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234 lines
8.7 KiB
234 lines
8.7 KiB
// This file is part of Eigen, a lightweight C++ template library |
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// for linear algebra. |
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// |
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// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr> |
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// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com> |
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// |
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// This Source Code Form is subject to the terms of the Mozilla |
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// Public License v. 2.0. If a copy of the MPL was not distributed |
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. |
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#ifndef EIGEN_ORTHOMETHODS_H |
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#define EIGEN_ORTHOMETHODS_H |
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namespace Eigen { |
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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 |
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* |
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* Here is a very good explanation of cross-product: http://xkcd.com/199/ |
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* |
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* 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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#ifndef EIGEN_PARSED_BY_DOXYGEN |
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EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type |
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#else |
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inline typename MatrixBase<Derived>::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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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(derived()); |
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typename internal::nested_eval<OtherDerived,2>::type rhs(other.derived()); |
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return typename cross_product_return_type<OtherDerived>::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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} |
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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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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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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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} |
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}; |
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} |
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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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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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typename internal::remove_all<DerivedNested>::type, |
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typename internal::remove_all<OtherDerivedNested>::type>::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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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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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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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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} |
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return res; |
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} |
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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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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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{ |
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VectorType perp = VectorType::Zero(src.size()); |
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Index maxi = 0; |
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Index sndi = 0; |
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src.cwiseAbs().maxCoeff(&maxi); |
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if (maxi==0) |
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sndi = 1; |
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RealScalar invnm = RealScalar(1)/(Vector2() << src.coeff(sndi),src.coeff(maxi)).finished().norm(); |
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perp.coeffRef(maxi) = -numext::conj(src.coeff(sndi)) * invnm; |
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perp.coeffRef(sndi) = numext::conj(src.coeff(maxi)) * invnm; |
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return perp; |
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} |
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}; |
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template<typename Derived> |
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struct unitOrthogonal_selector<Derived,3> |
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{ |
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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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EIGEN_DEVICE_FUNC |
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static inline VectorType run(const Derived& src) |
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{ |
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VectorType perp; |
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/* Let us compute the crossed product of *this with a vector |
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* that is not too close to being colinear to *this. |
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*/ |
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/* unless the x and y coords are both close to zero, we can |
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* simply take ( -y, x, 0 ) and normalize it. |
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*/ |
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if((!isMuchSmallerThan(src.x(), src.z())) |
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|| (!isMuchSmallerThan(src.y(), src.z()))) |
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{ |
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RealScalar invnm = RealScalar(1)/src.template head<2>().norm(); |
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perp.coeffRef(0) = -numext::conj(src.y())*invnm; |
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perp.coeffRef(1) = numext::conj(src.x())*invnm; |
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perp.coeffRef(2) = 0; |
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} |
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/* if both x and y are close to zero, then the vector is close |
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* to the z-axis, so it's far from colinear to the x-axis for instance. |
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* So we take the crossed product with (1,0,0) and normalize it. |
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*/ |
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else |
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{ |
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RealScalar invnm = RealScalar(1)/src.template tail<2>().norm(); |
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perp.coeffRef(0) = 0; |
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perp.coeffRef(1) = -numext::conj(src.z())*invnm; |
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perp.coeffRef(2) = numext::conj(src.y())*invnm; |
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} |
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return perp; |
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} |
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}; |
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template<typename Derived> |
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struct unitOrthogonal_selector<Derived,2> |
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{ |
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typedef typename plain_matrix_type<Derived>::type VectorType; |
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EIGEN_DEVICE_FUNC |
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static inline VectorType run(const Derived& src) |
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{ return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized(); } |
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}; |
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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 a unit vector which is orthogonal to \c *this |
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* |
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* The size of \c *this must be at least 2. If the size is exactly 2, |
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* then the returned vector is a counter clock wise rotation of \c *this, i.e., (-y,x).normalized(). |
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* |
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* \sa cross() |
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*/ |
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template<typename Derived> |
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EIGEN_DEVICE_FUNC typename MatrixBase<Derived>::PlainObject |
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MatrixBase<Derived>::unitOrthogonal() const |
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{ |
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) |
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return internal::unitOrthogonal_selector<Derived>::run(derived()); |
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} |
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} // end namespace Eigen |
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#endif // EIGEN_ORTHOMETHODS_H
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