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Tobias Wood
@@ -14,167 +14,157 @@
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// IWYU pragma: private
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#include "./InternalHeaderCheck.h"
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namespace Eigen {
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namespace Eigen {
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namespace internal {
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// Vector3 version (default)
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template<typename Derived, typename OtherDerived, int Size>
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struct cross_impl
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{
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typedef typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
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typedef Matrix<Scalar,MatrixBase<Derived>::RowsAtCompileTime,MatrixBase<Derived>::ColsAtCompileTime> return_type;
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template <typename Derived, typename OtherDerived, int Size>
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struct cross_impl {
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typedef typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,
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typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
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typedef Matrix<Scalar, MatrixBase<Derived>::RowsAtCompileTime, MatrixBase<Derived>::ColsAtCompileTime> return_type;
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static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
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return_type run(const MatrixBase<Derived>& first, const MatrixBase<OtherDerived>& second)
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{
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,3)
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
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static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE return_type run(const MatrixBase<Derived>& first,
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const MatrixBase<OtherDerived>& second) {
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived, 3)
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived, 3)
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// Note that there is no need for an expression here since the compiler
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// optimize such a small temporary very well (even within a complex expression)
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typename internal::nested_eval<Derived,2>::type lhs(first.derived());
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typename internal::nested_eval<OtherDerived,2>::type rhs(second.derived());
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return return_type(
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numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
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numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
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numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0))
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);
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typename internal::nested_eval<Derived, 2>::type lhs(first.derived());
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typename internal::nested_eval<OtherDerived, 2>::type rhs(second.derived());
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return return_type(numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
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numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
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numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)));
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}
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};
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// Vector2 version
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template<typename Derived, typename OtherDerived>
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struct cross_impl<Derived, OtherDerived, 2>
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{
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typedef typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
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template <typename Derived, typename OtherDerived>
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struct cross_impl<Derived, OtherDerived, 2> {
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typedef typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,
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typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
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typedef Scalar return_type;
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static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
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return_type run(const MatrixBase<Derived>& first, const MatrixBase<OtherDerived>& second)
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{
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,2);
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,2);
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typename internal::nested_eval<Derived,2>::type lhs(first.derived());
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typename internal::nested_eval<OtherDerived,2>::type rhs(second.derived());
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static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE return_type run(const MatrixBase<Derived>& first,
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const MatrixBase<OtherDerived>& second) {
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived, 2);
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived, 2);
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typename internal::nested_eval<Derived, 2>::type lhs(first.derived());
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typename internal::nested_eval<OtherDerived, 2>::type rhs(second.derived());
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return numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0));
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}
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};
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} // end namespace internal
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} // end namespace internal
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/** \geometry_module \ingroup Geometry_Module
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*
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* \returns the cross product of \c *this and \a other. This is either a scalar for size-2 vectors or a size-3 vector for size-3 vectors.
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*
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* This method is implemented for two different cases: between vectors of fixed size 2 and between vectors of fixed size 3.
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*
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* For vectors of size 3, the output is simply the traditional cross product.
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*
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* For vectors of size 2, the output is a scalar.
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* Given vectors \f$ v = \begin{bmatrix} v_1 & v_2 \end{bmatrix} \f$ and \f$ w = \begin{bmatrix} w_1 & w_2 \end{bmatrix} \f$,
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* the result is simply \f$ v\times w = \overline{v_1 w_2 - v_2 w_1} = \text{conj}\left|\begin{smallmatrix} v_1 & w_1 \\ v_2 & w_2 \end{smallmatrix}\right| \f$;
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* or, to put it differently, it is the third coordinate of the cross product of \f$ \begin{bmatrix} v_1 & v_2 & v_3 \end{bmatrix} \f$ and \f$ \begin{bmatrix} w_1 & w_2 & w_3 \end{bmatrix} \f$.
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* For real-valued inputs, the result can be interpreted as the signed area of a parallelogram spanned by the two vectors.
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*
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* \note With complex numbers, the cross product is implemented as
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* \f$ (\mathbf{a}+i\mathbf{b}) \times (\mathbf{c}+i\mathbf{d}) = (\mathbf{a} \times \mathbf{c} - \mathbf{b} \times \mathbf{d}) - i(\mathbf{a} \times \mathbf{d} + \mathbf{b} \times \mathbf{c})\f$
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*
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* \sa MatrixBase::cross3()
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*/
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template<typename Derived>
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template<typename OtherDerived>
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*
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* \returns the cross product of \c *this and \a other. This is either a scalar for size-2 vectors or a size-3 vector
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* for size-3 vectors.
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*
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* This method is implemented for two different cases: between vectors of fixed size 2 and between vectors of fixed
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* size 3.
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*
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* For vectors of size 3, the output is simply the traditional cross product.
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*
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* For vectors of size 2, the output is a scalar.
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* Given vectors \f$ v = \begin{bmatrix} v_1 & v_2 \end{bmatrix} \f$ and \f$ w = \begin{bmatrix} w_1 & w_2 \end{bmatrix}
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* \f$, the result is simply \f$ v\times w = \overline{v_1 w_2 - v_2 w_1} = \text{conj}\left|\begin{smallmatrix} v_1 &
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* w_1 \\ v_2 & w_2 \end{smallmatrix}\right| \f$; or, to put it differently, it is the third coordinate of the cross
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* product of \f$ \begin{bmatrix} v_1 & v_2 & v_3 \end{bmatrix} \f$ and \f$ \begin{bmatrix} w_1 & w_2 & w_3
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* \end{bmatrix} \f$. For real-valued inputs, the result can be interpreted as the signed area of a parallelogram
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* spanned by the two vectors.
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*
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* \note With complex numbers, the cross product is implemented as
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* \f$ (\mathbf{a}+i\mathbf{b}) \times (\mathbf{c}+i\mathbf{d}) = (\mathbf{a} \times \mathbf{c} - \mathbf{b} \times
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* \mathbf{d}) - i(\mathbf{a} \times \mathbf{d} + \mathbf{b} \times \mathbf{c})\f$
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*
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* \sa MatrixBase::cross3()
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*/
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template <typename Derived>
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template <typename OtherDerived>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
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#ifndef EIGEN_PARSED_BY_DOXYGEN
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typename internal::cross_impl<Derived, OtherDerived>::return_type
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typename internal::cross_impl<Derived, OtherDerived>::return_type
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#else
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inline std::conditional_t<SizeAtCompileTime==2, Scalar, PlainObject>
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inline std::conditional_t<SizeAtCompileTime == 2, Scalar, PlainObject>
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#endif
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MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const
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{
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MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const {
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return internal::cross_impl<Derived, OtherDerived>::run(*this, other);
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}
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namespace internal {
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template< int Arch,typename VectorLhs,typename VectorRhs,
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typename Scalar = typename VectorLhs::Scalar,
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bool Vectorizable = bool((VectorLhs::Flags&VectorRhs::Flags)&PacketAccessBit)>
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template <int Arch, typename VectorLhs, typename VectorRhs, typename Scalar = typename VectorLhs::Scalar,
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bool Vectorizable = bool((VectorLhs::Flags & VectorRhs::Flags) & PacketAccessBit)>
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struct cross3_impl {
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EIGEN_DEVICE_FUNC static inline typename internal::plain_matrix_type<VectorLhs>::type
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run(const VectorLhs& lhs, const VectorRhs& rhs)
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{
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EIGEN_DEVICE_FUNC static inline typename internal::plain_matrix_type<VectorLhs>::type run(const VectorLhs& lhs,
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const VectorRhs& rhs) {
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return typename internal::plain_matrix_type<VectorLhs>::type(
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numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
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numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
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numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)),
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0
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);
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numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
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numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
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numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)), 0);
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}
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};
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}
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} // namespace internal
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/** \geometry_module \ingroup Geometry_Module
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*
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* \returns the cross product of \c *this and \a other using only the x, y, and z coefficients
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*
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* The size of \c *this and \a other must be four. This function is especially useful
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* when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
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*
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* \sa MatrixBase::cross()
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*/
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template<typename Derived>
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template<typename OtherDerived>
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EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::PlainObject
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MatrixBase<Derived>::cross3(const MatrixBase<OtherDerived>& other) const
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{
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,4)
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,4)
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*
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* \returns the cross product of \c *this and \a other using only the x, y, and z coefficients
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*
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* The size of \c *this and \a other must be four. This function is especially useful
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* when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
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*
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* \sa MatrixBase::cross()
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*/
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template <typename Derived>
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template <typename OtherDerived>
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EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::PlainObject MatrixBase<Derived>::cross3(
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const MatrixBase<OtherDerived>& other) const {
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived, 4)
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived, 4)
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typedef typename internal::nested_eval<Derived,2>::type DerivedNested;
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typedef typename internal::nested_eval<OtherDerived,2>::type OtherDerivedNested;
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typedef typename internal::nested_eval<Derived, 2>::type DerivedNested;
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typedef typename internal::nested_eval<OtherDerived, 2>::type OtherDerivedNested;
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DerivedNested lhs(derived());
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OtherDerivedNested rhs(other.derived());
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return internal::cross3_impl<Architecture::Target,
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internal::remove_all_t<DerivedNested>,
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internal::remove_all_t<OtherDerivedNested>>::run(lhs,rhs);
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return internal::cross3_impl<Architecture::Target, internal::remove_all_t<DerivedNested>,
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internal::remove_all_t<OtherDerivedNested>>::run(lhs, rhs);
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}
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/** \geometry_module \ingroup Geometry_Module
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*
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* \returns a matrix expression of the cross product of each column or row
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* of the referenced expression with the \a other vector.
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*
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* The referenced matrix must have one dimension equal to 3.
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* The result matrix has the same dimensions than the referenced one.
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*
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* \sa MatrixBase::cross() */
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template<typename ExpressionType, int Direction>
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template<typename OtherDerived>
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EIGEN_DEVICE_FUNC
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const typename VectorwiseOp<ExpressionType,Direction>::CrossReturnType
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VectorwiseOp<ExpressionType,Direction>::cross(const MatrixBase<OtherDerived>& other) const
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{
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
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EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
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YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
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typename internal::nested_eval<ExpressionType,2>::type mat(_expression());
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typename internal::nested_eval<OtherDerived,2>::type vec(other.derived());
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*
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* \returns a matrix expression of the cross product of each column or row
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* of the referenced expression with the \a other vector.
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*
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* The referenced matrix must have one dimension equal to 3.
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* The result matrix has the same dimensions than the referenced one.
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*
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* \sa MatrixBase::cross() */
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template <typename ExpressionType, int Direction>
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template <typename OtherDerived>
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EIGEN_DEVICE_FUNC const typename VectorwiseOp<ExpressionType, Direction>::CrossReturnType
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VectorwiseOp<ExpressionType, Direction>::cross(const MatrixBase<OtherDerived>& other) const {
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived, 3)
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EIGEN_STATIC_ASSERT(
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(internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
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YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
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CrossReturnType res(_expression().rows(),_expression().cols());
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if(Direction==Vertical)
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{
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eigen_assert(CrossReturnType::RowsAtCompileTime==3 && "the matrix must have exactly 3 rows");
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typename internal::nested_eval<ExpressionType, 2>::type mat(_expression());
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typename internal::nested_eval<OtherDerived, 2>::type vec(other.derived());
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CrossReturnType res(_expression().rows(), _expression().cols());
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if (Direction == Vertical) {
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eigen_assert(CrossReturnType::RowsAtCompileTime == 3 && "the matrix must have exactly 3 rows");
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res.row(0) = (mat.row(1) * vec.coeff(2) - mat.row(2) * vec.coeff(1)).conjugate();
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res.row(1) = (mat.row(2) * vec.coeff(0) - mat.row(0) * vec.coeff(2)).conjugate();
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res.row(2) = (mat.row(0) * vec.coeff(1) - mat.row(1) * vec.coeff(0)).conjugate();
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}
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else
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{
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eigen_assert(CrossReturnType::ColsAtCompileTime==3 && "the matrix must have exactly 3 columns");
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} else {
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eigen_assert(CrossReturnType::ColsAtCompileTime == 3 && "the matrix must have exactly 3 columns");
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res.col(0) = (mat.col(1) * vec.coeff(2) - mat.col(2) * vec.coeff(1)).conjugate();
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res.col(1) = (mat.col(2) * vec.coeff(0) - mat.col(0) * vec.coeff(2)).conjugate();
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res.col(2) = (mat.col(0) * vec.coeff(1) - mat.col(1) * vec.coeff(0)).conjugate();
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@@ -184,39 +174,32 @@ VectorwiseOp<ExpressionType,Direction>::cross(const MatrixBase<OtherDerived>& ot
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namespace internal {
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template<typename Derived, int Size = Derived::SizeAtCompileTime>
|
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struct unitOrthogonal_selector
|
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{
|
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template <typename Derived, int Size = Derived::SizeAtCompileTime>
|
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struct unitOrthogonal_selector {
|
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typedef typename plain_matrix_type<Derived>::type VectorType;
|
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typedef typename traits<Derived>::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
|
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typedef Matrix<Scalar,2,1> Vector2;
|
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EIGEN_DEVICE_FUNC
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||||
static inline VectorType run(const Derived& src)
|
||||
{
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typedef Matrix<Scalar, 2, 1> Vector2;
|
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EIGEN_DEVICE_FUNC static inline VectorType run(const Derived& src) {
|
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VectorType perp = VectorType::Zero(src.size());
|
||||
Index maxi = 0;
|
||||
Index sndi = 0;
|
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src.cwiseAbs().maxCoeff(&maxi);
|
||||
if (maxi==0)
|
||||
sndi = 1;
|
||||
RealScalar invnm = RealScalar(1)/(Vector2() << src.coeff(sndi),src.coeff(maxi)).finished().norm();
|
||||
if (maxi == 0) sndi = 1;
|
||||
RealScalar invnm = RealScalar(1) / (Vector2() << src.coeff(sndi), src.coeff(maxi)).finished().norm();
|
||||
perp.coeffRef(maxi) = -numext::conj(src.coeff(sndi)) * invnm;
|
||||
perp.coeffRef(sndi) = numext::conj(src.coeff(maxi)) * invnm;
|
||||
perp.coeffRef(sndi) = numext::conj(src.coeff(maxi)) * invnm;
|
||||
|
||||
return perp;
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
template<typename Derived>
|
||||
struct unitOrthogonal_selector<Derived,3>
|
||||
{
|
||||
template <typename Derived>
|
||||
struct unitOrthogonal_selector<Derived, 3> {
|
||||
typedef typename plain_matrix_type<Derived>::type VectorType;
|
||||
typedef typename traits<Derived>::Scalar Scalar;
|
||||
typedef typename NumTraits<Scalar>::Real RealScalar;
|
||||
EIGEN_DEVICE_FUNC
|
||||
static inline VectorType run(const Derived& src)
|
||||
{
|
||||
EIGEN_DEVICE_FUNC static inline VectorType run(const Derived& src) {
|
||||
VectorType perp;
|
||||
/* Let us compute the crossed product of *this with a vector
|
||||
* that is not too close to being colinear to *this.
|
||||
@@ -225,58 +208,52 @@ struct unitOrthogonal_selector<Derived,3>
|
||||
/* unless the x and y coords are both close to zero, we can
|
||||
* simply take ( -y, x, 0 ) and normalize it.
|
||||
*/
|
||||
if((!isMuchSmallerThan(src.x(), src.z()))
|
||||
|| (!isMuchSmallerThan(src.y(), src.z())))
|
||||
{
|
||||
RealScalar invnm = RealScalar(1)/src.template head<2>().norm();
|
||||
perp.coeffRef(0) = -numext::conj(src.y())*invnm;
|
||||
perp.coeffRef(1) = numext::conj(src.x())*invnm;
|
||||
if ((!isMuchSmallerThan(src.x(), src.z())) || (!isMuchSmallerThan(src.y(), src.z()))) {
|
||||
RealScalar invnm = RealScalar(1) / src.template head<2>().norm();
|
||||
perp.coeffRef(0) = -numext::conj(src.y()) * invnm;
|
||||
perp.coeffRef(1) = numext::conj(src.x()) * invnm;
|
||||
perp.coeffRef(2) = 0;
|
||||
}
|
||||
/* if both x and y are close to zero, then the vector is close
|
||||
* to the z-axis, so it's far from colinear to the x-axis for instance.
|
||||
* So we take the crossed product with (1,0,0) and normalize it.
|
||||
*/
|
||||
else
|
||||
{
|
||||
RealScalar invnm = RealScalar(1)/src.template tail<2>().norm();
|
||||
else {
|
||||
RealScalar invnm = RealScalar(1) / src.template tail<2>().norm();
|
||||
perp.coeffRef(0) = 0;
|
||||
perp.coeffRef(1) = -numext::conj(src.z())*invnm;
|
||||
perp.coeffRef(2) = numext::conj(src.y())*invnm;
|
||||
perp.coeffRef(1) = -numext::conj(src.z()) * invnm;
|
||||
perp.coeffRef(2) = numext::conj(src.y()) * invnm;
|
||||
}
|
||||
|
||||
return perp;
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
template<typename Derived>
|
||||
struct unitOrthogonal_selector<Derived,2>
|
||||
{
|
||||
template <typename Derived>
|
||||
struct unitOrthogonal_selector<Derived, 2> {
|
||||
typedef typename plain_matrix_type<Derived>::type VectorType;
|
||||
EIGEN_DEVICE_FUNC
|
||||
static inline VectorType run(const Derived& src)
|
||||
{ return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized(); }
|
||||
EIGEN_DEVICE_FUNC static inline VectorType run(const Derived& src) {
|
||||
return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized();
|
||||
}
|
||||
};
|
||||
|
||||
} // end namespace internal
|
||||
} // end namespace internal
|
||||
|
||||
/** \geometry_module \ingroup Geometry_Module
|
||||
*
|
||||
* \returns a unit vector which is orthogonal to \c *this
|
||||
*
|
||||
* The size of \c *this must be at least 2. If the size is exactly 2,
|
||||
* then the returned vector is a counter clock wise rotation of \c *this, i.e., (-y,x).normalized().
|
||||
*
|
||||
* \sa cross()
|
||||
*/
|
||||
template<typename Derived>
|
||||
EIGEN_DEVICE_FUNC typename MatrixBase<Derived>::PlainObject
|
||||
MatrixBase<Derived>::unitOrthogonal() const
|
||||
{
|
||||
*
|
||||
* \returns a unit vector which is orthogonal to \c *this
|
||||
*
|
||||
* The size of \c *this must be at least 2. If the size is exactly 2,
|
||||
* then the returned vector is a counter clock wise rotation of \c *this, i.e., (-y,x).normalized().
|
||||
*
|
||||
* \sa cross()
|
||||
*/
|
||||
template <typename Derived>
|
||||
EIGEN_DEVICE_FUNC typename MatrixBase<Derived>::PlainObject MatrixBase<Derived>::unitOrthogonal() const {
|
||||
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
|
||||
return internal::unitOrthogonal_selector<Derived>::run(derived());
|
||||
}
|
||||
|
||||
} // end namespace Eigen
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // EIGEN_ORTHOMETHODS_H
|
||||
#endif // EIGEN_ORTHOMETHODS_H
|
||||
|
||||
Reference in New Issue
Block a user