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Edit File: AlignedBox.h

// This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> // // 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/. // Function void Eigen::AlignedBox::transform(const Transform& transform) // is provided under the following license agreement: // // Software License Agreement (BSD License) // // Copyright (c) 2011-2014, Willow Garage, Inc. // Copyright (c) 2014-2015, Open Source Robotics Foundation // All rights reserved. // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions // are met: // // * Redistributions of source code must retain the above copyright // notice, this list of conditions and the following disclaimer. // * Redistributions in binary form must reproduce the above // copyright notice, this list of conditions and the following // disclaimer in the documentation and/or other materials provided // with the distribution. // * Neither the name of Open Source Robotics Foundation nor the names of its // contributors may be used to endorse or promote products derived // from this software without specific prior written permission. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS // FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE // COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, // INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, // BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; // LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER // CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT // LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN // ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE // POSSIBILITY OF SUCH DAMAGE. #ifndef EIGEN_ALIGNEDBOX_H #define EIGEN_ALIGNEDBOX_H namespace Eigen { /** \geometry_module \ingroup Geometry_Module * * * \class AlignedBox * * \brief An axis aligned box * * \tparam _Scalar the type of the scalar coefficients * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic. * * This class represents an axis aligned box as a pair of the minimal and maximal corners. * \warning The result of most methods is undefined when applied to an empty box. You can check for empty boxes using isEmpty(). * \sa alignedboxtypedefs */ template <typename _Scalar, int _AmbientDim> class AlignedBox { public: EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim) enum { AmbientDimAtCompileTime = _AmbientDim }; typedef _Scalar Scalar; typedef NumTraits<Scalar> ScalarTraits; typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3 typedef typename ScalarTraits::Real RealScalar; typedef typename ScalarTraits::NonInteger NonInteger; typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType; typedef CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> VectorTypeSum; /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */ enum CornerType { /** 1D names @{ */ Min=0, Max=1, /** @} */ /** Identifier for 2D corner @{ */ BottomLeft=0, BottomRight=1, TopLeft=2, TopRight=3, /** @} */ /** Identifier for 3D corner @{ */ BottomLeftFloor=0, BottomRightFloor=1, TopLeftFloor=2, TopRightFloor=3, BottomLeftCeil=4, BottomRightCeil=5, TopLeftCeil=6, TopRightCeil=7 /** @} */ }; /** Default constructor initializing a null box. */ EIGEN_DEVICE_FUNC inline AlignedBox() { if (EIGEN_CONST_CONDITIONAL(AmbientDimAtCompileTime!=Dynamic)) setEmpty(); } /** Constructs a null box with \a _dim the dimension of the ambient space. */ EIGEN_DEVICE_FUNC inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim) { setEmpty(); } /** Constructs a box with extremities \a _min and \a _max. * \warning If either component of \a _min is larger than the same component of \a _max, the constructed box is empty. */ template<typename OtherVectorType1, typename OtherVectorType2> EIGEN_DEVICE_FUNC inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max) : m_min(_min), m_max(_max) {} /** Constructs a box containing a single point \a p. */ template<typename Derived> EIGEN_DEVICE_FUNC inline explicit AlignedBox(const MatrixBase<Derived>& p) : m_min(p), m_max(m_min) { } EIGEN_DEVICE_FUNC ~AlignedBox() {} /** \returns the dimension in which the box holds */ EIGEN_DEVICE_FUNC inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime); } /** \deprecated use isEmpty() */ EIGEN_DEVICE_FUNC inline bool isNull() const { return isEmpty(); } /** \deprecated use setEmpty() */ EIGEN_DEVICE_FUNC inline void setNull() { setEmpty(); } /** \returns true if the box is empty. * \sa setEmpty */ EIGEN_DEVICE_FUNC inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); } /** Makes \c *this an empty box. * \sa isEmpty */ EIGEN_DEVICE_FUNC inline void setEmpty() { m_min.setConstant( ScalarTraits::highest() ); m_max.setConstant( ScalarTraits::lowest() ); } /** \returns the minimal corner */ EIGEN_DEVICE_FUNC inline const VectorType& (min)() const { return m_min; } /** \returns a non const reference to the minimal corner */ EIGEN_DEVICE_FUNC inline VectorType& (min)() { return m_min; } /** \returns the maximal corner */ EIGEN_DEVICE_FUNC inline const VectorType& (max)() const { return m_max; } /** \returns a non const reference to the maximal corner */ EIGEN_DEVICE_FUNC inline VectorType& (max)() { return m_max; } /** \returns the center of the box */ EIGEN_DEVICE_FUNC inline const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(VectorTypeSum, RealScalar, quotient) center() const { return (m_min+m_max)/RealScalar(2); } /** \returns the lengths of the sides of the bounding box. * Note that this function does not get the same * result for integral or floating scalar types: see */ EIGEN_DEVICE_FUNC inline const CwiseBinaryOp< internal::scalar_difference_op<Scalar,Scalar>, const VectorType, const VectorType> sizes() const { return m_max - m_min; } /** \returns the volume of the bounding box */ EIGEN_DEVICE_FUNC inline Scalar volume() const { return sizes().prod(); } /** \returns an expression for the bounding box diagonal vector * if the length of the diagonal is needed: diagonal().norm() * will provide it. */ EIGEN_DEVICE_FUNC inline CwiseBinaryOp< internal::scalar_difference_op<Scalar,Scalar>, const VectorType, const VectorType> diagonal() const { return sizes(); } /** \returns the vertex of the bounding box at the corner defined by * the corner-id corner. It works only for a 1D, 2D or 3D bounding box. * For 1D bounding boxes corners are named by 2 enum constants: * BottomLeft and BottomRight. * For 2D bounding boxes, corners are named by 4 enum constants: * BottomLeft, BottomRight, TopLeft, TopRight. * For 3D bounding boxes, the following names are added: * BottomLeftCeil, BottomRightCeil, TopLeftCeil, TopRightCeil. */ EIGEN_DEVICE_FUNC inline VectorType corner(CornerType corner) const { EIGEN_STATIC_ASSERT(_AmbientDim <= 3, THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE); VectorType res; Index mult = 1; for(Index d=0; d<dim(); ++d) { if( mult & corner ) res[d] = m_max[d]; else res[d] = m_min[d]; mult *= 2; } return res; } /** \returns a random point inside the bounding box sampled with * a uniform distribution */ EIGEN_DEVICE_FUNC inline VectorType sample() const { VectorType r(dim()); for(Index d=0; d<dim(); ++d) { if(!ScalarTraits::IsInteger) { r[d] = m_min[d] + (m_max[d]-m_min[d]) * internal::random<Scalar>(Scalar(0), Scalar(1)); } else r[d] = internal::random(m_min[d], m_max[d]); } return r; } /** \returns true if the point \a p is inside the box \c *this. */ template<typename Derived> EIGEN_DEVICE_FUNC inline bool contains(const MatrixBase<Derived>& p) const { typename internal::nested_eval<Derived,2>::type p_n(p.derived()); return (m_min.array()<=p_n.array()).all() && (p_n.array()<=m_max.array()).all(); } /** \returns true if the box \a b is entirely inside the box \c *this. */ EIGEN_DEVICE_FUNC inline bool contains(const AlignedBox& b) const { return (m_min.array()<=(b.min)().array()).all() && ((b.max)().array()<=m_max.array()).all(); } /** \returns true if the box \a b is intersecting the box \c *this. * \sa intersection, clamp */ EIGEN_DEVICE_FUNC inline bool intersects(const AlignedBox& b) const { return (m_min.array()<=(b.max)().array()).all() && ((b.min)().array()<=m_max.array()).all(); } /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this. * \sa extend(const AlignedBox&) */ template<typename Derived> EIGEN_DEVICE_FUNC inline AlignedBox& extend(const MatrixBase<Derived>& p) { typename internal::nested_eval<Derived,2>::type p_n(p.derived()); m_min = m_min.cwiseMin(p_n); m_max = m_max.cwiseMax(p_n); return *this; } /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this. * \sa merged, extend(const MatrixBase&) */ EIGEN_DEVICE_FUNC inline AlignedBox& extend(const AlignedBox& b) { m_min = m_min.cwiseMin(b.m_min); m_max = m_max.cwiseMax(b.m_max); return *this; } /** Clamps \c *this by the box \a b and returns a reference to \c *this. * \note If the boxes don't intersect, the resulting box is empty. * \sa intersection(), intersects() */ EIGEN_DEVICE_FUNC inline AlignedBox& clamp(const AlignedBox& b) { m_min = m_min.cwiseMax(b.m_min); m_max = m_max.cwiseMin(b.m_max); return *this; } /** Returns an AlignedBox that is the intersection of \a b and \c *this * \note If the boxes don't intersect, the resulting box is empty. * \sa intersects(), clamp, contains() */ EIGEN_DEVICE_FUNC inline AlignedBox intersection(const AlignedBox& b) const {return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); } /** Returns an AlignedBox that is the union of \a b and \c *this. * \note Merging with an empty box may result in a box bigger than \c *this. * \sa extend(const AlignedBox&) */ EIGEN_DEVICE_FUNC inline AlignedBox merged(const AlignedBox& b) const { return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); } /** Translate \c *this by the vector \a t and returns a reference to \c *this. */ template<typename Derived> EIGEN_DEVICE_FUNC inline AlignedBox& translate(const MatrixBase<Derived>& a_t) { const typename internal::nested_eval<Derived,2>::type t(a_t.derived()); m_min += t; m_max += t; return *this; } /** \returns a copy of \c *this translated by the vector \a t. */ template<typename Derived> EIGEN_DEVICE_FUNC inline AlignedBox translated(const MatrixBase<Derived>& a_t) const { AlignedBox result(m_min, m_max); result.translate(a_t); return result; } /** \returns the squared distance between the point \a p and the box \c *this, * and zero if \a p is inside the box. * \sa exteriorDistance(const MatrixBase&), squaredExteriorDistance(const AlignedBox&) */ template<typename Derived> EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& p) const; /** \returns the squared distance between the boxes \a b and \c *this, * and zero if the boxes intersect. * \sa exteriorDistance(const AlignedBox&), squaredExteriorDistance(const MatrixBase&) */ EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const AlignedBox& b) const; /** \returns the distance between the point \a p and the box \c *this, * and zero if \a p is inside the box. * \sa squaredExteriorDistance(const MatrixBase&), exteriorDistance(const AlignedBox&) */ template<typename Derived> EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const { EIGEN_USING_STD(sqrt) return sqrt(NonInteger(squaredExteriorDistance(p))); } /** \returns the distance between the boxes \a b and \c *this, * and zero if the boxes intersect. * \sa squaredExteriorDistance(const AlignedBox&), exteriorDistance(const MatrixBase&) */ EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const AlignedBox& b) const { EIGEN_USING_STD(sqrt) return sqrt(NonInteger(squaredExteriorDistance(b))); } /** * Specialization of transform for pure translation. */ template<int Mode, int Options> EIGEN_DEVICE_FUNC inline void transform( const typename Transform<Scalar, AmbientDimAtCompileTime, Mode, Options>::TranslationType& translation) { this->translate(translation); } /** * Transforms this box by \a transform and recomputes it to * still be an axis-aligned box. * * \note This method is provided under BSD license (see the top of this file). */ template<int Mode, int Options> EIGEN_DEVICE_FUNC inline void transform(const Transform<Scalar, AmbientDimAtCompileTime, Mode, Options>& transform) { // Only Affine and Isometry transforms are currently supported. EIGEN_STATIC_ASSERT(Mode == Affine || Mode == AffineCompact || Mode == Isometry, THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS); // Method adapted from FCL src/shape/geometric_shapes_utility.cpp#computeBV<AABB, Box>(...) // https://github.com/flexible-collision-library/fcl/blob/fcl-0.4/src/shape/geometric_shapes_utility.cpp#L292 // // Here's a nice explanation why it works: https://zeuxcg.org/2010/10/17/aabb-from-obb-with-component-wise-abs/ // two times rotated extent const VectorType rotated_extent_2 = transform.linear().cwiseAbs() * sizes(); // two times new center const VectorType rotated_center_2 = transform.linear() * (this->m_max + this->m_min) + Scalar(2) * transform.translation(); this->m_max = (rotated_center_2 + rotated_extent_2) / Scalar(2); this->m_min = (rotated_center_2 - rotated_extent_2) / Scalar(2); } /** * \returns a copy of \c *this transformed by \a transform and recomputed to * still be an axis-aligned box. */ template<int Mode, int Options> EIGEN_DEVICE_FUNC AlignedBox transformed(const Transform<Scalar, AmbientDimAtCompileTime, Mode, Options>& transform) const { AlignedBox result(m_min, m_max); result.transform(transform); return result; } /** \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<AlignedBox, AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const { return typename internal::cast_return_type<AlignedBox, AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this); } /** Copy constructor with scalar type conversion */ template<typename OtherScalarType> EIGEN_DEVICE_FUNC inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other) { m_min = (other.min)().template cast<Scalar>(); m_max = (other.max)().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 AlignedBox& other, const RealScalar& prec = ScalarTraits::dummy_precision()) const { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); } protected: VectorType m_min, m_max; }; template<typename Scalar,int AmbientDim> template<typename Derived> EIGEN_DEVICE_FUNC inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const MatrixBase<Derived>& a_p) const { typename internal::nested_eval<Derived,2*AmbientDim>::type p(a_p.derived()); Scalar dist2(0); Scalar aux; for (Index k=0; k<dim(); ++k) { if( m_min[k] > p[k] ) { aux = m_min[k] - p[k]; dist2 += aux*aux; } else if( p[k] > m_max[k] ) { aux = p[k] - m_max[k]; dist2 += aux*aux; } } return dist2; } template<typename Scalar,int AmbientDim> EIGEN_DEVICE_FUNC inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const AlignedBox& b) const { Scalar dist2(0); Scalar aux; for (Index k=0; k<dim(); ++k) { if( m_min[k] > b.m_max[k] ) { aux = m_min[k] - b.m_max[k]; dist2 += aux*aux; } else if( b.m_min[k] > m_max[k] ) { aux = b.m_min[k] - m_max[k]; dist2 += aux*aux; } } return dist2; } /** \defgroup alignedboxtypedefs Global aligned box typedefs * * \ingroup Geometry_Module * * Eigen defines several typedef shortcuts for most common aligned box types. * * The general patterns are the following: * * \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, * and where \c Type can be \c i for integer, \c f for float, \c d for double. * * 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. * * \sa class AlignedBox */ #define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \ /** \ingroup alignedboxtypedefs */ \ typedef AlignedBox<Type, Size> AlignedBox##SizeSuffix##TypeSuffix; #define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \ EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 1, 1) \ EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \ EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \ EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \ EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X) EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i) EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f) EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d) #undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES #undef EIGEN_MAKE_TYPEDEFS } // end namespace Eigen #endif // EIGEN_ALIGNEDBOX_H