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 * \param _Scalar the type of the scalar coefficients
23 * \param _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 */
27 template <typename _Scalar, int _AmbientDim>
28 class AlignedBox
29 {
30 public:
31 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
32 enum { AmbientDimAtCompileTime = _AmbientDim };
33 typedef _Scalar Scalar;
34 typedef NumTraits<Scalar> ScalarTraits;
35 typedef DenseIndex Index;
36 typedef typename ScalarTraits::Real RealScalar;
37 typedef typename ScalarTraits::NonInteger NonInteger;
38 typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
39
40 /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */
41 enum CornerType
42 {
43 /** 1D names */
44 Min=0, Max=1,
45
46 /** Added names for 2D */
47 BottomLeft=0, BottomRight=1,
48 TopLeft=2, TopRight=3,
49
50 /** Added names for 3D */
51 BottomLeftFloor=0, BottomRightFloor=1,
52 TopLeftFloor=2, TopRightFloor=3,
53 BottomLeftCeil=4, BottomRightCeil=5,
54 TopLeftCeil=6, TopRightCeil=7
55 };
56
57
58 /** Default constructor initializing a null box. */
AlignedBox()59 inline explicit AlignedBox()
60 { if (AmbientDimAtCompileTime!=Dynamic) setEmpty(); }
61
62 /** Constructs a null box with \a _dim the dimension of the ambient space. */
AlignedBox(Index _dim)63 inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim)
64 { setEmpty(); }
65
66 /** Constructs a box with extremities \a _min and \a _max. */
67 template<typename OtherVectorType1, typename OtherVectorType2>
AlignedBox(const OtherVectorType1 & _min,const OtherVectorType2 & _max)68 inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max) : m_min(_min), m_max(_max) {}
69
70 /** Constructs a box containing a single point \a p. */
71 template<typename Derived>
AlignedBox(const MatrixBase<Derived> & a_p)72 inline explicit AlignedBox(const MatrixBase<Derived>& a_p)
73 {
74 const typename internal::nested<Derived,2>::type p(a_p.derived());
75 m_min = p;
76 m_max = p;
77 }
78
~AlignedBox()79 ~AlignedBox() {}
80
81 /** \returns the dimension in which the box holds */
dim()82 inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size()-1 : Index(AmbientDimAtCompileTime); }
83
84 /** \deprecated use isEmpty */
isNull()85 inline bool isNull() const { return isEmpty(); }
86
87 /** \deprecated use setEmpty */
setNull()88 inline void setNull() { setEmpty(); }
89
90 /** \returns true if the box is empty. */
isEmpty()91 inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); }
92
93 /** Makes \c *this an empty box. */
setEmpty()94 inline void setEmpty()
95 {
96 m_min.setConstant( ScalarTraits::highest() );
97 m_max.setConstant( ScalarTraits::lowest() );
98 }
99
100 /** \returns the minimal corner */
101 inline const VectorType& (min)() const { return m_min; }
102 /** \returns a non const reference to the minimal corner */
103 inline VectorType& (min)() { return m_min; }
104 /** \returns the maximal corner */
105 inline const VectorType& (max)() const { return m_max; }
106 /** \returns a non const reference to the maximal corner */
107 inline VectorType& (max)() { return m_max; }
108
109 /** \returns the center of the box */
110 inline const CwiseUnaryOp<internal::scalar_quotient1_op<Scalar>,
111 const CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> >
center()112 center() const
113 { return (m_min+m_max)/2; }
114
115 /** \returns the lengths of the sides of the bounding box.
116 * Note that this function does not get the same
117 * result for integral or floating scalar types: see
118 */
sizes()119 inline const CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType, const VectorType> sizes() const
120 { return m_max - m_min; }
121
122 /** \returns the volume of the bounding box */
volume()123 inline Scalar volume() const
124 { return sizes().prod(); }
125
126 /** \returns an expression for the bounding box diagonal vector
127 * if the length of the diagonal is needed: diagonal().norm()
128 * will provide it.
129 */
diagonal()130 inline CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType, const VectorType> diagonal() const
131 { return sizes(); }
132
133 /** \returns the vertex of the bounding box at the corner defined by
134 * the corner-id corner. It works only for a 1D, 2D or 3D bounding box.
135 * For 1D bounding boxes corners are named by 2 enum constants:
136 * BottomLeft and BottomRight.
137 * For 2D bounding boxes, corners are named by 4 enum constants:
138 * BottomLeft, BottomRight, TopLeft, TopRight.
139 * For 3D bounding boxes, the following names are added:
140 * BottomLeftCeil, BottomRightCeil, TopLeftCeil, TopRightCeil.
141 */
corner(CornerType corner)142 inline VectorType corner(CornerType corner) const
143 {
144 EIGEN_STATIC_ASSERT(_AmbientDim <= 3, THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE);
145
146 VectorType res;
147
148 Index mult = 1;
149 for(Index d=0; d<dim(); ++d)
150 {
151 if( mult & corner ) res[d] = m_max[d];
152 else res[d] = m_min[d];
153 mult *= 2;
154 }
155 return res;
156 }
157
158 /** \returns a random point inside the bounding box sampled with
159 * a uniform distribution */
sample()160 inline VectorType sample() const
161 {
162 VectorType r;
163 for(Index d=0; d<dim(); ++d)
164 {
165 if(!ScalarTraits::IsInteger)
166 {
167 r[d] = m_min[d] + (m_max[d]-m_min[d])
168 * internal::random<Scalar>(Scalar(0), Scalar(1));
169 }
170 else
171 r[d] = internal::random(m_min[d], m_max[d]);
172 }
173 return r;
174 }
175
176 /** \returns true if the point \a p is inside the box \c *this. */
177 template<typename Derived>
contains(const MatrixBase<Derived> & a_p)178 inline bool contains(const MatrixBase<Derived>& a_p) const
179 {
180 typename internal::nested<Derived,2>::type p(a_p.derived());
181 return (m_min.array()<=p.array()).all() && (p.array()<=m_max.array()).all();
182 }
183
184 /** \returns true if the box \a b is entirely inside the box \c *this. */
contains(const AlignedBox & b)185 inline bool contains(const AlignedBox& b) const
186 { return (m_min.array()<=(b.min)().array()).all() && ((b.max)().array()<=m_max.array()).all(); }
187
188 /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this. */
189 template<typename Derived>
extend(const MatrixBase<Derived> & a_p)190 inline AlignedBox& extend(const MatrixBase<Derived>& a_p)
191 {
192 typename internal::nested<Derived,2>::type p(a_p.derived());
193 m_min = m_min.cwiseMin(p);
194 m_max = m_max.cwiseMax(p);
195 return *this;
196 }
197
198 /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this. */
extend(const AlignedBox & b)199 inline AlignedBox& extend(const AlignedBox& b)
200 {
201 m_min = m_min.cwiseMin(b.m_min);
202 m_max = m_max.cwiseMax(b.m_max);
203 return *this;
204 }
205
206 /** Clamps \c *this by the box \a b and returns a reference to \c *this. */
clamp(const AlignedBox & b)207 inline AlignedBox& clamp(const AlignedBox& b)
208 {
209 m_min = m_min.cwiseMax(b.m_min);
210 m_max = m_max.cwiseMin(b.m_max);
211 return *this;
212 }
213
214 /** Returns an AlignedBox that is the intersection of \a b and \c *this */
intersection(const AlignedBox & b)215 inline AlignedBox intersection(const AlignedBox& b) const
216 {return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); }
217
218 /** Returns an AlignedBox that is the union of \a b and \c *this */
merged(const AlignedBox & b)219 inline AlignedBox merged(const AlignedBox& b) const
220 { return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); }
221
222 /** Translate \c *this by the vector \a t and returns a reference to \c *this. */
223 template<typename Derived>
translate(const MatrixBase<Derived> & a_t)224 inline AlignedBox& translate(const MatrixBase<Derived>& a_t)
225 {
226 const typename internal::nested<Derived,2>::type t(a_t.derived());
227 m_min += t;
228 m_max += t;
229 return *this;
230 }
231
232 /** \returns the squared distance between the point \a p and the box \c *this,
233 * and zero if \a p is inside the box.
234 * \sa exteriorDistance()
235 */
236 template<typename Derived>
237 inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& a_p) const;
238
239 /** \returns the squared distance between the boxes \a b and \c *this,
240 * and zero if the boxes intersect.
241 * \sa exteriorDistance()
242 */
243 inline Scalar squaredExteriorDistance(const AlignedBox& b) const;
244
245 /** \returns the distance between the point \a p and the box \c *this,
246 * and zero if \a p is inside the box.
247 * \sa squaredExteriorDistance()
248 */
249 template<typename Derived>
exteriorDistance(const MatrixBase<Derived> & p)250 inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const
251 { return internal::sqrt(NonInteger(squaredExteriorDistance(p))); }
252
253 /** \returns the distance between the boxes \a b and \c *this,
254 * and zero if the boxes intersect.
255 * \sa squaredExteriorDistance()
256 */
exteriorDistance(const AlignedBox & b)257 inline NonInteger exteriorDistance(const AlignedBox& b) const
258 { return internal::sqrt(NonInteger(squaredExteriorDistance(b))); }
259
260 /** \returns \c *this with scalar type casted to \a NewScalarType
261 *
262 * Note that if \a NewScalarType is equal to the current scalar type of \c *this
263 * then this function smartly returns a const reference to \c *this.
264 */
265 template<typename NewScalarType>
266 inline typename internal::cast_return_type<AlignedBox,
cast()267 AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
268 {
269 return typename internal::cast_return_type<AlignedBox,
270 AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
271 }
272
273 /** Copy constructor with scalar type conversion */
274 template<typename OtherScalarType>
AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime> & other)275 inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other)
276 {
277 m_min = (other.min)().template cast<Scalar>();
278 m_max = (other.max)().template cast<Scalar>();
279 }
280
281 /** \returns \c true if \c *this is approximately equal to \a other, within the precision
282 * determined by \a prec.
283 *
284 * \sa MatrixBase::isApprox() */
285 bool isApprox(const AlignedBox& other, RealScalar prec = ScalarTraits::dummy_precision()) const
286 { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); }
287
288 protected:
289
290 VectorType m_min, m_max;
291 };
292
293
294
295 template<typename Scalar,int AmbientDim>
296 template<typename Derived>
squaredExteriorDistance(const MatrixBase<Derived> & a_p)297 inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const MatrixBase<Derived>& a_p) const
298 {
299 const typename internal::nested<Derived,2*AmbientDim>::type p(a_p.derived());
300 Scalar dist2(0);
301 Scalar aux;
302 for (Index k=0; k<dim(); ++k)
303 {
304 if( m_min[k] > p[k] )
305 {
306 aux = m_min[k] - p[k];
307 dist2 += aux*aux;
308 }
309 else if( p[k] > m_max[k] )
310 {
311 aux = p[k] - m_max[k];
312 dist2 += aux*aux;
313 }
314 }
315 return dist2;
316 }
317
318 template<typename Scalar,int AmbientDim>
squaredExteriorDistance(const AlignedBox & b)319 inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const AlignedBox& b) const
320 {
321 Scalar dist2(0);
322 Scalar aux;
323 for (Index k=0; k<dim(); ++k)
324 {
325 if( m_min[k] > b.m_max[k] )
326 {
327 aux = m_min[k] - b.m_max[k];
328 dist2 += aux*aux;
329 }
330 else if( b.m_min[k] > m_max[k] )
331 {
332 aux = b.m_min[k] - m_max[k];
333 dist2 += aux*aux;
334 }
335 }
336 return dist2;
337 }
338
339 /** \defgroup alignedboxtypedefs Global aligned box typedefs
340 *
341 * \ingroup Geometry_Module
342 *
343 * Eigen defines several typedef shortcuts for most common aligned box types.
344 *
345 * The general patterns are the following:
346 *
347 * \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,
348 * and where \c Type can be \c i for integer, \c f for float, \c d for double.
349 *
350 * 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.
351 *
352 * \sa class AlignedBox
353 */
354
355 #define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \
356 /** \ingroup alignedboxtypedefs */ \
357 typedef AlignedBox<Type, Size> AlignedBox##SizeSuffix##TypeSuffix;
358
359 #define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
360 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 1, 1) \
361 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
362 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
363 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
364 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X)
365
366 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i)
367 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f)
368 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d)
369
370 #undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
371 #undef EIGEN_MAKE_TYPEDEFS
372
373 } // end namespace Eigen
374
375 #endif // EIGEN_ALIGNEDBOX_H
376