1, const Vector3<Real>& v2) { |
490 |
< |
SquareMatrix3<Real> result; |
547 |
> |
return result; |
548 |
> |
} |
549 |
|
|
550 |
< |
for (unsigned int i = 0; i < 3; i++) { |
551 |
< |
for (unsigned int j = 0; j < 3; j++) { |
552 |
< |
result(i, j) = v1[i] * v2[j]; |
553 |
< |
} |
554 |
< |
} |
555 |
< |
|
556 |
< |
return result; |
550 |
> |
template<typename Real> |
551 |
> |
inline SquareMatrix3<Real> outProduct(const Vector3<Real>& v1, const Vector3<Real>& v2) { |
552 |
> |
SquareMatrix3<Real> result; |
553 |
> |
|
554 |
> |
for (unsigned int i = 0; i < 3; i++) { |
555 |
> |
for (unsigned int j = 0; j < 3; j++) { |
556 |
> |
result(i, j) = v1[i] * v2[j]; |
557 |
> |
} |
558 |
|
} |
559 |
+ |
|
560 |
+ |
return result; |
561 |
+ |
} |
562 |
|
|
563 |
|
|
564 |
< |
typedef SquareMatrix3<double> Mat3x3d; |
565 |
< |
typedef SquareMatrix3<double> RotMat3x3d; |
564 |
> |
typedef SquareMatrix3<double> Mat3x3d; |
565 |
> |
typedef SquareMatrix3<double> RotMat3x3d; |
566 |
|
|
567 |
|
} //namespace oopse |
568 |
|
#endif // MATH_SQUAREMATRIX_HPP |