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/* |
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* Copyright (C) 2000-2004 Object Oriented Parallel Simulation Engine (OOPSE) project |
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* |
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* Contact: oopse@oopse.org |
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* |
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* This program is free software; you can redistribute it and/or |
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* modify it under the terms of the GNU Lesser General Public License |
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* as published by the Free Software Foundation; either version 2.1 |
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* of the License, or (at your option) any later version. |
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* All we ask is that proper credit is given for our work, which includes |
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* - but is not limited to - adding the above copyright notice to the beginning |
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* of your source code files, and to any copyright notice that you may distribute |
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* with programs based on this work. |
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* |
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* This program is distributed in the hope that it will be useful, |
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* but WITHOUT ANY WARRANTY; without even the implied warranty of |
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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* GNU Lesser General Public License for more details. |
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* |
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* You should have received a copy of the GNU Lesser General Public License |
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* along with this program; if not, write to the Free Software |
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* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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* |
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*/ |
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|
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/** |
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* @file SquareMatrix3.hpp |
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* @author Teng Lin |
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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_SQUAREMATRIX_HPP |
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#define MATH_SQUAREMATRIX_HPP |
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|
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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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|
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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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|
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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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/** 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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|
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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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*this = q.toRotationMatrix3(); |
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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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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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/** 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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} |
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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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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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data_[0][0] = cpsi * cphi - ctheta * sphi * spsi; |
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data_[0][1] = cpsi * sphi + ctheta * cphi * spsi; |
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data_[0][2] = spsi * stheta; |
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|
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data_[1][0] = -spsi * ctheta - ctheta * sphi * cpsi; |
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data_[1][1] = -spsi * stheta + ctheta * cphi * cpsi; |
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data_[1][2] = cpsi * stheta; |
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|
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data_[2][0] = stheta * sphi; |
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data_[2][1] = -stheta * cphi; |
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data_[2][2] = ctheta; |
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} |
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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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*this = quat.toRotationMatrix3(); |
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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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* @parma 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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/** |
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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 = data_[0][0] + data_[1][1] + data_[2][2] + 1.0; |
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|
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if( t > 0.0 ){ |
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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] = (data_[1][2] - data_[2][1]) * s; |
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q[2] = (data_[2][0] - data_[0][2]) * s; |
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q[3] = (data_[0][1] - data_[1][0]) * s; |
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} else { |
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|
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ad1 = fabs( data_[0][0] ); |
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ad2 = fabs( data_[1][1] ); |
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ad3 = fabs( 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 = 2.0 * sqrt( 1.0 + data_[0][0] - data_[1][1] - data_[2][2] ); |
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q[0] = (data_[1][2] + data_[2][1]) / s; |
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q[1] = 0.5 / s; |
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q[2] = (data_[0][1] + data_[1][0]) / s; |
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q[3] = (data_[0][2] + data_[2][0]) / s; |
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} else if ( ad2 >= ad1 && ad2 >= ad3 ) { |
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s = sqrt( 1.0 + data_[1][1] - data_[0][0] - data_[2][2] ) * 2.0; |
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q[0] = (data_[0][2] + data_[2][0]) / s; |
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q[1] = (data_[0][1] + data_[1][0]) / s; |
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q[2] = 0.5 / s; |
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q[3] = (data_[1][2] + data_[2][1]) / s; |
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} else { |
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s = sqrt( 1.0 + data_[2][2] - data_[0][0] - data_[1][1] ) * 2.0; |
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q[0] = (data_[0][1] + data_[1][0]) / s; |
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q[1] = (data_[0][2] + data_[2][0]) / s; |
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q[2] = (data_[1][2] + data_[2][1]) / s; |
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q[3] = 0.5 / 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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* Returns the euler angles from this rotation matrix |
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* @return the euler angles in a vector |
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* @exception invalid rotation matrix |
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* We use so-called "x-convention", which is the most common definition. |
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* In this convention, the rotation given by Euler angles (phi, theta, psi), where the first |
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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 |
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* z-axis (again). |
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*/ |
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Vector3<Real> toEulerAngles() { |
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Vector<Real> myEuler; |
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Real phi,theta,psi,eps; |
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Real ctheta,stheta; |
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|
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// set the tolerance for Euler angles and rotation elements |
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|
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theta = acos(min(1.0,max(-1.0,data_[2][2]))); |
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ctheta = data_[2][2]; |
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stheta = sqrt(1.0 - ctheta * ctheta); |
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|
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// when sin(theta) is close to 0, we need to consider singularity |
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// In this case, we can assign an arbitary value to phi (or psi), and then determine |
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// the psi (or phi) or vice-versa. We'll assume that phi always gets the rotation, and psi is 0 |
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// in cases of singularity. |
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// we use atan2 instead of atan, since atan2 will give us -Pi to Pi. |
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// Since 0 <= theta <= 180, sin(theta) will be always non-negative. Therefore, it never |
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// change the sign of both of the parameters passed to atan2. |
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|
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if (fabs(stheta) <= oopse::epsilon){ |
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psi = 0.0; |
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phi = atan2(-data_[1][0], data_[0][0]); |
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} |
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// we only have one unique solution |
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else{ |
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phi = atan2(data_[2][0], -data_[2][1]); |
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psi = atan2(data_[0][2], data_[1][2]); |
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} |
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//wrap phi and psi, make sure they are in the range from 0 to 2*Pi |
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if (phi < 0) |
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phi += M_PI; |
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|
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if (psi < 0) |
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psi += M_PI; |
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|
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myEuler[0] = phi; |
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myEuler[1] = theta; |
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myEuler[2] = psi; |
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|
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return myEuler; |
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} |
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|
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/** |
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* Sets the value of this matrix to the inversion of itself. |
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* @note since simple algorithm can be applied to inverse the 3 by 3 matrix, we hide the |
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* implementation of inverse in SquareMatrix class |
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*/ |
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void inverse(); |
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|
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void diagonalize(); |
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|
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}; |
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|
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typedef template SquareMatrix3<double> Mat3x3d |
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typedef template SquareMatrix3<double> RotMat3x3d; |
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|
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} //namespace oopse |
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#endif // MATH_SQUAREMATRIX_HPP |
