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ParametrizedLine.h
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ParametrizedLine.h
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// 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
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$.
*
* \param _Scalar the scalar type, i.e., the type of the coefficients
* \param _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 DenseIndex Index;
typedef Matrix<Scalar,AmbientDimAtCompileTime,1,Options> VectorType;
/** Default constructor without initialization */
inline ParametrizedLine() {}
template<int OtherOptions>
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 */
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.
*/
ParametrizedLine(const VectorType& origin, const VectorType& direction)
: m_origin(origin), m_direction(direction) {}
template <int OtherOptions>
explicit ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane);
/** Constructs a parametrized line going from \a p0 to \a p1. */
static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1)
{ return ParametrizedLine(p0, (p1-p0).normalized()); }
~ParametrizedLine() {}
/** \returns the dimension in which the line holds */
inline Index dim() const { return m_direction.size(); }
const VectorType& origin() const { return m_origin; }
VectorType& origin() { return m_origin; }
const VectorType& direction() const { return m_direction; }
VectorType& direction() { return m_direction; }
/** \returns the squared distance of a point \a p to its projection onto the line \c *this.
* \sa distance()
*/
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()
*/
RealScalar distance(const VectorType& p) const { using std::sqrt; return sqrt(squaredDistance(p)); }
/** \returns the projection of a point \a p onto the line \c *this. */
VectorType projection(const VectorType& p) const
{ return origin() + direction().dot(p-origin()) * direction(); }
VectorType pointAt(const Scalar& t) const;
template <int OtherOptions>
Scalar intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;
template <int OtherOptions>
Scalar intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;
template <int OtherOptions>
VectorType intersectionPoint(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;
/** \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>
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>
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() */
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>
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>
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>
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>
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>
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

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