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1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9 
10 #ifndef EIGEN_ALIGNEDBOX_H
11 #define EIGEN_ALIGNEDBOX_H
12 
13 namespace Eigen {
14 
15 /** \geometry_module \ingroup Geometry_Module
16   *
17   *
18   * \class AlignedBox
19   *
20   * \brief An axis aligned box
21   *
22   * \tparam _Scalar the type of the scalar coefficients
23   * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
24   *
25   * This class represents an axis aligned box as a pair of the minimal and maximal corners.
26   * \warning The result of most methods is undefined when applied to an empty box. You can check for empty boxes using isEmpty().
27   * \sa alignedboxtypedefs
28   */
29 template <typename _Scalar, int _AmbientDim>
30 class AlignedBox
31 {
32 public:
33 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
34   enum { AmbientDimAtCompileTime = _AmbientDim };
35   typedef _Scalar                                   Scalar;
36   typedef NumTraits<Scalar>                         ScalarTraits;
37   typedef Eigen::Index                              Index; ///< \deprecated since Eigen 3.3
38   typedef typename ScalarTraits::Real               RealScalar;
39   typedef typename ScalarTraits::NonInteger         NonInteger;
40   typedef Matrix<Scalar,AmbientDimAtCompileTime,1>  VectorType;
41   typedef CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> VectorTypeSum;
42 
43   /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */
44   enum CornerType
45   {
46     /** 1D names @{ */
47     Min=0, Max=1,
48     /** @} */
49 
50     /** Identifier for 2D corner @{ */
51     BottomLeft=0, BottomRight=1,
52     TopLeft=2, TopRight=3,
53     /** @} */
54 
55     /** Identifier for 3D corner  @{ */
56     BottomLeftFloor=0, BottomRightFloor=1,
57     TopLeftFloor=2, TopRightFloor=3,
58     BottomLeftCeil=4, BottomRightCeil=5,
59     TopLeftCeil=6, TopRightCeil=7
60     /** @} */
61   };
62 
63 
64   /** Default constructor initializing a null box. */
AlignedBox()65   EIGEN_DEVICE_FUNC inline AlignedBox()
66   { if (AmbientDimAtCompileTime!=Dynamic) setEmpty(); }
67 
68   /** Constructs a null box with \a _dim the dimension of the ambient space. */
AlignedBox(Index _dim)69   EIGEN_DEVICE_FUNC inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim)
70   { setEmpty(); }
71 
72   /** Constructs a box with extremities \a _min and \a _max.
73    * \warning If either component of \a _min is larger than the same component of \a _max, the constructed box is empty. */
74   template<typename OtherVectorType1, typename OtherVectorType2>
AlignedBox(const OtherVectorType1 & _min,const OtherVectorType2 & _max)75   EIGEN_DEVICE_FUNC inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max) : m_min(_min), m_max(_max) {}
76 
77   /** Constructs a box containing a single point \a p. */
78   template<typename Derived>
AlignedBox(const MatrixBase<Derived> & p)79   EIGEN_DEVICE_FUNC inline explicit AlignedBox(const MatrixBase<Derived>& p) : m_min(p), m_max(m_min)
80   { }
81 
~AlignedBox()82   EIGEN_DEVICE_FUNC ~AlignedBox() {}
83 
84   /** \returns the dimension in which the box holds */
dim()85   EIGEN_DEVICE_FUNC inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime); }
86 
87   /** \deprecated use isEmpty() */
isNull()88   EIGEN_DEVICE_FUNC inline bool isNull() const { return isEmpty(); }
89 
90   /** \deprecated use setEmpty() */
setNull()91   EIGEN_DEVICE_FUNC inline void setNull() { setEmpty(); }
92 
93   /** \returns true if the box is empty.
94    * \sa setEmpty */
isEmpty()95   EIGEN_DEVICE_FUNC inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); }
96 
97   /** Makes \c *this an empty box.
98    * \sa isEmpty */
setEmpty()99   EIGEN_DEVICE_FUNC inline void setEmpty()
100   {
101     m_min.setConstant( ScalarTraits::highest() );
102     m_max.setConstant( ScalarTraits::lowest() );
103   }
104 
105   /** \returns the minimal corner */
106   EIGEN_DEVICE_FUNC inline const VectorType& (min)() const { return m_min; }
107   /** \returns a non const reference to the minimal corner */
108   EIGEN_DEVICE_FUNC inline VectorType& (min)() { return m_min; }
109   /** \returns the maximal corner */
110   EIGEN_DEVICE_FUNC inline const VectorType& (max)() const { return m_max; }
111   /** \returns a non const reference to the maximal corner */
112   EIGEN_DEVICE_FUNC inline VectorType& (max)() { return m_max; }
113 
114   /** \returns the center of the box */
EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(VectorTypeSum,RealScalar,quotient)115   EIGEN_DEVICE_FUNC inline const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(VectorTypeSum, RealScalar, quotient)
116   center() const
117   { return (m_min+m_max)/RealScalar(2); }
118 
119   /** \returns the lengths of the sides of the bounding box.
120     * Note that this function does not get the same
121     * result for integral or floating scalar types: see
122     */
sizes()123   EIGEN_DEVICE_FUNC inline const CwiseBinaryOp< internal::scalar_difference_op<Scalar,Scalar>, const VectorType, const VectorType> sizes() const
124   { return m_max - m_min; }
125 
126   /** \returns the volume of the bounding box */
volume()127   EIGEN_DEVICE_FUNC inline Scalar volume() const
128   { return sizes().prod(); }
129 
130   /** \returns an expression for the bounding box diagonal vector
131     * if the length of the diagonal is needed: diagonal().norm()
132     * will provide it.
133     */
diagonal()134   EIGEN_DEVICE_FUNC inline CwiseBinaryOp< internal::scalar_difference_op<Scalar,Scalar>, const VectorType, const VectorType> diagonal() const
135   { return sizes(); }
136 
137   /** \returns the vertex of the bounding box at the corner defined by
138     * the corner-id corner. It works only for a 1D, 2D or 3D bounding box.
139     * For 1D bounding boxes corners are named by 2 enum constants:
140     * BottomLeft and BottomRight.
141     * For 2D bounding boxes, corners are named by 4 enum constants:
142     * BottomLeft, BottomRight, TopLeft, TopRight.
143     * For 3D bounding boxes, the following names are added:
144     * BottomLeftCeil, BottomRightCeil, TopLeftCeil, TopRightCeil.
145     */
corner(CornerType corner)146   EIGEN_DEVICE_FUNC inline VectorType corner(CornerType corner) const
147   {
148     EIGEN_STATIC_ASSERT(_AmbientDim <= 3, THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE);
149 
150     VectorType res;
151 
152     Index mult = 1;
153     for(Index d=0; d<dim(); ++d)
154     {
155       if( mult & corner ) res[d] = m_max[d];
156       else                res[d] = m_min[d];
157       mult *= 2;
158     }
159     return res;
160   }
161 
162   /** \returns a random point inside the bounding box sampled with
163    * a uniform distribution */
sample()164   EIGEN_DEVICE_FUNC inline VectorType sample() const
165   {
166     VectorType r(dim());
167     for(Index d=0; d<dim(); ++d)
168     {
169       if(!ScalarTraits::IsInteger)
170       {
171         r[d] = m_min[d] + (m_max[d]-m_min[d])
172              * internal::random<Scalar>(Scalar(0), Scalar(1));
173       }
174       else
175         r[d] = internal::random(m_min[d], m_max[d]);
176     }
177     return r;
178   }
179 
180   /** \returns true if the point \a p is inside the box \c *this. */
181   template<typename Derived>
contains(const MatrixBase<Derived> & p)182   EIGEN_DEVICE_FUNC inline bool contains(const MatrixBase<Derived>& p) const
183   {
184     typename internal::nested_eval<Derived,2>::type p_n(p.derived());
185     return (m_min.array()<=p_n.array()).all() && (p_n.array()<=m_max.array()).all();
186   }
187 
188   /** \returns true if the box \a b is entirely inside the box \c *this. */
contains(const AlignedBox & b)189   EIGEN_DEVICE_FUNC inline bool contains(const AlignedBox& b) const
190   { return (m_min.array()<=(b.min)().array()).all() && ((b.max)().array()<=m_max.array()).all(); }
191 
192   /** \returns true if the box \a b is intersecting the box \c *this.
193    * \sa intersection, clamp */
intersects(const AlignedBox & b)194   EIGEN_DEVICE_FUNC inline bool intersects(const AlignedBox& b) const
195   { return (m_min.array()<=(b.max)().array()).all() && ((b.min)().array()<=m_max.array()).all(); }
196 
197   /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this.
198    * \sa extend(const AlignedBox&) */
199   template<typename Derived>
extend(const MatrixBase<Derived> & p)200   EIGEN_DEVICE_FUNC inline AlignedBox& extend(const MatrixBase<Derived>& p)
201   {
202     typename internal::nested_eval<Derived,2>::type p_n(p.derived());
203     m_min = m_min.cwiseMin(p_n);
204     m_max = m_max.cwiseMax(p_n);
205     return *this;
206   }
207 
208   /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this.
209    * \sa merged, extend(const MatrixBase&) */
extend(const AlignedBox & b)210   EIGEN_DEVICE_FUNC inline AlignedBox& extend(const AlignedBox& b)
211   {
212     m_min = m_min.cwiseMin(b.m_min);
213     m_max = m_max.cwiseMax(b.m_max);
214     return *this;
215   }
216 
217   /** Clamps \c *this by the box \a b and returns a reference to \c *this.
218    * \note If the boxes don't intersect, the resulting box is empty.
219    * \sa intersection(), intersects() */
clamp(const AlignedBox & b)220   EIGEN_DEVICE_FUNC inline AlignedBox& clamp(const AlignedBox& b)
221   {
222     m_min = m_min.cwiseMax(b.m_min);
223     m_max = m_max.cwiseMin(b.m_max);
224     return *this;
225   }
226 
227   /** Returns an AlignedBox that is the intersection of \a b and \c *this
228    * \note If the boxes don't intersect, the resulting box is empty.
229    * \sa intersects(), clamp, contains()  */
intersection(const AlignedBox & b)230   EIGEN_DEVICE_FUNC inline AlignedBox intersection(const AlignedBox& b) const
231   {return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); }
232 
233   /** Returns an AlignedBox that is the union of \a b and \c *this.
234    * \note Merging with an empty box may result in a box bigger than \c *this.
235    * \sa extend(const AlignedBox&) */
merged(const AlignedBox & b)236   EIGEN_DEVICE_FUNC inline AlignedBox merged(const AlignedBox& b) const
237   { return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); }
238 
239   /** Translate \c *this by the vector \a t and returns a reference to \c *this. */
240   template<typename Derived>
translate(const MatrixBase<Derived> & a_t)241   EIGEN_DEVICE_FUNC inline AlignedBox& translate(const MatrixBase<Derived>& a_t)
242   {
243     const typename internal::nested_eval<Derived,2>::type t(a_t.derived());
244     m_min += t;
245     m_max += t;
246     return *this;
247   }
248 
249   /** \returns the squared distance between the point \a p and the box \c *this,
250     * and zero if \a p is inside the box.
251     * \sa exteriorDistance(const MatrixBase&), squaredExteriorDistance(const AlignedBox&)
252     */
253   template<typename Derived>
254   EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& p) const;
255 
256   /** \returns the squared distance between the boxes \a b and \c *this,
257     * and zero if the boxes intersect.
258     * \sa exteriorDistance(const AlignedBox&), squaredExteriorDistance(const MatrixBase&)
259     */
260   EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const AlignedBox& b) const;
261 
262   /** \returns the distance between the point \a p and the box \c *this,
263     * and zero if \a p is inside the box.
264     * \sa squaredExteriorDistance(const MatrixBase&), exteriorDistance(const AlignedBox&)
265     */
266   template<typename Derived>
exteriorDistance(const MatrixBase<Derived> & p)267   EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const
268   { EIGEN_USING_STD_MATH(sqrt) return sqrt(NonInteger(squaredExteriorDistance(p))); }
269 
270   /** \returns the distance between the boxes \a b and \c *this,
271     * and zero if the boxes intersect.
272     * \sa squaredExteriorDistance(const AlignedBox&), exteriorDistance(const MatrixBase&)
273     */
exteriorDistance(const AlignedBox & b)274   EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const AlignedBox& b) const
275   { EIGEN_USING_STD_MATH(sqrt) return sqrt(NonInteger(squaredExteriorDistance(b))); }
276 
277   /** \returns \c *this with scalar type casted to \a NewScalarType
278     *
279     * Note that if \a NewScalarType is equal to the current scalar type of \c *this
280     * then this function smartly returns a const reference to \c *this.
281     */
282   template<typename NewScalarType>
283   EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<AlignedBox,
cast()284            AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
285   {
286     return typename internal::cast_return_type<AlignedBox,
287                     AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
288   }
289 
290   /** Copy constructor with scalar type conversion */
291   template<typename OtherScalarType>
AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime> & other)292   EIGEN_DEVICE_FUNC inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other)
293   {
294     m_min = (other.min)().template cast<Scalar>();
295     m_max = (other.max)().template cast<Scalar>();
296   }
297 
298   /** \returns \c true if \c *this is approximately equal to \a other, within the precision
299     * determined by \a prec.
300     *
301     * \sa MatrixBase::isApprox() */
302   EIGEN_DEVICE_FUNC bool isApprox(const AlignedBox& other, const RealScalar& prec = ScalarTraits::dummy_precision()) const
303   { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); }
304 
305 protected:
306 
307   VectorType m_min, m_max;
308 };
309 
310 
311 
312 template<typename Scalar,int AmbientDim>
313 template<typename Derived>
squaredExteriorDistance(const MatrixBase<Derived> & a_p)314 EIGEN_DEVICE_FUNC inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const MatrixBase<Derived>& a_p) const
315 {
316   typename internal::nested_eval<Derived,2*AmbientDim>::type p(a_p.derived());
317   Scalar dist2(0);
318   Scalar aux;
319   for (Index k=0; k<dim(); ++k)
320   {
321     if( m_min[k] > p[k] )
322     {
323       aux = m_min[k] - p[k];
324       dist2 += aux*aux;
325     }
326     else if( p[k] > m_max[k] )
327     {
328       aux = p[k] - m_max[k];
329       dist2 += aux*aux;
330     }
331   }
332   return dist2;
333 }
334 
335 template<typename Scalar,int AmbientDim>
squaredExteriorDistance(const AlignedBox & b)336 EIGEN_DEVICE_FUNC inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const AlignedBox& b) const
337 {
338   Scalar dist2(0);
339   Scalar aux;
340   for (Index k=0; k<dim(); ++k)
341   {
342     if( m_min[k] > b.m_max[k] )
343     {
344       aux = m_min[k] - b.m_max[k];
345       dist2 += aux*aux;
346     }
347     else if( b.m_min[k] > m_max[k] )
348     {
349       aux = b.m_min[k] - m_max[k];
350       dist2 += aux*aux;
351     }
352   }
353   return dist2;
354 }
355 
356 /** \defgroup alignedboxtypedefs Global aligned box typedefs
357   *
358   * \ingroup Geometry_Module
359   *
360   * Eigen defines several typedef shortcuts for most common aligned box types.
361   *
362   * The general patterns are the following:
363   *
364   * \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,
365   * and where \c Type can be \c i for integer, \c f for float, \c d for double.
366   *
367   * 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.
368   *
369   * \sa class AlignedBox
370   */
371 
372 #define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix)    \
373 /** \ingroup alignedboxtypedefs */                                 \
374 typedef AlignedBox<Type, Size>   AlignedBox##SizeSuffix##TypeSuffix;
375 
376 #define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
377 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 1, 1) \
378 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
379 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
380 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
381 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X)
382 
383 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int,                  i)
384 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float,                f)
385 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double,               d)
386 
387 #undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
388 #undef EIGEN_MAKE_TYPEDEFS
389 
390 } // end namespace Eigen
391 
392 #endif // EIGEN_ALIGNEDBOX_H
393