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1 < /*
2 < * Copyright (C) 2000-2004  Object Oriented Parallel Simulation Engine (OOPSE) project
3 < *
4 < * Contact: oopse@oopse.org
5 < *
6 < * This program is free software; you can redistribute it and/or
7 < * modify it under the terms of the GNU Lesser General Public License
8 < * as published by the Free Software Foundation; either version 2.1
9 < * of the License, or (at your option) any later version.
10 < * All we ask is that proper credit is given for our work, which includes
11 < * - but is not limited to - adding the above copyright notice to the beginning
12 < * of your source code files, and to any copyright notice that you may distribute
13 < * with programs based on this work.
14 < *
15 < * This program is distributed in the hope that it will be useful,
16 < * but WITHOUT ANY WARRANTY; without even the implied warranty of
17 < * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
18 < * GNU Lesser General Public License for more details.
19 < *
20 < * You should have received a copy of the GNU Lesser General Public License
21 < * along with this program; if not, write to the Free Software
22 < * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
1 > /*
2 > * Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3   *
4 + * The University of Notre Dame grants you ("Licensee") a
5 + * non-exclusive, royalty free, license to use, modify and
6 + * redistribute this software in source and binary code form, provided
7 + * that the following conditions are met:
8 + *
9 + * 1. Acknowledgement of the program authors must be made in any
10 + *    publication of scientific results based in part on use of the
11 + *    program.  An acceptable form of acknowledgement is citation of
12 + *    the article in which the program was described (Matthew
13 + *    A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
14 + *    J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
15 + *    Parallel Simulation Engine for Molecular Dynamics,"
16 + *    J. Comput. Chem. 26, pp. 252-271 (2005))
17 + *
18 + * 2. Redistributions of source code must retain the above copyright
19 + *    notice, this list of conditions and the following disclaimer.
20 + *
21 + * 3. Redistributions in binary form must reproduce the above copyright
22 + *    notice, this list of conditions and the following disclaimer in the
23 + *    documentation and/or other materials provided with the
24 + *    distribution.
25 + *
26 + * This software is provided "AS IS," without a warranty of any
27 + * kind. All express or implied conditions, representations and
28 + * warranties, including any implied warranty of merchantability,
29 + * fitness for a particular purpose or non-infringement, are hereby
30 + * excluded.  The University of Notre Dame and its licensors shall not
31 + * be liable for any damages suffered by licensee as a result of
32 + * using, modifying or distributing the software or its
33 + * derivatives. In no event will the University of Notre Dame or its
34 + * licensors be liable for any lost revenue, profit or data, or for
35 + * direct, indirect, special, consequential, incidental or punitive
36 + * damages, however caused and regardless of the theory of liability,
37 + * arising out of the use of or inability to use software, even if the
38 + * University of Notre Dame has been advised of the possibility of
39 + * such damages.
40   */
41 <
41 >
42   /**
43   * @file Quaternion.hpp
44   * @author Teng Lin
# Line 33 | Line 49
49   #ifndef MATH_QUATERNION_HPP
50   #define MATH_QUATERNION_HPP
51  
52 + #include "math/Vector.hpp"
53 + #include "math/SquareMatrix.hpp"
54 +
55   namespace oopse{
56  
57      /**
58       * @class Quaternion Quaternion.hpp "math/Quaternion.hpp"
59 <     * @brief
59 >     * Quaternion is a sort of a higher-level complex number.
60 >     * It is defined as Q = w + x*i + y*j + z*k,
61 >     * where w, x, y, and z are numbers of type T (e.g. double), and
62 >     * i*i = -1; j*j = -1; k*k = -1;
63 >     * i*j = k; j*k = i; k*i = j;
64       */
65      template<typename Real>
66      class Quaternion : public Vector<Real, 4> {
67 +        public:
68 +            Quaternion() : Vector<Real, 4>() {}
69  
70 <    };
70 >            /** Constructs and initializes a Quaternion from w, x, y, z values */    
71 >            Quaternion(Real w, Real x, Real y, Real z) {
72 >                this->data_[0] = w;
73 >                this->data_[1] = x;
74 >                this->data_[2] = y;
75 >                this->data_[3] = z;                
76 >            }
77 >            
78 >            /** Constructs and initializes a Quaternion from a  Vector<Real,4> */    
79 >            Quaternion(const Vector<Real,4>& v)
80 >                : Vector<Real, 4>(v){
81 >            }
82  
83 +            /** copy assignment */
84 +            Quaternion& operator =(const Vector<Real, 4>& v){
85 +                if (this == & v)
86 +                    return *this;
87 +
88 +                Vector<Real, 4>::operator=(v);
89 +                
90 +                return *this;
91 +            }
92 +
93 +            /**
94 +             * Returns the value of the first element of this quaternion.
95 +             * @return the value of the first element of this quaternion
96 +             */
97 +            Real w() const {
98 +                return this->data_[0];
99 +            }
100 +
101 +            /**
102 +             * Returns the reference of the first element of this quaternion.
103 +             * @return the reference of the first element of this quaternion
104 +             */
105 +            Real& w() {
106 +                return this->data_[0];    
107 +            }
108 +
109 +            /**
110 +             * Returns the value of the first element of this quaternion.
111 +             * @return the value of the first element of this quaternion
112 +             */
113 +            Real x() const {
114 +                return this->data_[1];
115 +            }
116 +
117 +            /**
118 +             * Returns the reference of the second element of this quaternion.
119 +             * @return the reference of the second element of this quaternion
120 +             */
121 +            Real& x() {
122 +                return this->data_[1];    
123 +            }
124 +
125 +            /**
126 +             * Returns the value of the thirf element of this quaternion.
127 +             * @return the value of the third element of this quaternion
128 +             */
129 +            Real y() const {
130 +                return this->data_[2];
131 +            }
132 +
133 +            /**
134 +             * Returns the reference of the third element of this quaternion.
135 +             * @return the reference of the third element of this quaternion
136 +             */          
137 +            Real& y() {
138 +                return this->data_[2];    
139 +            }
140 +
141 +            /**
142 +             * Returns the value of the fourth element of this quaternion.
143 +             * @return the value of the fourth element of this quaternion
144 +             */
145 +            Real z() const {
146 +                return this->data_[3];
147 +            }
148 +            /**
149 +             * Returns the reference of the fourth element of this quaternion.
150 +             * @return the reference of the fourth element of this quaternion
151 +             */
152 +            Real& z() {
153 +                return this->data_[3];    
154 +            }
155 +
156 +            /**
157 +             * Tests if this quaternion is equal to other quaternion
158 +             * @return true if equal, otherwise return false
159 +             * @param q quaternion to be compared
160 +             */
161 +             inline bool operator ==(const Quaternion<Real>& q) {
162 +
163 +                for (unsigned int i = 0; i < 4; i ++) {
164 +                    if (!equal(this->data_[i], q[i])) {
165 +                        return false;
166 +                    }
167 +                }
168 +                
169 +                return true;
170 +            }
171 +            
172 +            /**
173 +             * Returns the inverse of this quaternion
174 +             * @return inverse
175 +             * @note since quaternion is a complex number, the inverse of quaternion
176 +             * q = w + xi + yj+ zk is inv_q = (w -xi - yj - zk)/(|q|^2)
177 +             */
178 +            Quaternion<Real> inverse() {
179 +                Quaternion<Real> q;
180 +                Real d = this->lengthSquare();
181 +                
182 +                q.w() = w() / d;
183 +                q.x() = -x() / d;
184 +                q.y() = -y() / d;
185 +                q.z() = -z() / d;
186 +                
187 +                return q;
188 +            }
189 +
190 +            /**
191 +             * Sets the value to the multiplication of itself and another quaternion
192 +             * @param q the other quaternion
193 +             */
194 +            void mul(const Quaternion<Real>& q) {
195 +                Quaternion<Real> tmp(*this);
196 +
197 +                this->data_[0] = (tmp[0]*q[0]) -(tmp[1]*q[1]) - (tmp[2]*q[2]) - (tmp[3]*q[3]);
198 +                this->data_[1] = (tmp[0]*q[1]) + (tmp[1]*q[0]) + (tmp[2]*q[3]) - (tmp[3]*q[2]);
199 +                this->data_[2] = (tmp[0]*q[2]) + (tmp[2]*q[0]) + (tmp[3]*q[1]) - (tmp[1]*q[3]);
200 +                this->data_[3] = (tmp[0]*q[3]) + (tmp[3]*q[0]) + (tmp[1]*q[2]) - (tmp[2]*q[1]);                
201 +            }
202 +
203 +            void mul(const Real& s) {
204 +                this->data_[0] *= s;
205 +                this->data_[1] *= s;
206 +                this->data_[2] *= s;
207 +                this->data_[3] *= s;
208 +            }
209 +
210 +            /** 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 +
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;
225 +            }
226 +
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 +            }
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 +            }
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;
255 +
256 +                Real w2;
257 +                Real x2;
258 +                Real y2;
259 +                Real z2;
260 +
261 +                if (!this->isNormalized())
262 +                    this->normalize();
263 +                
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() );
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() );
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;
280 +
281 +                return rotMat3;
282 +            }
283 +
284 +    };//end Quaternion
285 +
286 +
287 +    /**
288 +     * Returns the vaule of scalar multiplication of this quaterion q (q * s).
289 +     * @return  the vaule of scalar multiplication of this vector
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 +    }
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 +    }    
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 +    }
325 +
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 +    }
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) {
346 +
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 +    }
357 +    
358 +    typedef Quaternion<double> Quat4d;
359   }
360   #endif //MATH_QUATERNION_HPP

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