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>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
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// Eigen. If not, see <http://www.gnu.org/licenses/>.

#ifndef EIGEN_ALIGNEDBOX_H
#define EIGEN_ALIGNEDBOX_H

/** \geometry_module \ingroup Geometry_Module
  *
  *
  * \class AlignedBox
  *
  * \brief An axis aligned box
  *
  * \param _Scalar the type of the scalar coefficients
  * \param _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.
  */
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 DenseIndex                                Index;
  typedef typename ScalarTraits::Real               RealScalar;
  typedef typename ScalarTraits::NonInteger      NonInteger;
  typedef Matrix<Scalar,AmbientDimAtCompileTime,1>  VectorType;

  /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */
  enum CornerType
  {
    /** 1D names */
    Min=0, Max=1,

    /** Added names for 2D */
    BottomLeft=0, BottomRight=1,
    TopLeft=2, TopRight=3,

    /** Added names for 3D */
    BottomLeftFloor=0, BottomRightFloor=1,
    TopLeftFloor=2, TopRightFloor=3,
    BottomLeftCeil=4, BottomRightCeil=5,
    TopLeftCeil=6, TopRightCeil=7
  };


  /** Default constructor initializing a null box. */
  inline explicit AlignedBox()
  { if (AmbientDimAtCompileTime!=Dynamic) setEmpty(); }

  /** Constructs a null box with \a _dim the dimension of the ambient space. */
  inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim)
  { setEmpty(); }

  /** Constructs a box with extremities \a _min and \a _max. */
  template<typename OtherVectorType1, typename OtherVectorType2>
  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>
  inline explicit AlignedBox(const MatrixBase<Derived>& a_p)
  {
    const typename internal::nested<Derived,2>::type p(a_p.derived());
    m_min = p;
    m_max = p;
  }

  ~AlignedBox() {}

  /** \returns the dimension in which the box holds */
  inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size()-1 : Index(AmbientDimAtCompileTime); }

  /** \deprecated use isEmpty */
  inline bool isNull() const { return isEmpty(); }

  /** \deprecated use setEmpty */
  inline void setNull() { setEmpty(); }

  /** \returns true if the box is empty. */
  inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); }

  /** Makes \c *this an empty box. */
  inline void setEmpty()
  {
    m_min.setConstant( ScalarTraits::highest() );
    m_max.setConstant( ScalarTraits::lowest() );
  }

  /** \returns the minimal corner */
  inline const VectorType& min() const { return m_min; }
  /** \returns a non const reference to the minimal corner */
  inline VectorType& min() { return m_min; }
  /** \returns the maximal corner */
  inline const VectorType& max() const { return m_max; }
  /** \returns a non const reference to the maximal corner */
  inline VectorType& max() { return m_max; }

  /** \returns the center of the box */
  inline const CwiseUnaryOp<internal::scalar_quotient1_op<Scalar>,
                            const CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> >
  center() const
  { return (m_min+m_max)/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
    */
  inline const CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType, const VectorType> sizes() const
  { return m_max - m_min; }

  /** \returns the volume of the bounding box */
  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.
    */
  inline CwiseBinaryOp< internal::scalar_difference_op<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.
    */
  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 */
  inline VectorType sample() const
  {
    VectorType r;
    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>
  inline bool contains(const MatrixBase<Derived>& a_p) const
  {
    const typename internal::nested<Derived,2>::type p(a_p.derived());
    return (m_min.array()<=p.array()).all() && (p.array()<=m_max.array()).all();
  }

  /** \returns true if the box \a b is entirely inside the box \c *this. */
  inline bool contains(const AlignedBox& b) const
  { return (m_min.array()<=b.min().array()).all() && (b.max().array()<=m_max.array()).all(); }

  /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this. */
  template<typename Derived>
  inline AlignedBox& extend(const MatrixBase<Derived>& a_p)
  {
    const typename internal::nested<Derived,2>::type p(a_p.derived());
    m_min = m_min.cwiseMin(p);
    m_max = m_max.cwiseMax(p);
    return *this;
  }

  /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this. */
  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. */
  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 */
  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 */
  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>
  inline AlignedBox& translate(const MatrixBase<Derived>& a_t)
  {
    const typename internal::nested<Derived,2>::type t(a_t.derived());
    m_min += t;
    m_max += t;
    return *this;
  }

  /** \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()
    */
  template<typename Derived>
  inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& a_p) const;

  /** \returns the squared distance between the boxes \a b and \c *this,
    * and zero if the boxes intersect.
    * \sa exteriorDistance()
    */
  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()
    */
  template<typename Derived>
  inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const
  { return internal::sqrt(NonInteger(squaredExteriorDistance(p))); }

  /** \returns the distance between the boxes \a b and \c *this,
    * and zero if the boxes intersect.
    * \sa squaredExteriorDistance()
    */
  inline NonInteger exteriorDistance(const AlignedBox& b) const
  { return internal::sqrt(NonInteger(squaredExteriorDistance(b))); }

  /** \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<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>
  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() */
  bool isApprox(const AlignedBox& other, 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>
inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const MatrixBase<Derived>& a_p) const
{
  const typename internal::nested<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>
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;
}

#endif // EIGEN_ALIGNEDBOX_H