161 EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT(internal::IsValidAxis<AlphaAxis>::value,
162 ALPHA_AXIS_IS_INVALID);
164 EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT(internal::IsValidAxis<BetaAxis>::value,
165 BETA_AXIS_IS_INVALID);
167 EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT(internal::IsValidAxis<GammaAxis>::value,
168 GAMMA_AXIS_IS_INVALID);
171 ALPHA_AXIS_CANT_BE_EQUAL_TO_BETA_AXIS);
174 BETA_AXIS_CANT_BE_EQUAL_TO_GAMMA_AXIS);
186 template <
typename Derived>
192 typedef typename Derived::Scalar
Scalar;
197 const Scalar Rsum =
sqrt((mat(I_,I_) * mat(I_,I_) + mat(I_,J_) * mat(I_,J_) + mat(J_,K_) * mat(J_,K_) + mat(K_,K_) * mat(K_,K_))/2);
198 res[1] = atan2(plusMinus * mat(I_,K_), Rsum);
202 res[0] = atan2(minusPlus * mat(J_, K_), mat(K_, K_));
203 res[2] = atan2(minusPlus * mat(I_, J_), mat(I_, I_));
205 else if(plusMinus * mat(I_, K_) > 0) {
206 Scalar spos = mat(J_, I_) + plusMinus * mat(K_, J_);
207 Scalar cpos = mat(J_, J_) + minusPlus * mat(K_, I_);
208 Scalar alphaPlusMinusGamma = atan2(spos, cpos);
209 res[0] = alphaPlusMinusGamma;
213 Scalar sneg = plusMinus * (mat(K_, J_) + minusPlus * mat(J_, I_));
214 Scalar cneg = mat(J_, J_) + plusMinus * mat(K_, I_);
215 Scalar alphaMinusPlusBeta = atan2(sneg, cneg);
216 res[0] = alphaMinusPlusBeta;
221 template <
typename Derived>
223 const MatrixBase<Derived>& mat, internal::false_type )
228 typedef typename Derived::Scalar Scalar;
230 const Scalar plusMinus =
IsEven? 1 : -1;
231 const Scalar minusPlus =
IsOdd? 1 : -1;
233 const Scalar Rsum =
sqrt((mat(I_, J_) * mat(I_, J_) + mat(I_, K_) * mat(I_, K_) + mat(J_, I_) * mat(J_, I_) + mat(K_, I_) * mat(K_, I_)) / 2);
235 res[1] = atan2(Rsum, mat(I_, I_));
238 if(Rsum > 4 * NumTraits<Scalar>::epsilon()) {
239 res[0] = atan2(mat(J_, I_), minusPlus * mat(K_, I_));
240 res[2] = atan2(mat(I_, J_), plusMinus * mat(I_, K_));
242 else if(mat(I_, I_) > 0) {
243 Scalar spos = plusMinus * mat(K_, J_) + minusPlus * mat(J_, K_);
244 Scalar cpos = mat(J_, J_) + mat(K_, K_);
245 res[0] = atan2(spos, cpos);
249 Scalar sneg = plusMinus * mat(K_, J_) + plusMinus * mat(J_, K_);
250 Scalar cneg = mat(J_, J_) - mat(K_, K_);
251 res[0] = atan2(sneg, cneg);
256 template<
typename Scalar>
257 static void CalcEulerAngles(
258 EulerAngles<Scalar, EulerSystem>& res,
259 const typename EulerAngles<Scalar, EulerSystem>::Matrix3& mat)
263 typename internal::conditional<IsTaitBryan, internal::true_type, internal::false_type>::type());
266 res.alpha() = -res.alpha();
269 res.beta() = -res.beta();
272 res.gamma() = -res.gamma();
275 template <
typename _Scalar,
class _System>
276 friend class Eigen::EulerAngles;
278 template<
typename System,
282 friend struct internal::eulerangles_assign_impl;