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375 lines
12 KiB
375 lines
12 KiB
// This file is part of Eigen, a lightweight C++ template library |
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// for linear algebra. |
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// |
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// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> |
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// |
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// This Source Code Form is subject to the terms of the Mozilla |
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// Public License v. 2.0. If a copy of the MPL was not distributed |
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. |
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#ifndef EIGEN_ALIGNEDBOX_H |
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#define EIGEN_ALIGNEDBOX_H |
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namespace Eigen { |
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/** \geometry_module \ingroup Geometry_Module |
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* |
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* |
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* \class AlignedBox |
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* |
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* \brief An axis aligned box |
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* |
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* \param _Scalar the type of the scalar coefficients |
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* \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic. |
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* |
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* This class represents an axis aligned box as a pair of the minimal and maximal corners. |
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*/ |
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template <typename _Scalar, int _AmbientDim> |
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class AlignedBox |
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{ |
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public: |
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EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim) |
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enum { AmbientDimAtCompileTime = _AmbientDim }; |
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typedef _Scalar Scalar; |
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typedef NumTraits<Scalar> ScalarTraits; |
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typedef DenseIndex Index; |
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typedef typename ScalarTraits::Real RealScalar; |
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typedef typename ScalarTraits::NonInteger NonInteger; |
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typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType; |
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/** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */ |
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enum CornerType |
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{ |
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/** 1D names */ |
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Min=0, Max=1, |
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/** Added names for 2D */ |
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BottomLeft=0, BottomRight=1, |
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TopLeft=2, TopRight=3, |
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/** Added names for 3D */ |
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BottomLeftFloor=0, BottomRightFloor=1, |
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TopLeftFloor=2, TopRightFloor=3, |
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BottomLeftCeil=4, BottomRightCeil=5, |
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TopLeftCeil=6, TopRightCeil=7 |
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}; |
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/** Default constructor initializing a null box. */ |
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inline AlignedBox() |
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{ if (AmbientDimAtCompileTime!=Dynamic) setEmpty(); } |
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/** Constructs a null box with \a _dim the dimension of the ambient space. */ |
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inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim) |
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{ setEmpty(); } |
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/** Constructs a box with extremities \a _min and \a _max. */ |
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template<typename OtherVectorType1, typename OtherVectorType2> |
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inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max) : m_min(_min), m_max(_max) {} |
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/** Constructs a box containing a single point \a p. */ |
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template<typename Derived> |
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inline explicit AlignedBox(const MatrixBase<Derived>& a_p) |
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{ |
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typename internal::nested<Derived,2>::type p(a_p.derived()); |
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m_min = p; |
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m_max = p; |
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} |
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~AlignedBox() {} |
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/** \returns the dimension in which the box holds */ |
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inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime); } |
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/** \deprecated use isEmpty */ |
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inline bool isNull() const { return isEmpty(); } |
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/** \deprecated use setEmpty */ |
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inline void setNull() { setEmpty(); } |
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/** \returns true if the box is empty. */ |
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inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); } |
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/** Makes \c *this an empty box. */ |
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inline void setEmpty() |
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{ |
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m_min.setConstant( ScalarTraits::highest() ); |
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m_max.setConstant( ScalarTraits::lowest() ); |
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} |
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/** \returns the minimal corner */ |
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inline const VectorType& (min)() const { return m_min; } |
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/** \returns a non const reference to the minimal corner */ |
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inline VectorType& (min)() { return m_min; } |
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/** \returns the maximal corner */ |
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inline const VectorType& (max)() const { return m_max; } |
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/** \returns a non const reference to the maximal corner */ |
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inline VectorType& (max)() { return m_max; } |
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/** \returns the center of the box */ |
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inline const CwiseUnaryOp<internal::scalar_quotient1_op<Scalar>, |
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const CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> > |
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center() const |
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{ return (m_min+m_max)/2; } |
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/** \returns the lengths of the sides of the bounding box. |
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* Note that this function does not get the same |
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* result for integral or floating scalar types: see |
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*/ |
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inline const CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType, const VectorType> sizes() const |
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{ return m_max - m_min; } |
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/** \returns the volume of the bounding box */ |
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inline Scalar volume() const |
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{ return sizes().prod(); } |
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/** \returns an expression for the bounding box diagonal vector |
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* if the length of the diagonal is needed: diagonal().norm() |
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* will provide it. |
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*/ |
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inline CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType, const VectorType> diagonal() const |
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{ return sizes(); } |
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/** \returns the vertex of the bounding box at the corner defined by |
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* the corner-id corner. It works only for a 1D, 2D or 3D bounding box. |
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* For 1D bounding boxes corners are named by 2 enum constants: |
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* BottomLeft and BottomRight. |
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* For 2D bounding boxes, corners are named by 4 enum constants: |
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* BottomLeft, BottomRight, TopLeft, TopRight. |
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* For 3D bounding boxes, the following names are added: |
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* BottomLeftCeil, BottomRightCeil, TopLeftCeil, TopRightCeil. |
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*/ |
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inline VectorType corner(CornerType corner) const |
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{ |
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EIGEN_STATIC_ASSERT(_AmbientDim <= 3, THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE); |
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VectorType res; |
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Index mult = 1; |
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for(Index d=0; d<dim(); ++d) |
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{ |
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if( mult & corner ) res[d] = m_max[d]; |
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else res[d] = m_min[d]; |
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mult *= 2; |
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} |
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return res; |
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} |
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/** \returns a random point inside the bounding box sampled with |
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* a uniform distribution */ |
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inline VectorType sample() const |
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{ |
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VectorType r; |
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for(Index d=0; d<dim(); ++d) |
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{ |
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if(!ScalarTraits::IsInteger) |
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{ |
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r[d] = m_min[d] + (m_max[d]-m_min[d]) |
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* internal::random<Scalar>(Scalar(0), Scalar(1)); |
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} |
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else |
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r[d] = internal::random(m_min[d], m_max[d]); |
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} |
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return r; |
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} |
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/** \returns true if the point \a p is inside the box \c *this. */ |
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template<typename Derived> |
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inline bool contains(const MatrixBase<Derived>& a_p) const |
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{ |
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typename internal::nested<Derived,2>::type p(a_p.derived()); |
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return (m_min.array()<=p.array()).all() && (p.array()<=m_max.array()).all(); |
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} |
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/** \returns true if the box \a b is entirely inside the box \c *this. */ |
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inline bool contains(const AlignedBox& b) const |
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{ return (m_min.array()<=(b.min)().array()).all() && ((b.max)().array()<=m_max.array()).all(); } |
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/** Extends \c *this such that it contains the point \a p and returns a reference to \c *this. */ |
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template<typename Derived> |
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inline AlignedBox& extend(const MatrixBase<Derived>& a_p) |
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{ |
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typename internal::nested<Derived,2>::type p(a_p.derived()); |
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m_min = m_min.cwiseMin(p); |
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m_max = m_max.cwiseMax(p); |
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return *this; |
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} |
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/** Extends \c *this such that it contains the box \a b and returns a reference to \c *this. */ |
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inline AlignedBox& extend(const AlignedBox& b) |
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{ |
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m_min = m_min.cwiseMin(b.m_min); |
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m_max = m_max.cwiseMax(b.m_max); |
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return *this; |
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} |
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/** Clamps \c *this by the box \a b and returns a reference to \c *this. */ |
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inline AlignedBox& clamp(const AlignedBox& b) |
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{ |
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m_min = m_min.cwiseMax(b.m_min); |
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m_max = m_max.cwiseMin(b.m_max); |
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return *this; |
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} |
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/** Returns an AlignedBox that is the intersection of \a b and \c *this */ |
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inline AlignedBox intersection(const AlignedBox& b) const |
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{return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); } |
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/** Returns an AlignedBox that is the union of \a b and \c *this */ |
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inline AlignedBox merged(const AlignedBox& b) const |
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{ return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); } |
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/** Translate \c *this by the vector \a t and returns a reference to \c *this. */ |
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template<typename Derived> |
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inline AlignedBox& translate(const MatrixBase<Derived>& a_t) |
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{ |
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const typename internal::nested<Derived,2>::type t(a_t.derived()); |
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m_min += t; |
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m_max += t; |
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return *this; |
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} |
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/** \returns the squared distance between the point \a p and the box \c *this, |
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* and zero if \a p is inside the box. |
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* \sa exteriorDistance() |
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*/ |
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template<typename Derived> |
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inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& a_p) const; |
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/** \returns the squared distance between the boxes \a b and \c *this, |
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* and zero if the boxes intersect. |
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* \sa exteriorDistance() |
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*/ |
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inline Scalar squaredExteriorDistance(const AlignedBox& b) const; |
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/** \returns the distance between the point \a p and the box \c *this, |
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* and zero if \a p is inside the box. |
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* \sa squaredExteriorDistance() |
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*/ |
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template<typename Derived> |
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inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const |
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{ using std::sqrt; return sqrt(NonInteger(squaredExteriorDistance(p))); } |
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/** \returns the distance between the boxes \a b and \c *this, |
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* and zero if the boxes intersect. |
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* \sa squaredExteriorDistance() |
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*/ |
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inline NonInteger exteriorDistance(const AlignedBox& b) const |
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{ using std::sqrt; return sqrt(NonInteger(squaredExteriorDistance(b))); } |
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/** \returns \c *this with scalar type casted to \a NewScalarType |
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* |
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* Note that if \a NewScalarType is equal to the current scalar type of \c *this |
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* then this function smartly returns a const reference to \c *this. |
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*/ |
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template<typename NewScalarType> |
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inline typename internal::cast_return_type<AlignedBox, |
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AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const |
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{ |
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return typename internal::cast_return_type<AlignedBox, |
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AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this); |
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} |
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/** Copy constructor with scalar type conversion */ |
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template<typename OtherScalarType> |
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inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other) |
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{ |
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m_min = (other.min)().template cast<Scalar>(); |
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m_max = (other.max)().template cast<Scalar>(); |
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} |
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/** \returns \c true if \c *this is approximately equal to \a other, within the precision |
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* determined by \a prec. |
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* |
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* \sa MatrixBase::isApprox() */ |
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bool isApprox(const AlignedBox& other, const RealScalar& prec = ScalarTraits::dummy_precision()) const |
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{ return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); } |
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protected: |
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VectorType m_min, m_max; |
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}; |
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template<typename Scalar,int AmbientDim> |
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template<typename Derived> |
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inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const MatrixBase<Derived>& a_p) const |
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{ |
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typename internal::nested<Derived,2*AmbientDim>::type p(a_p.derived()); |
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Scalar dist2(0); |
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Scalar aux; |
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for (Index k=0; k<dim(); ++k) |
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{ |
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if( m_min[k] > p[k] ) |
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{ |
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aux = m_min[k] - p[k]; |
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dist2 += aux*aux; |
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} |
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else if( p[k] > m_max[k] ) |
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{ |
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aux = p[k] - m_max[k]; |
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dist2 += aux*aux; |
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} |
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} |
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return dist2; |
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} |
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template<typename Scalar,int AmbientDim> |
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inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const AlignedBox& b) const |
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{ |
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Scalar dist2(0); |
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Scalar aux; |
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for (Index k=0; k<dim(); ++k) |
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{ |
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if( m_min[k] > b.m_max[k] ) |
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{ |
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aux = m_min[k] - b.m_max[k]; |
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dist2 += aux*aux; |
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} |
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else if( b.m_min[k] > m_max[k] ) |
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{ |
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aux = b.m_min[k] - m_max[k]; |
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dist2 += aux*aux; |
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} |
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} |
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return dist2; |
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} |
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/** \defgroup alignedboxtypedefs Global aligned box typedefs |
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* |
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* \ingroup Geometry_Module |
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* |
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* Eigen defines several typedef shortcuts for most common aligned box types. |
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* |
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* The general patterns are the following: |
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* |
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* \c AlignedBoxSizeType where \c Size can be \c 1, \c 2,\c 3,\c 4 for fixed size boxes or \c X for dynamic size, |
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* and where \c Type can be \c i for integer, \c f for float, \c d for double. |
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* |
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* For example, \c AlignedBox3d is a fixed-size 3x3 aligned box type of doubles, and \c AlignedBoxXf is a dynamic-size aligned box of floats. |
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* |
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* \sa class AlignedBox |
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*/ |
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#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \ |
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/** \ingroup alignedboxtypedefs */ \ |
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typedef AlignedBox<Type, Size> AlignedBox##SizeSuffix##TypeSuffix; |
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#define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \ |
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EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 1, 1) \ |
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EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \ |
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EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \ |
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EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \ |
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EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X) |
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EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i) |
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EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f) |
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EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d) |
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#undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES |
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#undef EIGEN_MAKE_TYPEDEFS |
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} // end namespace Eigen |
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#endif // EIGEN_ALIGNEDBOX_H
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