src/Geometry/AlignedBox.h

0001 // This file is part of Eigen, a lightweight C++ template library
0002 // for linear algebra.
0003 //
0004 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
0005 //
0006 // This Source Code Form is subject to the terms of the Mozilla
0007 // Public License v. 2.0. If a copy of the MPL was not distributed
0008 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
0009
0010 // Function void Eigen::AlignedBox::transform(const Transform& transform)
0011 // is provided under the following license agreement:
0012 //
0013 // Software License Agreement (BSD License)
0014 //
0015 // Copyright (c) 2011-2014, Willow Garage, Inc.
0016 // Copyright (c) 2014-2015, Open Source Robotics Foundation
0017 // All rights reserved.
0018 //
0019 // Redistribution and use in source and binary forms, with or without
0020 // modification, are permitted provided that the following conditions
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0022 //
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0025 //  * Redistributions in binary form must reproduce the above
0026 //    copyright notice, this list of conditions and the following
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0045
0046 #ifndef EIGEN_ALIGNEDBOX_H
0047 #define EIGEN_ALIGNEDBOX_H
0048
0049 namespace Eigen {
0050
0051 /** \geometry_module \ingroup Geometry_Module
0052   *
0053   *
0054   * \class AlignedBox
0055   *
0056   * \brief An axis aligned box
0057   *
0058   * \tparam _Scalar the type of the scalar coefficients
0059   * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
0060   *
0061   * This class represents an axis aligned box as a pair of the minimal and maximal corners.
0062   * \warning The result of most methods is undefined when applied to an empty box. You can check for empty boxes using isEmpty().
0063   * \sa alignedboxtypedefs
0064   */
0065 template <typename _Scalar, int _AmbientDim>
0066 class AlignedBox
0067 {
0068 public:
0069 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
0070   enum { AmbientDimAtCompileTime = _AmbientDim };
0071   typedef _Scalar                                   Scalar;
0072   typedef NumTraits<Scalar>                         ScalarTraits;
0073   typedef Eigen::Index                              Index; ///< \deprecated since Eigen 3.3
0074   typedef typename ScalarTraits::Real               RealScalar;
0075   typedef typename ScalarTraits::NonInteger         NonInteger;
0076   typedef Matrix<Scalar,AmbientDimAtCompileTime,1>  VectorType;
0077   typedef CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> VectorTypeSum;
0078
0079   /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */
0080   enum CornerType
0081   {
0082     /** 1D names @{ */
0083     Min=0, Max=1,
0084     /** @} */
0085
0086     /** Identifier for 2D corner @{ */
0087     BottomLeft=0, BottomRight=1,
0088     TopLeft=2, TopRight=3,
0089     /** @} */
0090
0091     /** Identifier for 3D corner  @{ */
0092     BottomLeftFloor=0, BottomRightFloor=1,
0093     TopLeftFloor=2, TopRightFloor=3,
0094     BottomLeftCeil=4, BottomRightCeil=5,
0095     TopLeftCeil=6, TopRightCeil=7
0096     /** @} */
0097   };
0098
0099
0100   /** Default constructor initializing a null box. */
0101   EIGEN_DEVICE_FUNC inline AlignedBox()
0102   { if (EIGEN_CONST_CONDITIONAL(AmbientDimAtCompileTime!=Dynamic)) setEmpty(); }
0103
0104   /** Constructs a null box with \a _dim the dimension of the ambient space. */
0105   EIGEN_DEVICE_FUNC inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim)
0106   { setEmpty(); }
0107
0108   /** Constructs a box with extremities \a _min and \a _max.
0109    * \warning If either component of \a _min is larger than the same component of \a _max, the constructed box is empty. */
0110   template<typename OtherVectorType1, typename OtherVectorType2>
0111   EIGEN_DEVICE_FUNC inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max) : m_min(_min), m_max(_max) {}
0112
0113   /** Constructs a box containing a single point \a p. */
0114   template<typename Derived>
0115   EIGEN_DEVICE_FUNC inline explicit AlignedBox(const MatrixBase<Derived>& p) : m_min(p), m_max(m_min)
0116   { }
0117
0118   EIGEN_DEVICE_FUNC ~AlignedBox() {}
0119
0120   /** \returns the dimension in which the box holds */
0121   EIGEN_DEVICE_FUNC inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime); }
0122
0123   /** \deprecated use isEmpty() */
0124   EIGEN_DEVICE_FUNC inline bool isNull() const { return isEmpty(); }
0125
0126   /** \deprecated use setEmpty() */
0127   EIGEN_DEVICE_FUNC inline void setNull() { setEmpty(); }
0128
0129   /** \returns true if the box is empty.
0130    * \sa setEmpty */
0131   EIGEN_DEVICE_FUNC inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); }
0132
0133   /** Makes \c *this an empty box.
0134    * \sa isEmpty */
0135   EIGEN_DEVICE_FUNC inline void setEmpty()
0136   {
0137     m_min.setConstant( ScalarTraits::highest() );
0138     m_max.setConstant( ScalarTraits::lowest() );
0139   }
0140
0141   /** \returns the minimal corner */
0142   EIGEN_DEVICE_FUNC inline const VectorType& (min)() const { return m_min; }
0143   /** \returns a non const reference to the minimal corner */
0144   EIGEN_DEVICE_FUNC inline VectorType& (min)() { return m_min; }
0145   /** \returns the maximal corner */
0146   EIGEN_DEVICE_FUNC inline const VectorType& (max)() const { return m_max; }
0147   /** \returns a non const reference to the maximal corner */
0148   EIGEN_DEVICE_FUNC inline VectorType& (max)() { return m_max; }
0149
0150   /** \returns the center of the box */
0151   EIGEN_DEVICE_FUNC inline const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(VectorTypeSum, RealScalar, quotient)
0152   center() const
0153   { return (m_min+m_max)/RealScalar(2); }
0154
0155   /** \returns the lengths of the sides of the bounding box.
0156     * Note that this function does not get the same
0157     * result for integral or floating scalar types: see
0158     */
0159   EIGEN_DEVICE_FUNC inline const CwiseBinaryOp< internal::scalar_difference_op<Scalar,Scalar>, const VectorType, const VectorType> sizes() const
0160   { return m_max - m_min; }
0161
0162   /** \returns the volume of the bounding box */
0163   EIGEN_DEVICE_FUNC inline Scalar volume() const
0164   { return sizes().prod(); }
0165
0166   /** \returns an expression for the bounding box diagonal vector
0167     * if the length of the diagonal is needed: diagonal().norm()
0168     * will provide it.
0169     */
0170   EIGEN_DEVICE_FUNC inline CwiseBinaryOp< internal::scalar_difference_op<Scalar,Scalar>, const VectorType, const VectorType> diagonal() const
0171   { return sizes(); }
0172
0173   /** \returns the vertex of the bounding box at the corner defined by
0174     * the corner-id corner. It works only for a 1D, 2D or 3D bounding box.
0175     * For 1D bounding boxes corners are named by 2 enum constants:
0176     * BottomLeft and BottomRight.
0177     * For 2D bounding boxes, corners are named by 4 enum constants:
0178     * BottomLeft, BottomRight, TopLeft, TopRight.
0179     * For 3D bounding boxes, the following names are added:
0180     * BottomLeftCeil, BottomRightCeil, TopLeftCeil, TopRightCeil.
0181     */
0182   EIGEN_DEVICE_FUNC inline VectorType corner(CornerType corner) const
0183   {
0184     EIGEN_STATIC_ASSERT(_AmbientDim <= 3, THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE);
0185
0186     VectorType res;
0187
0188     Index mult = 1;
0189     for(Index d=0; d<dim(); ++d)
0190     {
0191       if( mult & corner ) res[d] = m_max[d];
0192       else                res[d] = m_min[d];
0193       mult *= 2;
0194     }
0195     return res;
0196   }
0197
0198   /** \returns a random point inside the bounding box sampled with
0199    * a uniform distribution */
0200   EIGEN_DEVICE_FUNC inline VectorType sample() const
0201   {
0202     VectorType r(dim());
0203     for(Index d=0; d<dim(); ++d)
0204     {
0205       if(!ScalarTraits::IsInteger)
0206       {
0207         r[d] = m_min[d] + (m_max[d]-m_min[d])
0208              * internal::random<Scalar>(Scalar(0), Scalar(1));
0209       }
0210       else
0211         r[d] = internal::random(m_min[d], m_max[d]);
0212     }
0213     return r;
0214   }
0215
0216   /** \returns true if the point \a p is inside the box \c *this. */
0217   template<typename Derived>
0218   EIGEN_DEVICE_FUNC inline bool contains(const MatrixBase<Derived>& p) const
0219   {
0220     typename internal::nested_eval<Derived,2>::type p_n(p.derived());
0221     return (m_min.array()<=p_n.array()).all() && (p_n.array()<=m_max.array()).all();
0222   }
0223
0224   /** \returns true if the box \a b is entirely inside the box \c *this. */
0225   EIGEN_DEVICE_FUNC inline bool contains(const AlignedBox& b) const
0226   { return (m_min.array()<=(b.min)().array()).all() && ((b.max)().array()<=m_max.array()).all(); }
0227
0228   /** \returns true if the box \a b is intersecting the box \c *this.
0229    * \sa intersection, clamp */
0230   EIGEN_DEVICE_FUNC inline bool intersects(const AlignedBox& b) const
0231   { return (m_min.array()<=(b.max)().array()).all() && ((b.min)().array()<=m_max.array()).all(); }
0232
0233   /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this.
0234    * \sa extend(const AlignedBox&) */
0235   template<typename Derived>
0236   EIGEN_DEVICE_FUNC inline AlignedBox& extend(const MatrixBase<Derived>& p)
0237   {
0238     typename internal::nested_eval<Derived,2>::type p_n(p.derived());
0239     m_min = m_min.cwiseMin(p_n);
0240     m_max = m_max.cwiseMax(p_n);
0241     return *this;
0242   }
0243
0244   /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this.
0245    * \sa merged, extend(const MatrixBase&) */
0246   EIGEN_DEVICE_FUNC inline AlignedBox& extend(const AlignedBox& b)
0247   {
0248     m_min = m_min.cwiseMin(b.m_min);
0249     m_max = m_max.cwiseMax(b.m_max);
0250     return *this;
0251   }
0252
0253   /** Clamps \c *this by the box \a b and returns a reference to \c *this.
0254    * \note If the boxes don't intersect, the resulting box is empty.
0255    * \sa intersection(), intersects() */
0256   EIGEN_DEVICE_FUNC inline AlignedBox& clamp(const AlignedBox& b)
0257   {
0258     m_min = m_min.cwiseMax(b.m_min);
0259     m_max = m_max.cwiseMin(b.m_max);
0260     return *this;
0261   }
0262
0263   /** Returns an AlignedBox that is the intersection of \a b and \c *this
0264    * \note If the boxes don't intersect, the resulting box is empty.
0265    * \sa intersects(), clamp, contains()  */
0266   EIGEN_DEVICE_FUNC inline AlignedBox intersection(const AlignedBox& b) const
0267   {return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); }
0268
0269   /** Returns an AlignedBox that is the union of \a b and \c *this.
0270    * \note Merging with an empty box may result in a box bigger than \c *this.
0271    * \sa extend(const AlignedBox&) */
0272   EIGEN_DEVICE_FUNC inline AlignedBox merged(const AlignedBox& b) const
0273   { return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); }
0274
0275   /** Translate \c *this by the vector \a t and returns a reference to \c *this. */
0276   template<typename Derived>
0277   EIGEN_DEVICE_FUNC inline AlignedBox& translate(const MatrixBase<Derived>& a_t)
0278   {
0279     const typename internal::nested_eval<Derived,2>::type t(a_t.derived());
0280     m_min += t;
0281     m_max += t;
0282     return *this;
0283   }
0284
0285   /** \returns a copy of \c *this translated by the vector \a t. */
0286   template<typename Derived>
0287   EIGEN_DEVICE_FUNC inline AlignedBox translated(const MatrixBase<Derived>& a_t) const
0288   {
0289     AlignedBox result(m_min, m_max);
0290     result.translate(a_t);
0291     return result;
0292   }
0293
0294   /** \returns the squared distance between the point \a p and the box \c *this,
0295     * and zero if \a p is inside the box.
0296     * \sa exteriorDistance(const MatrixBase&), squaredExteriorDistance(const AlignedBox&)
0297     */
0298   template<typename Derived>
0299   EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& p) const;
0300
0301   /** \returns the squared distance between the boxes \a b and \c *this,
0302     * and zero if the boxes intersect.
0303     * \sa exteriorDistance(const AlignedBox&), squaredExteriorDistance(const MatrixBase&)
0304     */
0305   EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const AlignedBox& b) const;
0306
0307   /** \returns the distance between the point \a p and the box \c *this,
0308     * and zero if \a p is inside the box.
0309     * \sa squaredExteriorDistance(const MatrixBase&), exteriorDistance(const AlignedBox&)
0310     */
0311   template<typename Derived>
0312   EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const
0313   { EIGEN_USING_STD(sqrt) return sqrt(NonInteger(squaredExteriorDistance(p))); }
0314
0315   /** \returns the distance between the boxes \a b and \c *this,
0316     * and zero if the boxes intersect.
0317     * \sa squaredExteriorDistance(const AlignedBox&), exteriorDistance(const MatrixBase&)
0318     */
0319   EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const AlignedBox& b) const
0320   { EIGEN_USING_STD(sqrt) return sqrt(NonInteger(squaredExteriorDistance(b))); }
0321
0322   /**
0323    * Specialization of transform for pure translation.
0324    */
0325   template<int Mode, int Options>
0326   EIGEN_DEVICE_FUNC inline void transform(
0327       const typename Transform<Scalar, AmbientDimAtCompileTime, Mode, Options>::TranslationType& translation)
0328   {
0329     this->translate(translation);
0330   }
0331
0332   /**
0333    * Transforms this box by \a transform and recomputes it to
0334    * still be an axis-aligned box.
0335    *
0336    * \note This method is provided under BSD license (see the top of this file).
0337    */
0338   template<int Mode, int Options>
0339   EIGEN_DEVICE_FUNC inline void transform(const Transform<Scalar, AmbientDimAtCompileTime, Mode, Options>& transform)
0340   {
0341     // Only Affine and Isometry transforms are currently supported.
0342     EIGEN_STATIC_ASSERT(Mode == Affine || Mode == AffineCompact || Mode == Isometry, THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS);
0343
0344     // Method adapted from FCL src/shape/geometric_shapes_utility.cpp#computeBV<AABB, Box>(...)
0345     // https://github.com/flexible-collision-library/fcl/blob/fcl-0.4/src/shape/geometric_shapes_utility.cpp#L292
0346     //
0347     // Here's a nice explanation why it works: https://zeuxcg.org/2010/10/17/aabb-from-obb-with-component-wise-abs/
0348
0349     // two times rotated extent
0350     const VectorType rotated_extent_2 = transform.linear().cwiseAbs() * sizes();
0351     // two times new center
0352     const VectorType rotated_center_2 = transform.linear() * (this->m_max + this->m_min) +
0353         Scalar(2) * transform.translation();
0354
0355     this->m_max = (rotated_center_2 + rotated_extent_2) / Scalar(2);
0356     this->m_min = (rotated_center_2 - rotated_extent_2) / Scalar(2);
0357   }
0358
0359   /**
0360    * \returns a copy of \c *this transformed by \a transform and recomputed to
0361    * still be an axis-aligned box.
0362    */
0363   template<int Mode, int Options>
0364   EIGEN_DEVICE_FUNC AlignedBox transformed(const Transform<Scalar, AmbientDimAtCompileTime, Mode, Options>& transform) const
0365   {
0366     AlignedBox result(m_min, m_max);
0367     result.transform(transform);
0368     return result;
0369   }
0370
0371   /** \returns \c *this with scalar type casted to \a NewScalarType
0372     *
0373     * Note that if \a NewScalarType is equal to the current scalar type of \c *this
0374     * then this function smartly returns a const reference to \c *this.
0375     */
0376   template<typename NewScalarType>
0377   EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<AlignedBox,
0378            AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
0379   {
0380     return typename internal::cast_return_type<AlignedBox,
0381                     AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
0382   }
0383
0384   /** Copy constructor with scalar type conversion */
0385   template<typename OtherScalarType>
0386   EIGEN_DEVICE_FUNC inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other)
0387   {
0388     m_min = (other.min)().template cast<Scalar>();
0389     m_max = (other.max)().template cast<Scalar>();
0390   }
0391
0392   /** \returns \c true if \c *this is approximately equal to \a other, within the precision
0393     * determined by \a prec.
0394     *
0395     * \sa MatrixBase::isApprox() */
0396   EIGEN_DEVICE_FUNC bool isApprox(const AlignedBox& other, const RealScalar& prec = ScalarTraits::dummy_precision()) const
0397   { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); }
0398
0399 protected:
0400
0401   VectorType m_min, m_max;
0402 };
0403
0404
0405
0406 template<typename Scalar,int AmbientDim>
0407 template<typename Derived>
0408 EIGEN_DEVICE_FUNC inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const MatrixBase<Derived>& a_p) const
0409 {
0410   typename internal::nested_eval<Derived,2*AmbientDim>::type p(a_p.derived());
0411   Scalar dist2(0);
0412   Scalar aux;
0413   for (Index k=0; k<dim(); ++k)
0414   {
0415     if( m_min[k] > p[k] )
0416     {
0417       aux = m_min[k] - p[k];
0418       dist2 += aux*aux;
0419     }
0420     else if( p[k] > m_max[k] )
0421     {
0422       aux = p[k] - m_max[k];
0423       dist2 += aux*aux;
0424     }
0425   }
0426   return dist2;
0427 }
0428
0429 template<typename Scalar,int AmbientDim>
0430 EIGEN_DEVICE_FUNC inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const AlignedBox& b) const
0431 {
0432   Scalar dist2(0);
0433   Scalar aux;
0434   for (Index k=0; k<dim(); ++k)
0435   {
0436     if( m_min[k] > b.m_max[k] )
0437     {
0438       aux = m_min[k] - b.m_max[k];
0439       dist2 += aux*aux;
0440     }
0441     else if( b.m_min[k] > m_max[k] )
0442     {
0443       aux = b.m_min[k] - m_max[k];
0444       dist2 += aux*aux;
0445     }
0446   }
0447   return dist2;
0448 }
0449
0450 /** \defgroup alignedboxtypedefs Global aligned box typedefs
0451   *
0452   * \ingroup Geometry_Module
0453   *
0454   * Eigen defines several typedef shortcuts for most common aligned box types.
0455   *
0456   * The general patterns are the following:
0457   *
0458   * \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,
0459   * and where \c Type can be \c i for integer, \c f for float, \c d for double.
0460   *
0461   * 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.
0462   *
0463   * \sa class AlignedBox
0464   */
0465
0466 #define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix)    \
0467 /** \ingroup alignedboxtypedefs */                                 \
0468 typedef AlignedBox<Type, Size>   AlignedBox##SizeSuffix##TypeSuffix;
0469
0470 #define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
0471 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 1, 1) \
0472 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
0473 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
0474 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
0475 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X)
0476
0477 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int,                  i)
0478 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float,                f)
0479 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double,               d)
0480
0481 #undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
0482 #undef EIGEN_MAKE_TYPEDEFS
0483
0484 } // end namespace Eigen
0485
0486 #endif // EIGEN_ALIGNEDBOX_H