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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>
//
// 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_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 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,
/** @} */
/** 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. */
inline 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.
* \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>
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>& p) : m_min(p), m_max(m_min)
{ }
~AlignedBox() {}
/** \returns the dimension in which the box holds */
inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size() : 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.
* \sa setEmpty */
inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); }
/** Makes \c *this an empty box.
* \sa isEmpty */
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(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>
inline bool contains(const MatrixBase<Derived>& p) const
{
typename internal::nested<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. */
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 */
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>
inline AlignedBox& extend(const MatrixBase<Derived>& p)
{
typename internal::nested<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&) */
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() */
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() */
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&) */
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(const MatrixBase&), squaredExteriorDistance(const AlignedBox&)
*/
template<typename Derived>
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&)
*/
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>
inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const
{ 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&)
*/
inline NonInteger exteriorDistance(const AlignedBox& b) const
{ using std::sqrt; return 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, 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>
inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const MatrixBase<Derived>& a_p) 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;
}
/** \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
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