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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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* 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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/** |
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* @file Quaternion.hpp |
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* @author Teng Lin |
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namespace oopse{ |
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|
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/** |
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* @class Quaternion Quaternion.hpp "math/Quaternion.hpp" |
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* Quaternion is a sort of a higher-level complex number. |
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* It is defined as Q = w + x*i + y*j + z*k, |
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* where w, x, y, and z are numbers of type T (e.g. double), and |
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* i*i = -1; j*j = -1; k*k = -1; |
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* i*j = k; j*k = i; k*i = j; |
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*/ |
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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() : Vector<Real, 4>() {} |
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/** |
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* @class Quaternion Quaternion.hpp "math/Quaternion.hpp" |
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* Quaternion is a sort of a higher-level complex number. |
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* It is defined as Q = w + x*i + y*j + z*k, |
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* where w, x, y, and z are numbers of type T (e.g. RealType), and |
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* i*i = -1; j*j = -1; k*k = -1; |
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* i*j = k; j*k = i; k*i = j; |
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*/ |
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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() : Vector<Real, 4>() {} |
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|
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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_[0] = w; |
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data_[1] = x; |
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data_[2] = y; |
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data_[3] = z; |
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} |
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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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this->data_[0] = w; |
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this->data_[1] = x; |
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this->data_[2] = y; |
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this->data_[3] = z; |
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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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/** 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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/** 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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Vector<Real, 4>::operator=(v); |
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Vector<Real, 4>::operator=(v); |
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|
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return *this; |
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} |
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return *this; |
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} |
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|
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/** |
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* Returns the value of the first element of this quaternion. |
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* @return the value of the first element of this quaternion |
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*/ |
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Real w() const { |
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return data_[0]; |
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} |
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/** |
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* Returns the value of the first element of this quaternion. |
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* @return the value of the first element of this quaternion |
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*/ |
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Real w() const { |
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return this->data_[0]; |
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} |
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|
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/** |
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* Returns the reference of the first element of this quaternion. |
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* @return the reference of the first element of this quaternion |
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*/ |
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Real& w() { |
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return data_[0]; |
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} |
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/** |
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* Returns the reference of the first element of this quaternion. |
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* @return the reference of the first element of this quaternion |
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*/ |
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Real& w() { |
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return this->data_[0]; |
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} |
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|
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/** |
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* Returns the value of the first element of this quaternion. |
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* @return the value of the first element of this quaternion |
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*/ |
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Real x() const { |
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return data_[1]; |
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} |
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/** |
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* Returns the value of the first element of this quaternion. |
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* @return the value of the first element of this quaternion |
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*/ |
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Real x() const { |
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return this->data_[1]; |
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} |
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|
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/** |
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* Returns the reference of the second element of this quaternion. |
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* @return the reference of the second element of this quaternion |
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*/ |
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Real& x() { |
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return data_[1]; |
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} |
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/** |
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* Returns the reference of the second element of this quaternion. |
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* @return the reference of the second element of this quaternion |
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*/ |
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Real& x() { |
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return this->data_[1]; |
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} |
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|
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/** |
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* Returns the value of the thirf element of this quaternion. |
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* @return the value of the third element of this quaternion |
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*/ |
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Real y() const { |
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return data_[2]; |
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} |
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/** |
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* Returns the value of the thirf element of this quaternion. |
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* @return the value of the third element of this quaternion |
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*/ |
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Real y() const { |
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return this->data_[2]; |
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} |
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|
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/** |
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* Returns the reference of the third element of this quaternion. |
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* @return the reference of the third element of this quaternion |
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*/ |
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Real& y() { |
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return data_[2]; |
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} |
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/** |
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* Returns the reference of the third element of this quaternion. |
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* @return the reference of the third element of this quaternion |
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*/ |
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Real& y() { |
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return this->data_[2]; |
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} |
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|
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/** |
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* Returns the value of the fourth element of this quaternion. |
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* @return the value of the fourth element of this quaternion |
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*/ |
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Real z() const { |
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return data_[3]; |
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} |
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/** |
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* Returns the reference of the fourth element of this quaternion. |
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* @return the reference of the fourth element of this quaternion |
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*/ |
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Real& z() { |
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return data_[3]; |
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} |
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/** |
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* Returns the value of the fourth element of this quaternion. |
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* @return the value of the fourth element of this quaternion |
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*/ |
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Real z() const { |
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return this->data_[3]; |
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} |
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/** |
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* Returns the reference of the fourth element of this quaternion. |
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* @return the reference of the fourth element of this quaternion |
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*/ |
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Real& z() { |
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return this->data_[3]; |
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} |
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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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* 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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for (unsigned int i = 0; i < 4; i ++) { |
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if (!equal(this->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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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> q; |
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Real d = this->lengthSquare(); |
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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> q; |
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Real d = this->lengthSquare(); |
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|
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q.w() = w() / d; |
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q.x() = -x() / d; |
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q.y() = -y() / d; |
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q.z() = -z() / d; |
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q.w() = w() / d; |
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q.x() = -x() / d; |
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q.y() = -y() / d; |
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q.z() = -z() / d; |
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|
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return q; |
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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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* Sets the value to the multiplication of itself and another quaternion |
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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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|
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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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/** |
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* Sets the value to the multiplication of itself and another quaternion |
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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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|
|
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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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this->data_[0] = (tmp[0]*q[0]) -(tmp[1]*q[1]) - (tmp[2]*q[2]) - (tmp[3]*q[3]); |
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this->data_[1] = (tmp[0]*q[1]) + (tmp[1]*q[0]) + (tmp[2]*q[3]) - (tmp[3]*q[2]); |
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this->data_[2] = (tmp[0]*q[2]) + (tmp[2]*q[0]) + (tmp[3]*q[1]) - (tmp[1]*q[3]); |
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this->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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|
|
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/** Set the value of this quaternion to the division of itself by another quaternion */ |
204 |
< |
void div(Quaternion<Real>& q) { |
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mul(q.inverse()); |
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} |
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void mul(const Real& s) { |
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this->data_[0] *= s; |
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this->data_[1] *= s; |
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this->data_[2] *= s; |
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this->data_[3] *= s; |
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> |
} |
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|
|
210 |
< |
void div(const Real& s) { |
211 |
< |
data_[0] /= s; |
212 |
< |
data_[1] /= s; |
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< |
data_[2] /= s; |
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< |
data_[3] /= s; |
215 |
< |
} |
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/** Set the value of this quaternion to the division of itself by another quaternion */ |
211 |
> |
void div(Quaternion<Real>& q) { |
212 |
> |
mul(q.inverse()); |
213 |
> |
} |
214 |
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|
215 |
> |
void div(const Real& s) { |
216 |
> |
this->data_[0] /= s; |
217 |
> |
this->data_[1] /= s; |
218 |
> |
this->data_[2] /= s; |
219 |
> |
this->data_[3] /= s; |
220 |
> |
} |
221 |
|
|
222 |
< |
Quaternion<Real>& operator *=(const Quaternion<Real>& q) { |
223 |
< |
mul(q); |
224 |
< |
return *this; |
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< |
} |
222 |
> |
Quaternion<Real>& operator *=(const Quaternion<Real>& q) { |
223 |
> |
mul(q); |
224 |
> |
return *this; |
225 |
> |
} |
226 |
|
|
227 |
< |
Quaternion<Real>& operator *=(const Real& s) { |
228 |
< |
mul(s); |
229 |
< |
return *this; |
230 |
< |
} |
227 |
> |
Quaternion<Real>& operator *=(const Real& s) { |
228 |
> |
mul(s); |
229 |
> |
return *this; |
230 |
> |
} |
231 |
|
|
232 |
< |
Quaternion<Real>& operator /=(Quaternion<Real>& q) { |
233 |
< |
*this *= q.inverse(); |
234 |
< |
return *this; |
235 |
< |
} |
232 |
> |
Quaternion<Real>& operator /=(Quaternion<Real>& q) { |
233 |
> |
*this *= q.inverse(); |
234 |
> |
return *this; |
235 |
> |
} |
236 |
|
|
237 |
< |
Quaternion<Real>& operator /=(const Real& s) { |
238 |
< |
div(s); |
239 |
< |
return *this; |
240 |
< |
} |
241 |
< |
/** |
242 |
< |
* Returns the conjugate quaternion of this quaternion |
243 |
< |
* @return the conjugate quaternion of this quaternion |
244 |
< |
*/ |
245 |
< |
Quaternion<Real> conjugate() { |
246 |
< |
return Quaternion<Real>(w(), -x(), -y(), -z()); |
247 |
< |
} |
237 |
> |
Quaternion<Real>& operator /=(const Real& s) { |
238 |
> |
div(s); |
239 |
> |
return *this; |
240 |
> |
} |
241 |
> |
/** |
242 |
> |
* Returns the conjugate quaternion of this quaternion |
243 |
> |
* @return the conjugate quaternion of this quaternion |
244 |
> |
*/ |
245 |
> |
Quaternion<Real> conjugate() { |
246 |
> |
return Quaternion<Real>(w(), -x(), -y(), -z()); |
247 |
> |
} |
248 |
|
|
249 |
< |
/** |
250 |
< |
* Returns the corresponding rotation matrix (3x3) |
251 |
< |
* @return a 3x3 rotation matrix |
252 |
< |
*/ |
253 |
< |
SquareMatrix<Real, 3> toRotationMatrix3() { |
254 |
< |
SquareMatrix<Real, 3> rotMat3; |
249 |
> |
/** |
250 |
> |
* Returns the corresponding rotation matrix (3x3) |
251 |
> |
* @return a 3x3 rotation matrix |
252 |
> |
*/ |
253 |
> |
SquareMatrix<Real, 3> toRotationMatrix3() { |
254 |
> |
SquareMatrix<Real, 3> rotMat3; |
255 |
|
|
256 |
< |
Real w2; |
257 |
< |
Real x2; |
258 |
< |
Real y2; |
259 |
< |
Real z2; |
256 |
> |
Real w2; |
257 |
> |
Real x2; |
258 |
> |
Real y2; |
259 |
> |
Real z2; |
260 |
|
|
261 |
< |
if (!isNormalized()) |
262 |
< |
normalize(); |
261 |
> |
if (!this->isNormalized()) |
262 |
> |
this->normalize(); |
263 |
|
|
264 |
< |
w2 = w() * w(); |
265 |
< |
x2 = x() * x(); |
266 |
< |
y2 = y() * y(); |
267 |
< |
z2 = z() * z(); |
264 |
> |
w2 = w() * w(); |
265 |
> |
x2 = x() * x(); |
266 |
> |
y2 = y() * y(); |
267 |
> |
z2 = z() * z(); |
268 |
|
|
269 |
< |
rotMat3(0, 0) = w2 + x2 - y2 - z2; |
270 |
< |
rotMat3(0, 1) = 2.0 * ( x() * y() + w() * z() ); |
271 |
< |
rotMat3(0, 2) = 2.0 * ( x() * z() - w() * y() ); |
269 |
> |
rotMat3(0, 0) = w2 + x2 - y2 - z2; |
270 |
> |
rotMat3(0, 1) = 2.0 * ( x() * y() + w() * z() ); |
271 |
> |
rotMat3(0, 2) = 2.0 * ( x() * z() - w() * y() ); |
272 |
|
|
273 |
< |
rotMat3(1, 0) = 2.0 * ( x() * y() - w() * z() ); |
274 |
< |
rotMat3(1, 1) = w2 - x2 + y2 - z2; |
275 |
< |
rotMat3(1, 2) = 2.0 * ( y() * z() + w() * x() ); |
273 |
> |
rotMat3(1, 0) = 2.0 * ( x() * y() - w() * z() ); |
274 |
> |
rotMat3(1, 1) = w2 - x2 + y2 - z2; |
275 |
> |
rotMat3(1, 2) = 2.0 * ( y() * z() + w() * x() ); |
276 |
|
|
277 |
< |
rotMat3(2, 0) = 2.0 * ( x() * z() + w() * y() ); |
278 |
< |
rotMat3(2, 1) = 2.0 * ( y() * z() - w() * x() ); |
279 |
< |
rotMat3(2, 2) = w2 - x2 -y2 +z2; |
277 |
> |
rotMat3(2, 0) = 2.0 * ( x() * z() + w() * y() ); |
278 |
> |
rotMat3(2, 1) = 2.0 * ( y() * z() - w() * x() ); |
279 |
> |
rotMat3(2, 2) = w2 - x2 -y2 +z2; |
280 |
|
|
281 |
< |
return rotMat3; |
282 |
< |
} |
281 |
> |
return rotMat3; |
282 |
> |
} |
283 |
|
|
284 |
< |
};//end Quaternion |
284 |
> |
};//end Quaternion |
285 |
|
|
286 |
|
|
287 |
|
/** |
290 |
|
* @param q the source quaternion |
291 |
|
* @param s the scalar value |
292 |
|
*/ |
293 |
< |
template<typename Real, unsigned int Dim> |
294 |
< |
Quaternion<Real> operator * ( const Quaternion<Real>& q, Real s) { |
295 |
< |
Quaternion<Real> result(q); |
296 |
< |
result.mul(s); |
297 |
< |
return result; |
298 |
< |
} |
293 |
> |
template<typename Real, unsigned int Dim> |
294 |
> |
Quaternion<Real> operator * ( const Quaternion<Real>& q, Real s) { |
295 |
> |
Quaternion<Real> result(q); |
296 |
> |
result.mul(s); |
297 |
> |
return result; |
298 |
> |
} |
299 |
|
|
300 |
< |
/** |
301 |
< |
* Returns the vaule of scalar multiplication of this quaterion q (q * s). |
302 |
< |
* @return the vaule of scalar multiplication of this vector |
303 |
< |
* @param s the scalar value |
304 |
< |
* @param q the source quaternion |
305 |
< |
*/ |
306 |
< |
template<typename Real, unsigned int Dim> |
307 |
< |
Quaternion<Real> operator * ( const Real& s, const Quaternion<Real>& q ) { |
308 |
< |
Quaternion<Real> result(q); |
309 |
< |
result.mul(s); |
310 |
< |
return result; |
311 |
< |
} |
300 |
> |
/** |
301 |
> |
* Returns the vaule of scalar multiplication of this quaterion q (q * s). |
302 |
> |
* @return the vaule of scalar multiplication of this vector |
303 |
> |
* @param s the scalar value |
304 |
> |
* @param q the source quaternion |
305 |
> |
*/ |
306 |
> |
template<typename Real, unsigned int Dim> |
307 |
> |
Quaternion<Real> operator * ( const Real& s, const Quaternion<Real>& q ) { |
308 |
> |
Quaternion<Real> result(q); |
309 |
> |
result.mul(s); |
310 |
> |
return result; |
311 |
> |
} |
312 |
|
|
313 |
< |
/** |
314 |
< |
* Returns the multiplication of two quaternion |
315 |
< |
* @return the multiplication of two quaternion |
316 |
< |
* @param q1 the first quaternion |
317 |
< |
* @param q2 the second quaternion |
318 |
< |
*/ |
319 |
< |
template<typename Real> |
320 |
< |
inline Quaternion<Real> operator *(const Quaternion<Real>& q1, const Quaternion<Real>& q2) { |
321 |
< |
Quaternion<Real> result(q1); |
322 |
< |
result *= q2; |
323 |
< |
return result; |
324 |
< |
} |
313 |
> |
/** |
314 |
> |
* Returns the multiplication of two quaternion |
315 |
> |
* @return the multiplication of two quaternion |
316 |
> |
* @param q1 the first quaternion |
317 |
> |
* @param q2 the second quaternion |
318 |
> |
*/ |
319 |
> |
template<typename Real> |
320 |
> |
inline Quaternion<Real> operator *(const Quaternion<Real>& q1, const Quaternion<Real>& q2) { |
321 |
> |
Quaternion<Real> result(q1); |
322 |
> |
result *= q2; |
323 |
> |
return result; |
324 |
> |
} |
325 |
|
|
326 |
< |
/** |
327 |
< |
* Returns the division of two quaternion |
328 |
< |
* @param q1 divisor |
329 |
< |
* @param q2 dividen |
330 |
< |
*/ |
326 |
> |
/** |
327 |
> |
* Returns the division of two quaternion |
328 |
> |
* @param q1 divisor |
329 |
> |
* @param q2 dividen |
330 |
> |
*/ |
331 |
|
|
332 |
< |
template<typename Real> |
333 |
< |
inline Quaternion<Real> operator /( Quaternion<Real>& q1, Quaternion<Real>& q2) { |
334 |
< |
return q1 * q2.inverse(); |
335 |
< |
} |
332 |
> |
template<typename Real> |
333 |
> |
inline Quaternion<Real> operator /( Quaternion<Real>& q1, Quaternion<Real>& q2) { |
334 |
> |
return q1 * q2.inverse(); |
335 |
> |
} |
336 |
|
|
337 |
< |
/** |
338 |
< |
* Returns the value of the division of a scalar by a quaternion |
339 |
< |
* @return the value of the division of a scalar by a quaternion |
340 |
< |
* @param s scalar |
341 |
< |
* @param q quaternion |
342 |
< |
* @note for a quaternion q, 1/q = q.inverse() |
343 |
< |
*/ |
344 |
< |
template<typename Real> |
345 |
< |
Quaternion<Real> operator /(const Real& s, Quaternion<Real>& q) { |
337 |
> |
/** |
338 |
> |
* Returns the value of the division of a scalar by a quaternion |
339 |
> |
* @return the value of the division of a scalar by a quaternion |
340 |
> |
* @param s scalar |
341 |
> |
* @param q quaternion |
342 |
> |
* @note for a quaternion q, 1/q = q.inverse() |
343 |
> |
*/ |
344 |
> |
template<typename Real> |
345 |
> |
Quaternion<Real> operator /(const Real& s, Quaternion<Real>& q) { |
346 |
|
|
347 |
< |
Quaternion<Real> x; |
348 |
< |
x = q.inverse(); |
349 |
< |
x *= s; |
350 |
< |
return x; |
351 |
< |
} |
347 |
> |
Quaternion<Real> x; |
348 |
> |
x = q.inverse(); |
349 |
> |
x *= s; |
350 |
> |
return x; |
351 |
> |
} |
352 |
|
|
353 |
< |
template <class T> |
354 |
< |
inline bool operator==(const Quaternion<T>& lhs, const Quaternion<T>& rhs) { |
355 |
< |
return equal(lhs[0] ,rhs[0]) && equal(lhs[1] , rhs[1]) && equal(lhs[2], rhs[2]) && equal(lhs[3], rhs[3]); |
356 |
< |
} |
353 |
> |
template <class T> |
354 |
> |
inline bool operator==(const Quaternion<T>& lhs, const Quaternion<T>& rhs) { |
355 |
> |
return equal(lhs[0] ,rhs[0]) && equal(lhs[1] , rhs[1]) && equal(lhs[2], rhs[2]) && equal(lhs[3], rhs[3]); |
356 |
> |
} |
357 |
|
|
358 |
< |
typedef Quaternion<double> Quat4d; |
358 |
> |
typedef Quaternion<RealType> Quat4d; |
359 |
|
} |
360 |
|
#endif //MATH_QUATERNION_HPP |