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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ORTHOMETHODS_H
#define EIGEN_ORTHOMETHODS_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
// Vector3 version (default)
template <typename Derived, typename OtherDerived, int Size>
struct cross_impl {
typedef typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,
typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
typedef Matrix<Scalar, MatrixBase<Derived>::RowsAtCompileTime, MatrixBase<Derived>::ColsAtCompileTime> return_type;
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE return_type run(const MatrixBase<Derived>& first,
const MatrixBase<OtherDerived>& second) {
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived, 3)
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived, 3)
// Note that there is no need for an expression here since the compiler
// optimize such a small temporary very well (even within a complex expression)
typename internal::nested_eval<Derived, 2>::type lhs(first.derived());
typename internal::nested_eval<OtherDerived, 2>::type rhs(second.derived());
return return_type(numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)));
}
};
// Vector2 version
template <typename Derived, typename OtherDerived>
struct cross_impl<Derived, OtherDerived, 2> {
typedef typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,
typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
typedef Scalar return_type;
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE return_type run(const MatrixBase<Derived>& first,
const MatrixBase<OtherDerived>& second) {
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived, 2);
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived, 2);
typename internal::nested_eval<Derived, 2>::type lhs(first.derived());
typename internal::nested_eval<OtherDerived, 2>::type rhs(second.derived());
return numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0));
}
};
} // end namespace internal
/** \geometry_module \ingroup Geometry_Module
*
* \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.
*
* This method is implemented for two different cases: between vectors of fixed size 2 and between vectors of fixed
* size 3.
*
* For vectors of size 3, the output is simply the traditional cross product.
*
* For vectors of size 2, the output is a scalar.
* 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$, the result is simply \f$ 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$; or, to put it differently, it is the third coordinate of the cross
* product of \f$ \begin{bmatrix} v_1 & v_2 & v_3 \end{bmatrix} \f$ and \f$ \begin{bmatrix} w_1 & w_2 & w_3
* \end{bmatrix} \f$. For real-valued inputs, the result can be interpreted as the signed area of a parallelogram
* spanned by the two vectors.
*
* \note With complex numbers, the cross product is implemented as
* \f$ (\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$
*
* \sa MatrixBase::cross3()
*/
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
#ifndef EIGEN_PARSED_BY_DOXYGEN
typename internal::cross_impl<Derived, OtherDerived>::return_type
#else
inline std::conditional_t<SizeAtCompileTime == 2, Scalar, PlainObject>
#endif
MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const {
return internal::cross_impl<Derived, OtherDerived>::run(*this, other);
}
namespace internal {
template <int Arch, typename VectorLhs, typename VectorRhs, typename Scalar = typename VectorLhs::Scalar,
bool Vectorizable = bool((VectorLhs::Flags & VectorRhs::Flags) & PacketAccessBit)>
struct cross3_impl {
EIGEN_DEVICE_FUNC static inline typename internal::plain_matrix_type<VectorLhs>::type run(const VectorLhs& lhs,
const VectorRhs& rhs) {
return typename internal::plain_matrix_type<VectorLhs>::type(
numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)), 0);
}
};
} // namespace internal
/** \geometry_module \ingroup Geometry_Module
*
* \returns the cross product of \c *this and \a other using only the x, y, and z coefficients
*
* The size of \c *this and \a other must be four. This function is especially useful
* when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
*
* \sa MatrixBase::cross()
*/
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::PlainObject MatrixBase<Derived>::cross3(
const MatrixBase<OtherDerived>& other) const {
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived, 4)
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived, 4)
typedef typename internal::nested_eval<Derived, 2>::type DerivedNested;
typedef typename internal::nested_eval<OtherDerived, 2>::type OtherDerivedNested;
DerivedNested lhs(derived());
OtherDerivedNested rhs(other.derived());
return internal::cross3_impl<Architecture::Target, internal::remove_all_t<DerivedNested>,
internal::remove_all_t<OtherDerivedNested>>::run(lhs, rhs);
}
/** \geometry_module \ingroup Geometry_Module
*
* \returns a matrix expression of the cross product of each column or row
* of the referenced expression with the \a other vector.
*
* The referenced matrix must have one dimension equal to 3.
* The result matrix has the same dimensions than the referenced one.
*
* \sa MatrixBase::cross() */
template <typename ExpressionType, int Direction>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC const typename VectorwiseOp<ExpressionType, Direction>::CrossReturnType
VectorwiseOp<ExpressionType, Direction>::cross(const MatrixBase<OtherDerived>& other) const {
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived, 3)
EIGEN_STATIC_ASSERT(
(internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
typename internal::nested_eval<ExpressionType, 2>::type mat(_expression());
typename internal::nested_eval<OtherDerived, 2>::type vec(other.derived());
CrossReturnType res(_expression().rows(), _expression().cols());
if (Direction == Vertical) {
eigen_assert(CrossReturnType::RowsAtCompileTime == 3 && "the matrix must have exactly 3 rows");
res.row(0) = (mat.row(1) * vec.coeff(2) - mat.row(2) * vec.coeff(1)).conjugate();
res.row(1) = (mat.row(2) * vec.coeff(0) - mat.row(0) * vec.coeff(2)).conjugate();
res.row(2) = (mat.row(0) * vec.coeff(1) - mat.row(1) * vec.coeff(0)).conjugate();
} else {
eigen_assert(CrossReturnType::ColsAtCompileTime == 3 && "the matrix must have exactly 3 columns");
res.col(0) = (mat.col(1) * vec.coeff(2) - mat.col(2) * vec.coeff(1)).conjugate();
res.col(1) = (mat.col(2) * vec.coeff(0) - mat.col(0) * vec.coeff(2)).conjugate();
res.col(2) = (mat.col(0) * vec.coeff(1) - mat.col(1) * vec.coeff(0)).conjugate();
}
return res;
}
namespace internal {
template <typename Derived, int Size = Derived::SizeAtCompileTime>
struct unitOrthogonal_selector {
typedef typename plain_matrix_type<Derived>::type VectorType;
typedef typename traits<Derived>::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, 2, 1> Vector2;
EIGEN_DEVICE_FUNC static inline VectorType run(const Derived& src) {
VectorType perp = VectorType::Zero(src.size());
Index maxi = 0;
Index sndi = 0;
src.cwiseAbs().maxCoeff(&maxi);
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;
return perp;
}
};
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) {
VectorType perp;
/* Let us compute the crossed product of *this with a vector
* that is not too close to being colinear to *this.
*/
/* 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;
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();
perp.coeffRef(0) = 0;
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> {
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();
}
};
} // 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 {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
return internal::unitOrthogonal_selector<Derived>::run(derived());
}
} // end namespace Eigen
#endif // EIGEN_ORTHOMETHODS_H