mirror of
https://gitlab.com/libeigen/eigen.git
synced 2026-04-10 11:34:33 +08:00
233 lines
9.8 KiB
C++
233 lines
9.8 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
|
|
// for linear algebra.
|
|
//
|
|
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
|
|
// Copyright (C) 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_PARAMETRIZEDLINE_H
|
|
#define EIGEN_PARAMETRIZEDLINE_H
|
|
|
|
// IWYU pragma: private
|
|
#include "./InternalHeaderCheck.h"
|
|
|
|
namespace Eigen {
|
|
|
|
/** \geometry_module \ingroup Geometry_Module
|
|
*
|
|
* \class ParametrizedLine
|
|
*
|
|
* \brief A parametrized line
|
|
*
|
|
* A parametrized line is defined by an origin point \f$ \mathbf{o} \f$ and a unit
|
|
* direction vector \f$ \mathbf{d} \f$ such that the line corresponds to
|
|
* the set \f$ l(t) = \mathbf{o} + t \mathbf{d} \f$, \f$ t \in \mathbf{R} \f$.
|
|
*
|
|
* \tparam Scalar_ the scalar type, i.e., the type of the coefficients
|
|
* \tparam AmbientDim_ the dimension of the ambient space, can be a compile time value or Dynamic.
|
|
*/
|
|
template <typename Scalar_, int AmbientDim_, int Options_>
|
|
class ParametrizedLine {
|
|
public:
|
|
EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar_, AmbientDim_)
|
|
enum { AmbientDimAtCompileTime = AmbientDim_, Options = Options_ };
|
|
typedef Scalar_ Scalar;
|
|
typedef typename NumTraits<Scalar>::Real RealScalar;
|
|
typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
|
|
typedef Matrix<Scalar, AmbientDimAtCompileTime, 1, Options> VectorType;
|
|
|
|
/** Default constructor without initialization */
|
|
EIGEN_DEVICE_FUNC inline ParametrizedLine() {}
|
|
|
|
template <int OtherOptions>
|
|
EIGEN_DEVICE_FUNC ParametrizedLine(const ParametrizedLine<Scalar, AmbientDimAtCompileTime, OtherOptions>& other)
|
|
: m_origin(other.origin()), m_direction(other.direction()) {}
|
|
|
|
/** Constructs a dynamic-size line with \a _dim the dimension
|
|
* of the ambient space */
|
|
EIGEN_DEVICE_FUNC inline explicit ParametrizedLine(Index _dim) : m_origin(_dim), m_direction(_dim) {}
|
|
|
|
/** Initializes a parametrized line of direction \a direction and origin \a origin.
|
|
* \warning the vector direction is assumed to be normalized.
|
|
*/
|
|
EIGEN_DEVICE_FUNC ParametrizedLine(const VectorType& origin, const VectorType& direction)
|
|
: m_origin(origin), m_direction(direction) {}
|
|
|
|
template <int OtherOptions>
|
|
EIGEN_DEVICE_FUNC explicit ParametrizedLine(const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane);
|
|
|
|
/** Constructs a parametrized line going from \a p0 to \a p1. */
|
|
EIGEN_DEVICE_FUNC static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1) {
|
|
return ParametrizedLine(p0, (p1 - p0).normalized());
|
|
}
|
|
|
|
EIGEN_DEVICE_FUNC ~ParametrizedLine() {}
|
|
|
|
/** \returns the dimension in which the line holds */
|
|
EIGEN_DEVICE_FUNC inline Index dim() const { return m_direction.size(); }
|
|
|
|
EIGEN_DEVICE_FUNC const VectorType& origin() const { return m_origin; }
|
|
EIGEN_DEVICE_FUNC VectorType& origin() { return m_origin; }
|
|
|
|
EIGEN_DEVICE_FUNC const VectorType& direction() const { return m_direction; }
|
|
EIGEN_DEVICE_FUNC VectorType& direction() { return m_direction; }
|
|
|
|
/** \returns the squared distance of a point \a p to its projection onto the line \c *this.
|
|
* \sa distance()
|
|
*/
|
|
EIGEN_DEVICE_FUNC RealScalar squaredDistance(const VectorType& p) const {
|
|
VectorType diff = p - origin();
|
|
return (diff - direction().dot(diff) * direction()).squaredNorm();
|
|
}
|
|
/** \returns the distance of a point \a p to its projection onto the line \c *this.
|
|
* \sa squaredDistance()
|
|
*/
|
|
EIGEN_DEVICE_FUNC RealScalar distance(const VectorType& p) const {
|
|
EIGEN_USING_STD(sqrt) return sqrt(squaredDistance(p));
|
|
}
|
|
|
|
/** \returns the projection of a point \a p onto the line \c *this. */
|
|
EIGEN_DEVICE_FUNC VectorType projection(const VectorType& p) const {
|
|
return origin() + direction().dot(p - origin()) * direction();
|
|
}
|
|
|
|
EIGEN_DEVICE_FUNC VectorType pointAt(const Scalar& t) const;
|
|
|
|
template <int OtherOptions>
|
|
EIGEN_DEVICE_FUNC Scalar
|
|
intersectionParameter(const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) const;
|
|
|
|
template <int OtherOptions>
|
|
EIGEN_DEVICE_FUNC Scalar intersection(const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) const;
|
|
|
|
template <int OtherOptions>
|
|
EIGEN_DEVICE_FUNC VectorType
|
|
intersectionPoint(const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) const;
|
|
|
|
/** Applies the transformation matrix \a mat to \c *this and returns a reference to \c *this.
|
|
*
|
|
* \param mat the Dim x Dim transformation matrix
|
|
* \param traits specifies whether the matrix \a mat represents an #Isometry
|
|
* or a more generic #Affine transformation. The default is #Affine.
|
|
*/
|
|
template <typename XprType>
|
|
EIGEN_DEVICE_FUNC inline ParametrizedLine& transform(const MatrixBase<XprType>& mat,
|
|
TransformTraits traits = Affine) {
|
|
if (traits == Affine)
|
|
direction() = (mat * direction()).normalized();
|
|
else if (traits == Isometry)
|
|
direction() = mat * direction();
|
|
else {
|
|
eigen_assert(0 && "invalid traits value in ParametrizedLine::transform()");
|
|
}
|
|
origin() = mat * origin();
|
|
return *this;
|
|
}
|
|
|
|
/** Applies the transformation \a t to \c *this and returns a reference to \c *this.
|
|
*
|
|
* \param t the transformation of dimension Dim
|
|
* \param traits specifies whether the transformation \a t represents an #Isometry
|
|
* or a more generic #Affine transformation. The default is #Affine.
|
|
* Other kind of transformations are not supported.
|
|
*/
|
|
template <int TrOptions>
|
|
EIGEN_DEVICE_FUNC inline ParametrizedLine& transform(
|
|
const Transform<Scalar, AmbientDimAtCompileTime, Affine, TrOptions>& t, TransformTraits traits = Affine) {
|
|
transform(t.linear(), traits);
|
|
origin() += t.translation();
|
|
return *this;
|
|
}
|
|
|
|
/** \returns \c *this with scalar type casted to \a NewScalarType
|
|
*
|
|
* Note that if \a NewScalarType is equal to the current scalar type of \c *this
|
|
* then this function smartly returns a const reference to \c *this.
|
|
*/
|
|
template <typename NewScalarType>
|
|
EIGEN_DEVICE_FUNC inline
|
|
typename internal::cast_return_type<ParametrizedLine,
|
|
ParametrizedLine<NewScalarType, AmbientDimAtCompileTime, Options> >::type
|
|
cast() const {
|
|
return typename internal::cast_return_type<
|
|
ParametrizedLine, ParametrizedLine<NewScalarType, AmbientDimAtCompileTime, Options> >::type(*this);
|
|
}
|
|
|
|
/** Copy constructor with scalar type conversion */
|
|
template <typename OtherScalarType, int OtherOptions>
|
|
EIGEN_DEVICE_FUNC inline explicit ParametrizedLine(
|
|
const ParametrizedLine<OtherScalarType, AmbientDimAtCompileTime, OtherOptions>& other) {
|
|
m_origin = other.origin().template cast<Scalar>();
|
|
m_direction = other.direction().template cast<Scalar>();
|
|
}
|
|
|
|
/** \returns \c true if \c *this is approximately equal to \a other, within the precision
|
|
* determined by \a prec.
|
|
*
|
|
* \sa MatrixBase::isApprox() */
|
|
EIGEN_DEVICE_FUNC bool isApprox(const ParametrizedLine& other, const typename NumTraits<Scalar>::Real& prec =
|
|
NumTraits<Scalar>::dummy_precision()) const {
|
|
return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec);
|
|
}
|
|
|
|
protected:
|
|
VectorType m_origin, m_direction;
|
|
};
|
|
|
|
/** Constructs a parametrized line from a 2D hyperplane
|
|
*
|
|
* \warning the ambient space must have dimension 2 such that the hyperplane actually describes a line
|
|
*/
|
|
template <typename Scalar_, int AmbientDim_, int Options_>
|
|
template <int OtherOptions>
|
|
EIGEN_DEVICE_FUNC inline ParametrizedLine<Scalar_, AmbientDim_, Options_>::ParametrizedLine(
|
|
const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) {
|
|
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
|
|
direction() = hyperplane.normal().unitOrthogonal();
|
|
origin() = -hyperplane.normal() * hyperplane.offset();
|
|
}
|
|
|
|
/** \returns the point at \a t along this line
|
|
*/
|
|
template <typename Scalar_, int AmbientDim_, int Options_>
|
|
EIGEN_DEVICE_FUNC inline typename ParametrizedLine<Scalar_, AmbientDim_, Options_>::VectorType
|
|
ParametrizedLine<Scalar_, AmbientDim_, Options_>::pointAt(const Scalar_& t) const {
|
|
return origin() + (direction() * t);
|
|
}
|
|
|
|
/** \returns the parameter value of the intersection between \c *this and the given \a hyperplane
|
|
*/
|
|
template <typename Scalar_, int AmbientDim_, int Options_>
|
|
template <int OtherOptions>
|
|
EIGEN_DEVICE_FUNC inline Scalar_ ParametrizedLine<Scalar_, AmbientDim_, Options_>::intersectionParameter(
|
|
const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) const {
|
|
return -(hyperplane.offset() + hyperplane.normal().dot(origin())) / hyperplane.normal().dot(direction());
|
|
}
|
|
|
|
/** \deprecated use intersectionParameter()
|
|
* \returns the parameter value of the intersection between \c *this and the given \a hyperplane
|
|
*/
|
|
template <typename Scalar_, int AmbientDim_, int Options_>
|
|
template <int OtherOptions>
|
|
EIGEN_DEVICE_FUNC inline Scalar_ ParametrizedLine<Scalar_, AmbientDim_, Options_>::intersection(
|
|
const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) const {
|
|
return intersectionParameter(hyperplane);
|
|
}
|
|
|
|
/** \returns the point of the intersection between \c *this and the given hyperplane
|
|
*/
|
|
template <typename Scalar_, int AmbientDim_, int Options_>
|
|
template <int OtherOptions>
|
|
EIGEN_DEVICE_FUNC inline typename ParametrizedLine<Scalar_, AmbientDim_, Options_>::VectorType
|
|
ParametrizedLine<Scalar_, AmbientDim_, Options_>::intersectionPoint(
|
|
const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) const {
|
|
return pointAt(intersectionParameter(hyperplane));
|
|
}
|
|
|
|
} // end namespace Eigen
|
|
|
|
#endif // EIGEN_PARAMETRIZEDLINE_H
|