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Cross product for vectors of size 2. Fixes #1037

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This commit is contained in:
Gabriele Buondonno
2022-11-15 22:39:42 +00:00
committed by Antonio Sánchez
parent 8588d8c74b
commit 6431dfdb50
7 changed files with 108 additions and 34 deletions
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13
Eigen/src/Core/MatrixBase.h
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@@ -387,20 +387,9 @@ template<typename Derived> class MatrixBase
/////////// Geometry module ///////////
#ifndef EIGEN_PARSED_BY_DOXYGEN
/// \internal helper struct to form the return type of the cross product
template<typename OtherDerived> struct cross_product_return_type {
typedef typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
typedef Matrix<Scalar,MatrixBase::RowsAtCompileTime,MatrixBase::ColsAtCompileTime> type;
};
#endif // EIGEN_PARSED_BY_DOXYGEN
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
#ifndef EIGEN_PARSED_BY_DOXYGEN
inline typename cross_product_return_type<OtherDerived>::type
#else
inline PlainObject
#endif
inline typename internal::cross_impl<Derived, OtherDerived>::return_type
cross(const MatrixBase<OtherDerived>& other) const;
template<typename OtherDerived>

4
Eigen/src/Core/util/ForwardDeclarations.h
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@@ -270,8 +270,10 @@ template<typename VectorsType, typename CoeffsType, int Side=OnTheLeft> class Ho
template<typename Scalar> class JacobiRotation;
// Geometry module:
namespace internal {
template<typename Derived, typename OtherDerived, int Size = MatrixBase<Derived>::SizeAtCompileTime> struct cross_impl;
}
template<typename Derived, int Dim_> class RotationBase;
template<typename Lhs, typename Rhs> class Cross;
template<typename Derived> class QuaternionBase;
template<typename Scalar> class Rotation2D;
template<typename Scalar> class AngleAxis;

82
Eigen/src/Geometry/OrthoMethods.h
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@@ -15,39 +15,83 @@
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
* \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.
*
* Here is a very good explanation of cross-product: http://xkcd.com/199/
* This method is implemented for two different cases: between vectors of fixed size 2 and between vectors of fixed size 3.
*
* 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$
* 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>
#ifndef EIGEN_PARSED_BY_DOXYGEN
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type
#ifndef EIGEN_PARSED_BY_DOXYGEN
typename internal::cross_impl<Derived, OtherDerived>::return_type
#else
typename MatrixBase<Derived>::PlainObject
inline std::conditional_t<SizeAtCompileTime==2, Scalar, PlainObject>
#endif
MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const
{
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(derived());
typename internal::nested_eval<OtherDerived,2>::type rhs(other.derived());
return typename cross_product_return_type<OtherDerived>::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))
);
return internal::cross_impl<Derived, OtherDerived>::run(*this, other);
}
namespace internal {