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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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* 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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* non-exclusive, royalty free, license to use, modify and |
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* redistribute this software in source and binary code form, provided |
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* that the following conditions are met: |
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* |
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* 1. Acknowledgement of the program authors must be made in any |
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* publication of scientific results based in part on use of the |
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* program. An acceptable form of acknowledgement is citation of |
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* the article in which the program was described (Matthew |
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* A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher |
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* J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented |
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* Parallel Simulation Engine for Molecular Dynamics," |
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* J. Comput. Chem. 26, pp. 252-271 (2005)) |
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* |
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* 2. Redistributions of source code must retain the above copyright |
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* notice, this list of conditions and the following disclaimer. |
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* |
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* 3. Redistributions in binary form must reproduce the above copyright |
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* notice, this list of conditions and the following disclaimer in the |
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* documentation and/or other materials provided with the |
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* distribution. |
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* |
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* This software is provided "AS IS," without a warranty of any |
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* kind. All express or implied conditions, representations and |
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* warranties, including any implied warranty of merchantability, |
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* fitness for a particular purpose or non-infringement, are hereby |
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* excluded. The University of Notre Dame and its licensors shall not |
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* be liable for any damages suffered by licensee as a result of |
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* using, modifying or distributing the software or its |
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* derivatives. In no event will the University of Notre Dame or its |
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* licensors be liable for any lost revenue, profit or data, or for |
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* direct, indirect, special, consequential, incidental or punitive |
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* damages, however caused and regardless of the theory of liability, |
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* arising out of the use of or inability to use software, even if the |
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* University of Notre Dame has been advised of the possibility of |
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* such damages. |
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*/ |
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/** |
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* @file Quaternion.hpp |
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* @author Teng Lin |
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#define MATH_QUATERNION_HPP |
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#include "math/Vector.hpp" |
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#include "math/SquareMatrix.hpp" |
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namespace oopse{ |
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template<typename Real> |
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class Quaternion : public Vector<Real, 4> { |
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public: |
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Quaternion(); |
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Quaternion() : Vector<Real, 4>() {} |
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/** Constructs and initializes a Quaternion from w, x, y, z values */ |
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Quaternion(Real w, Real x, Real y, Real z) { |
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data_[3] = z; |
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} |
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/** |
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* |
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*/ |
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/** Constructs and initializes a Quaternion from a Vector<Real,4> */ |
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Quaternion(const Vector<Real,4>& v) |
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: Vector<Real, 4>(v){ |
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} |
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/** */ |
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/** copy assignment */ |
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Quaternion& operator =(const Vector<Real, 4>& v){ |
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if (this == & v) |
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return *this; |
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} |
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/** |
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* Tests if this quaternion is equal to other quaternion |
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* @return true if equal, otherwise return false |
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* @param q quaternion to be compared |
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*/ |
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inline bool operator ==(const Quaternion<Real>& q) { |
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|
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for (unsigned int i = 0; i < 4; i ++) { |
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if (!equal(data_[i], q[i])) { |
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return false; |
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} |
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} |
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|
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return true; |
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} |
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|
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/** |
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* Returns the inverse of this quaternion |
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* @return inverse |
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* @note since quaternion is a complex number, the inverse of quaternion |
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* q = w + xi + yj+ zk is inv_q = (w -xi - yj - zk)/(|q|^2) |
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*/ |
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Quaternion<Real> inverse(){ |
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Quaternion<Real> inverse() { |
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Quaternion<Real> q; |
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Real d = this->lengthSquared(); |
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Real d = this->lengthSquare(); |
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q.w() = w() / d; |
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q.x() = -x() / d; |
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* @param q the other quaternion |
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*/ |
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void mul(const Quaternion<Real>& q) { |
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Quaternion<Real> tmp(*this); |
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Real a0( (z() - y()) * (q.y() - q.z()) ); |
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Real a1( (w() + x()) * (q.w() + q.x()) ); |
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Real a2( (w() - x()) * (q.y() + q.z()) ); |
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Real a3( (y() + z()) * (q.w() - q.x()) ); |
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Real b0( -(x() - z()) * (q.x() - q.y()) ); |
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Real b1( -(x() + z()) * (q.x() + q.y()) ); |
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Real b2( (w() + y()) * (q.w() - q.z()) ); |
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Real b3( (w() - y()) * (q.w() + q.z()) ); |
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data_[0] = (tmp[0]*q[0]) -(tmp[1]*q[1]) - (tmp[2]*q[2]) - (tmp[3]*q[3]); |
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data_[1] = (tmp[0]*q[1]) + (tmp[1]*q[0]) + (tmp[2]*q[3]) - (tmp[3]*q[2]); |
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data_[2] = (tmp[0]*q[2]) + (tmp[2]*q[0]) + (tmp[3]*q[1]) - (tmp[1]*q[3]); |
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data_[3] = (tmp[0]*q[3]) + (tmp[3]*q[0]) + (tmp[1]*q[2]) - (tmp[2]*q[1]); |
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} |
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data_[0] = a0 + 0.5*(b0 + b1 + b2 + b3),; |
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data_[1] = a1 + 0.5*(b0 + b1 - b2 - b3); |
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data_[2] = a2 + 0.5*(b0 - b1 + b2 - b3), |
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data_[3] = a3 + 0.5*(b0 - b1 - b2 + b3) ); |
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void mul(const Real& s) { |
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data_[0] *= s; |
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data_[1] *= s; |
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data_[2] *= s; |
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data_[3] *= s; |
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} |
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/** Set the value of this quaternion to the division of itself by another quaternion */ |
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void div(const Quaternion<Real>& q) { |
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void div(Quaternion<Real>& q) { |
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mul(q.inverse()); |
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} |
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|
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void div(const Real& s) { |
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data_[0] /= s; |
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data_[1] /= s; |
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data_[2] /= s; |
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data_[3] /= s; |
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} |
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Quaternion<Real>& operator *=(const Quaternion<Real>& q) { |
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mul(q); |
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return *this; |
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} |
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Quaternion<Real>& operator /=(const Quaternion<Real>& q) { |
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mul(q.inverse()); |
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Quaternion<Real>& operator *=(const Real& s) { |
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mul(s); |
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return *this; |
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} |
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Quaternion<Real>& operator /=(Quaternion<Real>& q) { |
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*this *= q.inverse(); |
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return *this; |
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} |
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|
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Quaternion<Real>& operator /=(const Real& s) { |
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div(s); |
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return *this; |
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} |
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/** |
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* Returns the conjugate quaternion of this quaternion |
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* @return the conjugate quaternion of this quaternion |
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* Returns the corresponding rotation matrix (3x3) |
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* @return a 3x3 rotation matrix |
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*/ |
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SquareMatrix<Real, 3, 3> toRotationMatrix3() { |
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SquareMatrix<Real, 3, 3> rotMat3; |
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SquareMatrix<Real, 3> toRotationMatrix3() { |
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SquareMatrix<Real, 3> rotMat3; |
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Real w2; |
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Real x2; |
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rotMat3(2, 0) = 2.0 * ( x() * z() + w() * y() ); |
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rotMat3(2, 1) = 2.0 * ( y() * z() - w() * x() ); |
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rotMat3(2, 2) = w2 - x2 -y2 +z2; |
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return rotMat3; |
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} |
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};//end Quaternion |
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|
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/** |
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* Returns the vaule of scalar multiplication of this quaterion q (q * s). |
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* @return the vaule of scalar multiplication of this vector |
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* @param q the source quaternion |
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* @param s the scalar value |
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*/ |
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template<typename Real, unsigned int Dim> |
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Quaternion<Real> operator * ( const Quaternion<Real>& q, Real s) { |
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Quaternion<Real> result(q); |
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result.mul(s); |
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return result; |
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} |
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|
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/** |
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* Returns the vaule of scalar multiplication of this quaterion q (q * s). |
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* @return the vaule of scalar multiplication of this vector |
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* @param s the scalar value |
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* @param q the source quaternion |
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*/ |
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template<typename Real, unsigned int Dim> |
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Quaternion<Real> operator * ( const Real& s, const Quaternion<Real>& q ) { |
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Quaternion<Real> result(q); |
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result.mul(s); |
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return result; |
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} |
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|
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/** |
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* Returns the multiplication of two quaternion |
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* @return the multiplication of two quaternion |
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* @param q1 the first quaternion |
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*/ |
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template<typename Real> |
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inline Quaternion<Real> operator /(const Quaternion<Real>& q1, const Quaternion<Real>& q2) { |
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inline Quaternion<Real> operator /( Quaternion<Real>& q1, Quaternion<Real>& q2) { |
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return q1 * q2.inverse(); |
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} |
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* @note for a quaternion q, 1/q = q.inverse() |
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*/ |
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template<typename Real> |
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Quaternion<Real> operator /(const Quaternion<Real>& s, const Quaternion<Real>& q) { |
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Quaternion<Real> operator /(const Real& s, Quaternion<Real>& q) { |
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|
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Quaternion<Real> x = q.inv(); |
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return x * s; |
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Quaternion<Real> x; |
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x = q.inverse(); |
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x *= s; |
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return x; |
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} |
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template <class T> |
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inline bool operator==(const Quaternion<T>& lhs, const Quaternion<T>& rhs) { |
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return equal(lhs[0] ,rhs[0]) && equal(lhs[1] , rhs[1]) && equal(lhs[2], rhs[2]) && equal(lhs[3], rhs[3]); |
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} |
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|
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typedef Quaternion<double> Quat4d; |
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} |
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#endif //MATH_QUATERNION_HPP |