| 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. |
| 23 |
* |
| 24 |
*/ |
| 25 |
|
| 26 |
/** |
| 27 |
* @file Quaternion.hpp |
| 28 |
* @author Teng Lin |
| 29 |
* @date 10/11/2004 |
| 30 |
* @version 1.0 |
| 31 |
*/ |
| 32 |
|
| 33 |
#ifndef MATH_QUATERNION_HPP |
| 34 |
#define MATH_QUATERNION_HPP |
| 35 |
|
| 36 |
#include "math/Vector.hpp" |
| 37 |
#include "math/SquareMatrix.hpp" |
| 38 |
|
| 39 |
namespace oopse{ |
| 40 |
|
| 41 |
/** |
| 42 |
* @class Quaternion Quaternion.hpp "math/Quaternion.hpp" |
| 43 |
* Quaternion is a sort of a higher-level complex number. |
| 44 |
* It is defined as Q = w + x*i + y*j + z*k, |
| 45 |
* where w, x, y, and z are numbers of type T (e.g. double), and |
| 46 |
* i*i = -1; j*j = -1; k*k = -1; |
| 47 |
* i*j = k; j*k = i; k*i = j; |
| 48 |
*/ |
| 49 |
template<typename Real> |
| 50 |
class Quaternion : public Vector<Real, 4> { |
| 51 |
public: |
| 52 |
Quaternion() : Vector<Real, 4>() {} |
| 53 |
|
| 54 |
/** Constructs and initializes a Quaternion from w, x, y, z values */ |
| 55 |
Quaternion(Real w, Real x, Real y, Real z) { |
| 56 |
data_[0] = w; |
| 57 |
data_[1] = x; |
| 58 |
data_[2] = y; |
| 59 |
data_[3] = z; |
| 60 |
} |
| 61 |
|
| 62 |
/** Constructs and initializes a Quaternion from a Vector<Real,4> */ |
| 63 |
Quaternion(const Vector<Real,4>& v) |
| 64 |
: Vector<Real, 4>(v){ |
| 65 |
} |
| 66 |
|
| 67 |
/** copy assignment */ |
| 68 |
Quaternion& operator =(const Vector<Real, 4>& v){ |
| 69 |
if (this == & v) |
| 70 |
return *this; |
| 71 |
|
| 72 |
Vector<Real, 4>::operator=(v); |
| 73 |
|
| 74 |
return *this; |
| 75 |
} |
| 76 |
|
| 77 |
/** |
| 78 |
* Returns the value of the first element of this quaternion. |
| 79 |
* @return the value of the first element of this quaternion |
| 80 |
*/ |
| 81 |
Real w() const { |
| 82 |
return data_[0]; |
| 83 |
} |
| 84 |
|
| 85 |
/** |
| 86 |
* Returns the reference of the first element of this quaternion. |
| 87 |
* @return the reference of the first element of this quaternion |
| 88 |
*/ |
| 89 |
Real& w() { |
| 90 |
return data_[0]; |
| 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 x() const { |
| 98 |
return data_[1]; |
| 99 |
} |
| 100 |
|
| 101 |
/** |
| 102 |
* Returns the reference of the second element of this quaternion. |
| 103 |
* @return the reference of the second element of this quaternion |
| 104 |
*/ |
| 105 |
Real& x() { |
| 106 |
return data_[1]; |
| 107 |
} |
| 108 |
|
| 109 |
/** |
| 110 |
* Returns the value of the thirf element of this quaternion. |
| 111 |
* @return the value of the third element of this quaternion |
| 112 |
*/ |
| 113 |
Real y() const { |
| 114 |
return data_[2]; |
| 115 |
} |
| 116 |
|
| 117 |
/** |
| 118 |
* Returns the reference of the third element of this quaternion. |
| 119 |
* @return the reference of the third element of this quaternion |
| 120 |
*/ |
| 121 |
Real& y() { |
| 122 |
return data_[2]; |
| 123 |
} |
| 124 |
|
| 125 |
/** |
| 126 |
* Returns the value of the fourth element of this quaternion. |
| 127 |
* @return the value of the fourth element of this quaternion |
| 128 |
*/ |
| 129 |
Real z() const { |
| 130 |
return data_[3]; |
| 131 |
} |
| 132 |
/** |
| 133 |
* Returns the reference of the fourth element of this quaternion. |
| 134 |
* @return the reference of the fourth element of this quaternion |
| 135 |
*/ |
| 136 |
Real& z() { |
| 137 |
return data_[3]; |
| 138 |
} |
| 139 |
|
| 140 |
/** |
| 141 |
* Tests if this quaternion is equal to other quaternion |
| 142 |
* @return true if equal, otherwise return false |
| 143 |
* @param q quaternion to be compared |
| 144 |
*/ |
| 145 |
inline bool operator ==(const Quaternion<Real>& q) { |
| 146 |
|
| 147 |
for (unsigned int i = 0; i < 4; i ++) { |
| 148 |
if (!equal(data_[i], q[i])) { |
| 149 |
return false; |
| 150 |
} |
| 151 |
} |
| 152 |
|
| 153 |
return true; |
| 154 |
} |
| 155 |
|
| 156 |
/** |
| 157 |
* Returns the inverse of this quaternion |
| 158 |
* @return inverse |
| 159 |
* @note since quaternion is a complex number, the inverse of quaternion |
| 160 |
* q = w + xi + yj+ zk is inv_q = (w -xi - yj - zk)/(|q|^2) |
| 161 |
*/ |
| 162 |
Quaternion<Real> inverse() { |
| 163 |
Quaternion<Real> q; |
| 164 |
Real d = this->lengthSquare(); |
| 165 |
|
| 166 |
q.w() = w() / d; |
| 167 |
q.x() = -x() / d; |
| 168 |
q.y() = -y() / d; |
| 169 |
q.z() = -z() / d; |
| 170 |
|
| 171 |
return q; |
| 172 |
} |
| 173 |
|
| 174 |
/** |
| 175 |
* Sets the value to the multiplication of itself and another quaternion |
| 176 |
* @param q the other quaternion |
| 177 |
*/ |
| 178 |
void mul(const Quaternion<Real>& q) { |
| 179 |
Quaternion<Real> tmp(*this); |
| 180 |
|
| 181 |
data_[0] = (tmp[0]*q[0]) -(tmp[1]*q[1]) - (tmp[2]*q[2]) - (tmp[3]*q[3]); |
| 182 |
data_[1] = (tmp[0]*q[1]) + (tmp[1]*q[0]) + (tmp[2]*q[3]) - (tmp[3]*q[2]); |
| 183 |
data_[2] = (tmp[0]*q[2]) + (tmp[2]*q[0]) + (tmp[3]*q[1]) - (tmp[1]*q[3]); |
| 184 |
data_[3] = (tmp[0]*q[3]) + (tmp[3]*q[0]) + (tmp[1]*q[2]) - (tmp[2]*q[1]); |
| 185 |
} |
| 186 |
|
| 187 |
void mul(const Real& s) { |
| 188 |
data_[0] *= s; |
| 189 |
data_[1] *= s; |
| 190 |
data_[2] *= s; |
| 191 |
data_[3] *= s; |
| 192 |
} |
| 193 |
|
| 194 |
/** Set the value of this quaternion to the division of itself by another quaternion */ |
| 195 |
void div(Quaternion<Real>& q) { |
| 196 |
mul(q.inverse()); |
| 197 |
} |
| 198 |
|
| 199 |
void div(const Real& s) { |
| 200 |
data_[0] /= s; |
| 201 |
data_[1] /= s; |
| 202 |
data_[2] /= s; |
| 203 |
data_[3] /= s; |
| 204 |
} |
| 205 |
|
| 206 |
Quaternion<Real>& operator *=(const Quaternion<Real>& q) { |
| 207 |
mul(q); |
| 208 |
return *this; |
| 209 |
} |
| 210 |
|
| 211 |
Quaternion<Real>& operator *=(const Real& s) { |
| 212 |
mul(s); |
| 213 |
return *this; |
| 214 |
} |
| 215 |
|
| 216 |
Quaternion<Real>& operator /=(Quaternion<Real>& q) { |
| 217 |
*this *= q.inverse(); |
| 218 |
return *this; |
| 219 |
} |
| 220 |
|
| 221 |
Quaternion<Real>& operator /=(const Real& s) { |
| 222 |
div(s); |
| 223 |
return *this; |
| 224 |
} |
| 225 |
/** |
| 226 |
* Returns the conjugate quaternion of this quaternion |
| 227 |
* @return the conjugate quaternion of this quaternion |
| 228 |
*/ |
| 229 |
Quaternion<Real> conjugate() { |
| 230 |
return Quaternion<Real>(w(), -x(), -y(), -z()); |
| 231 |
} |
| 232 |
|
| 233 |
/** |
| 234 |
* Returns the corresponding rotation matrix (3x3) |
| 235 |
* @return a 3x3 rotation matrix |
| 236 |
*/ |
| 237 |
SquareMatrix<Real, 3> toRotationMatrix3() { |
| 238 |
SquareMatrix<Real, 3> rotMat3; |
| 239 |
|
| 240 |
Real w2; |
| 241 |
Real x2; |
| 242 |
Real y2; |
| 243 |
Real z2; |
| 244 |
|
| 245 |
if (!isNormalized()) |
| 246 |
normalize(); |
| 247 |
|
| 248 |
w2 = w() * w(); |
| 249 |
x2 = x() * x(); |
| 250 |
y2 = y() * y(); |
| 251 |
z2 = z() * z(); |
| 252 |
|
| 253 |
rotMat3(0, 0) = w2 + x2 - y2 - z2; |
| 254 |
rotMat3(0, 1) = 2.0 * ( x() * y() + w() * z() ); |
| 255 |
rotMat3(0, 2) = 2.0 * ( x() * z() - w() * y() ); |
| 256 |
|
| 257 |
rotMat3(1, 0) = 2.0 * ( x() * y() - w() * z() ); |
| 258 |
rotMat3(1, 1) = w2 - x2 + y2 - z2; |
| 259 |
rotMat3(1, 2) = 2.0 * ( y() * z() + w() * x() ); |
| 260 |
|
| 261 |
rotMat3(2, 0) = 2.0 * ( x() * z() + w() * y() ); |
| 262 |
rotMat3(2, 1) = 2.0 * ( y() * z() - w() * x() ); |
| 263 |
rotMat3(2, 2) = w2 - x2 -y2 +z2; |
| 264 |
|
| 265 |
return rotMat3; |
| 266 |
} |
| 267 |
|
| 268 |
};//end Quaternion |
| 269 |
|
| 270 |
|
| 271 |
/** |
| 272 |
* Returns the vaule of scalar multiplication of this quaterion q (q * s). |
| 273 |
* @return the vaule of scalar multiplication of this vector |
| 274 |
* @param q the source quaternion |
| 275 |
* @param s the scalar value |
| 276 |
*/ |
| 277 |
template<typename Real, unsigned int Dim> |
| 278 |
Quaternion<Real> operator * ( const Quaternion<Real>& q, Real s) { |
| 279 |
Quaternion<Real> result(q); |
| 280 |
result.mul(s); |
| 281 |
return result; |
| 282 |
} |
| 283 |
|
| 284 |
/** |
| 285 |
* Returns the vaule of scalar multiplication of this quaterion q (q * s). |
| 286 |
* @return the vaule of scalar multiplication of this vector |
| 287 |
* @param s the scalar value |
| 288 |
* @param q the source quaternion |
| 289 |
*/ |
| 290 |
template<typename Real, unsigned int Dim> |
| 291 |
Quaternion<Real> operator * ( const Real& s, const Quaternion<Real>& q ) { |
| 292 |
Quaternion<Real> result(q); |
| 293 |
result.mul(s); |
| 294 |
return result; |
| 295 |
} |
| 296 |
|
| 297 |
/** |
| 298 |
* Returns the multiplication of two quaternion |
| 299 |
* @return the multiplication of two quaternion |
| 300 |
* @param q1 the first quaternion |
| 301 |
* @param q2 the second quaternion |
| 302 |
*/ |
| 303 |
template<typename Real> |
| 304 |
inline Quaternion<Real> operator *(const Quaternion<Real>& q1, const Quaternion<Real>& q2) { |
| 305 |
Quaternion<Real> result(q1); |
| 306 |
result *= q2; |
| 307 |
return result; |
| 308 |
} |
| 309 |
|
| 310 |
/** |
| 311 |
* Returns the division of two quaternion |
| 312 |
* @param q1 divisor |
| 313 |
* @param q2 dividen |
| 314 |
*/ |
| 315 |
|
| 316 |
template<typename Real> |
| 317 |
inline Quaternion<Real> operator /( Quaternion<Real>& q1, Quaternion<Real>& q2) { |
| 318 |
return q1 * q2.inverse(); |
| 319 |
} |
| 320 |
|
| 321 |
/** |
| 322 |
* Returns the value of the division of a scalar by a quaternion |
| 323 |
* @return the value of the division of a scalar by a quaternion |
| 324 |
* @param s scalar |
| 325 |
* @param q quaternion |
| 326 |
* @note for a quaternion q, 1/q = q.inverse() |
| 327 |
*/ |
| 328 |
template<typename Real> |
| 329 |
Quaternion<Real> operator /(const Real& s, Quaternion<Real>& q) { |
| 330 |
|
| 331 |
Quaternion<Real> x; |
| 332 |
x = q.inverse(); |
| 333 |
x *= s; |
| 334 |
return x; |
| 335 |
} |
| 336 |
|
| 337 |
template <class T> |
| 338 |
inline bool operator==(const Quaternion<T>& lhs, const Quaternion<T>& rhs) { |
| 339 |
return equal(lhs[0] ,rhs[0]) && equal(lhs[1] , rhs[1]) && equal(lhs[2], rhs[2]) && equal(lhs[3], rhs[3]); |
| 340 |
} |
| 341 |
|
| 342 |
typedef Quaternion<double> Quat4d; |
| 343 |
} |
| 344 |
#endif //MATH_QUATERNION_HPP |
