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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_HYPERPLANE_H
- #define EIGEN_HYPERPLANE_H
- namespace Eigen {
- /** \geometry_module \ingroup Geometry_Module
- *
- * \class Hyperplane
- *
- * \brief A hyperplane
- *
- * A hyperplane is an affine subspace of dimension n-1 in a space of dimension n.
- * For example, a hyperplane in a plane is a line; a hyperplane in 3-space is a plane.
- *
- * \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.
- * Notice that the dimension of the hyperplane is _AmbientDim-1.
- *
- * This class represents an hyperplane as the zero set of the implicit equation
- * \f$ n \cdot x + d = 0 \f$ where \f$ n \f$ is a unit normal vector of the plane (linear part)
- * and \f$ d \f$ is the distance (offset) to the origin.
- */
- template <typename _Scalar, int _AmbientDim, int _Options>
- class Hyperplane
- {
- public:
- EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim==Dynamic ? Dynamic : _AmbientDim+1)
- 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> VectorType;
- typedef Matrix<Scalar,Index(AmbientDimAtCompileTime)==Dynamic
- ? Dynamic
- : Index(AmbientDimAtCompileTime)+1,1,Options> Coefficients;
- typedef Block<Coefficients,AmbientDimAtCompileTime,1> NormalReturnType;
- typedef const Block<const Coefficients,AmbientDimAtCompileTime,1> ConstNormalReturnType;
- /** Default constructor without initialization */
- EIGEN_DEVICE_FUNC inline Hyperplane() {}
-
- template<int OtherOptions>
- EIGEN_DEVICE_FUNC Hyperplane(const Hyperplane<Scalar,AmbientDimAtCompileTime,OtherOptions>& other)
- : m_coeffs(other.coeffs())
- {}
- /** Constructs a dynamic-size hyperplane with \a _dim the dimension
- * of the ambient space */
- EIGEN_DEVICE_FUNC inline explicit Hyperplane(Index _dim) : m_coeffs(_dim+1) {}
- /** Construct a plane from its normal \a n and a point \a e onto the plane.
- * \warning the vector normal is assumed to be normalized.
- */
- EIGEN_DEVICE_FUNC inline Hyperplane(const VectorType& n, const VectorType& e)
- : m_coeffs(n.size()+1)
- {
- normal() = n;
- offset() = -n.dot(e);
- }
- /** Constructs a plane from its normal \a n and distance to the origin \a d
- * such that the algebraic equation of the plane is \f$ n \cdot x + d = 0 \f$.
- * \warning the vector normal is assumed to be normalized.
- */
- EIGEN_DEVICE_FUNC inline Hyperplane(const VectorType& n, const Scalar& d)
- : m_coeffs(n.size()+1)
- {
- normal() = n;
- offset() = d;
- }
- /** Constructs a hyperplane passing through the two points. If the dimension of the ambient space
- * is greater than 2, then there isn't uniqueness, so an arbitrary choice is made.
- */
- EIGEN_DEVICE_FUNC static inline Hyperplane Through(const VectorType& p0, const VectorType& p1)
- {
- Hyperplane result(p0.size());
- result.normal() = (p1 - p0).unitOrthogonal();
- result.offset() = -p0.dot(result.normal());
- return result;
- }
- /** Constructs a hyperplane passing through the three points. The dimension of the ambient space
- * is required to be exactly 3.
- */
- EIGEN_DEVICE_FUNC static inline Hyperplane Through(const VectorType& p0, const VectorType& p1, const VectorType& p2)
- {
- EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3)
- Hyperplane result(p0.size());
- VectorType v0(p2 - p0), v1(p1 - p0);
- result.normal() = v0.cross(v1);
- RealScalar norm = result.normal().norm();
- if(norm <= v0.norm() * v1.norm() * NumTraits<RealScalar>::epsilon())
- {
- Matrix<Scalar,2,3> m; m << v0.transpose(), v1.transpose();
- JacobiSVD<Matrix<Scalar,2,3> > svd(m, ComputeFullV);
- result.normal() = svd.matrixV().col(2);
- }
- else
- result.normal() /= norm;
- result.offset() = -p0.dot(result.normal());
- return result;
- }
- /** Constructs a hyperplane passing through the parametrized line \a parametrized.
- * If the dimension of the ambient space is greater than 2, then there isn't uniqueness,
- * so an arbitrary choice is made.
- */
- // FIXME to be consitent with the rest this could be implemented as a static Through function ??
- EIGEN_DEVICE_FUNC explicit Hyperplane(const ParametrizedLine<Scalar, AmbientDimAtCompileTime>& parametrized)
- {
- normal() = parametrized.direction().unitOrthogonal();
- offset() = -parametrized.origin().dot(normal());
- }
- EIGEN_DEVICE_FUNC ~Hyperplane() {}
- /** \returns the dimension in which the plane holds */
- EIGEN_DEVICE_FUNC inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_coeffs.size()-1 : Index(AmbientDimAtCompileTime); }
- /** normalizes \c *this */
- EIGEN_DEVICE_FUNC void normalize(void)
- {
- m_coeffs /= normal().norm();
- }
- /** \returns the signed distance between the plane \c *this and a point \a p.
- * \sa absDistance()
- */
- EIGEN_DEVICE_FUNC inline Scalar signedDistance(const VectorType& p) const { return normal().dot(p) + offset(); }
- /** \returns the absolute distance between the plane \c *this and a point \a p.
- * \sa signedDistance()
- */
- EIGEN_DEVICE_FUNC inline Scalar absDistance(const VectorType& p) const { return numext::abs(signedDistance(p)); }
- /** \returns the projection of a point \a p onto the plane \c *this.
- */
- EIGEN_DEVICE_FUNC inline VectorType projection(const VectorType& p) const { return p - signedDistance(p) * normal(); }
- /** \returns a constant reference to the unit normal vector of the plane, which corresponds
- * to the linear part of the implicit equation.
- */
- EIGEN_DEVICE_FUNC inline ConstNormalReturnType normal() const { return ConstNormalReturnType(m_coeffs,0,0,dim(),1); }
- /** \returns a non-constant reference to the unit normal vector of the plane, which corresponds
- * to the linear part of the implicit equation.
- */
- EIGEN_DEVICE_FUNC inline NormalReturnType normal() { return NormalReturnType(m_coeffs,0,0,dim(),1); }
- /** \returns the distance to the origin, which is also the "constant term" of the implicit equation
- * \warning the vector normal is assumed to be normalized.
- */
- EIGEN_DEVICE_FUNC inline const Scalar& offset() const { return m_coeffs.coeff(dim()); }
- /** \returns a non-constant reference to the distance to the origin, which is also the constant part
- * of the implicit equation */
- EIGEN_DEVICE_FUNC inline Scalar& offset() { return m_coeffs(dim()); }
- /** \returns a constant reference to the coefficients c_i of the plane equation:
- * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
- */
- EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs; }
- /** \returns a non-constant reference to the coefficients c_i of the plane equation:
- * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
- */
- EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs; }
- /** \returns the intersection of *this with \a other.
- *
- * \warning The ambient space must be a plane, i.e. have dimension 2, so that \c *this and \a other are lines.
- *
- * \note If \a other is approximately parallel to *this, this method will return any point on *this.
- */
- EIGEN_DEVICE_FUNC VectorType intersection(const Hyperplane& other) const
- {
- EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
- Scalar det = coeffs().coeff(0) * other.coeffs().coeff(1) - coeffs().coeff(1) * other.coeffs().coeff(0);
- // since the line equations ax+by=c are normalized with a^2+b^2=1, the following tests
- // whether the two lines are approximately parallel.
- if(internal::isMuchSmallerThan(det, Scalar(1)))
- { // special case where the two lines are approximately parallel. Pick any point on the first line.
- if(numext::abs(coeffs().coeff(1))>numext::abs(coeffs().coeff(0)))
- return VectorType(coeffs().coeff(1), -coeffs().coeff(2)/coeffs().coeff(1)-coeffs().coeff(0));
- else
- return VectorType(-coeffs().coeff(2)/coeffs().coeff(0)-coeffs().coeff(1), coeffs().coeff(0));
- }
- else
- { // general case
- Scalar invdet = Scalar(1) / det;
- return VectorType(invdet*(coeffs().coeff(1)*other.coeffs().coeff(2)-other.coeffs().coeff(1)*coeffs().coeff(2)),
- invdet*(other.coeffs().coeff(0)*coeffs().coeff(2)-coeffs().coeff(0)*other.coeffs().coeff(2)));
- }
- }
- /** 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 Hyperplane& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine)
- {
- if (traits==Affine)
- {
- normal() = mat.inverse().transpose() * normal();
- m_coeffs /= normal().norm();
- }
- else if (traits==Isometry)
- normal() = mat * normal();
- else
- {
- eigen_assert(0 && "invalid traits value in Hyperplane::transform()");
- }
- 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 Hyperplane& transform(const Transform<Scalar,AmbientDimAtCompileTime,Affine,TrOptions>& t,
- TransformTraits traits = Affine)
- {
- transform(t.linear(), traits);
- offset() -= normal().dot(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<Hyperplane,
- Hyperplane<NewScalarType,AmbientDimAtCompileTime,Options> >::type cast() const
- {
- return typename internal::cast_return_type<Hyperplane,
- Hyperplane<NewScalarType,AmbientDimAtCompileTime,Options> >::type(*this);
- }
- /** Copy constructor with scalar type conversion */
- template<typename OtherScalarType,int OtherOptions>
- EIGEN_DEVICE_FUNC inline explicit Hyperplane(const Hyperplane<OtherScalarType,AmbientDimAtCompileTime,OtherOptions>& other)
- { m_coeffs = other.coeffs().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() */
- template<int OtherOptions>
- EIGEN_DEVICE_FUNC bool isApprox(const Hyperplane<Scalar,AmbientDimAtCompileTime,OtherOptions>& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
- { return m_coeffs.isApprox(other.m_coeffs, prec); }
- protected:
- Coefficients m_coeffs;
- };
- } // end namespace Eigen
- #endif // EIGEN_HYPERPLANE_H
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