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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 | < | * @brief |
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 | < | }; |
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 |
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