DGtal 1.3.0
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EhrhartPolynomial.h
1
17#pragma once
18
31#if defined(EhrhartPolynomial_RECURSES)
32#error Recursive header files inclusion detected in EhrhartPolynomial.h
33#else // defined(EhrhartPolynomial_RECURSES)
35#define EhrhartPolynomial_RECURSES
36
37#if !defined EhrhartPolynomial_h
39#define EhrhartPolynomial_h
40
42// Inclusions
43#include <iostream>
44#include <vector>
45#include "DGtal/base/Common.h"
46#include "DGtal/kernel/NumberTraits.h"
47#include "DGtal/kernel/CInteger.h"
48#include "DGtal/kernel/CSpace.h"
49#include "DGtal/math/LagrangeInterpolation.h"
50#include "DGtal/geometry/volumes/BoundedLatticePolytope.h"
52
53namespace DGtal
54{
65 template <typename TSpace, typename TInteger>
67 {
70
71 // ----------------------- public types -----------------------------------
72 public:
74 typedef TSpace Space;
75 typedef TInteger Integer;
79 typedef std::size_t Size;
80
81 // ----------------------- Standard services ------------------------------
82 public:
83
87 ~EhrhartPolynomial() = default;
88
93 : myE(), myD( NumberTraits< Integer >::ZERO )
94 {}
95
100 {
101 init( polytope );
102 }
103
108 EhrhartPolynomial( const EhrhartPolynomial & other ) = default;
109
115
121 EhrhartPolynomial & operator=( const EhrhartPolynomial & other ) = default;
122
129
131 inline Polynomial numerator() const
132 {
133 return myE;
134 }
135
137 inline Integer denominator() const
138 {
139 return myD;
140 }
141
145 void init( const LatticePolytope& polytope )
146 {
147 std::vector< Integer > X( Space::dimension + 1 );
148 std::vector< Integer > Y( Space::dimension + 1 );
151 for ( Integer i = 1; i <= Space::dimension; ++i )
152 {
153 LatticePolytope Q = i * polytope;
154 Integer nb = Q.count();
155 X[ i ] = i;
156 Y[ i ] = nb;
157 }
158 // Compute polynomial (degree d)
159 Lagrange L( X );
160 myE = L.polynomial( Y );
161 myD = L.denominator();
162 }
163
164 // @param t the dilation factor for this polytope P
165 // @return the number of lattice points of t * P
167 {
168 return myE( t ) / myD;
169 }
170
171 // @param t the dilation factor for this polytope P
172 // @return 0 if everything is correct.
174 {
175 return myE( t ) % myD;
176 }
177
178 // @param t the dilation factor for this polytope P
179 // @return the number of lattice points interior to t * P
180 // @note Use reciprocity formula (-1)^d E(-t)
182 return myE.degree() % 2 == 0
183 ? ( myE( -t ) / myD )
184 : - ( myE( -t ) / myD );
185 }
186
187 // @param t the dilation factor for this polytope P
188 // @return 0 if everything is correct.
190 return myE.degree() % 2 == 0
191 ? ( myE( -t ) % myD )
192 : - ( myE( -t ) % myD );
193 }
194
195 // ----------------------- Interface --------------------------------------
196 public:
197
202 void selfDisplay( std::ostream & that_stream ) const
203 {
204 that_stream << "[EhrhartPolynomial num=" << numerator()
205 << " den=" << denominator() << " ]" << std::endl;
206 }
207
212 bool OK() const
213 {
215 }
216
217 // ------------------------- Datas ----------------------------------------
218 protected:
219
224
225 };
226
235 template <typename TSpace, typename TInteger>
236 std::ostream&
237 operator<<( std::ostream & that_stream,
238 const EhrhartPolynomial< TSpace, TInteger > & that_object_to_display )
239 {
240 that_object_to_display.selfDisplay( that_stream );
241 return that_stream;
242 }
243
244
245} // namespace DGtal
246
247
249// Includes inline functions/methods if necessary.
250
251// //
253
254#endif // !defined EhrhartPolynomial_h
255
256#undef EhrhartPolynomial_RECURSES
257#endif // else defined(EhrhartPolynomial_RECURSES)
Aim: Represents an nD lattice polytope, i.e. a convex polyhedron bounded with vertices with integer c...
Aim: This class implements the class Ehrhart Polynomial which is related to lattice point enumeration...
Integer countInterior(Integer t) const
void init(const LatticePolytope &polytope)
BoundedLatticePolytope< Space > LatticePolytope
LagrangeInterpolation< Integer > Lagrange
void selfDisplay(std::ostream &that_stream) const
EhrhartPolynomial< TSpace, TInteger > Self
EhrhartPolynomial(const LatticePolytope &polytope)
EhrhartPolynomial(EhrhartPolynomial &&other)=default
Integer myD
The (integral) denominator of the Ehrhart polynomial.
Integer remainder(Integer t) const
Integer denominator() const
The (integral) denominator of the Ehrhart polynomial.
Lagrange::Polynomial Polynomial
Polynomial myE
The Ehrhart polynomial (integral numerator part)
BOOST_CONCEPT_ASSERT((concepts::CInteger< TInteger >))
EhrhartPolynomial(const EhrhartPolynomial &other)=default
EhrhartPolynomial & operator=(EhrhartPolynomial &&other)=default
EhrhartPolynomial & operator=(const EhrhartPolynomial &other)=default
Polynomial numerator() const
Integer count(Integer t) const
Integer remainderInterior(Integer t) const
BOOST_CONCEPT_ASSERT((concepts::CSpace< TSpace >))
Aim: This class implements Lagrange basis functions and Lagrange interpolation.
Polynomial polynomial(const std::vector< Ring > &yvalues)
Aim: Represents a multivariate polynomial, i.e. an element of , where K is some ring or field.
Definition: MPolynomial.h:955
int degree() const
Definition: MPolynomial.h:1109
static const Dimension dimension
static constants to store the dimension.
Definition: SpaceND.h:132
DGtal is the top-level namespace which contains all DGtal functions and types.
std::ostream & operator<<(std::ostream &out, const ClosedIntegerHalfPlane< TSpace > &object)
Aim: The traits class for all models of Cinteger.
Definition: NumberTraits.h:564
Aim: Concept checking for Integer Numbers. More precisely, this concept is a refinement of both CEucl...
Definition: CInteger.h:88
Aim: Defines the concept describing a digital space, ie a cartesian product of integer lines.
Definition: CSpace.h:106