Squashed 'third_party/eigen/' content from commit 61d72f6
Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/Eigen/src/Geometry/AlignedBox.h b/Eigen/src/Geometry/AlignedBox.h
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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;
+ 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