DGtal  1.3.beta
BoundedLatticePolytope.h
1 
17 #pragma once
18 
31 #if defined(BoundedLatticePolytope_RECURSES)
32 #error Recursive header files inclusion detected in BoundedLatticePolytope.h
33 #else // defined(BoundedLatticePolytope_RECURSES)
34 
35 #define BoundedLatticePolytope_RECURSES
36 
37 #if !defined BoundedLatticePolytope_h
38 
39 #define BoundedLatticePolytope_h
40 
42 // Inclusions
43 #include <iostream>
44 #include <list>
45 #include <vector>
46 #include <string>
47 #include "DGtal/base/Common.h"
48 #include "DGtal/kernel/CSpace.h"
49 #include "DGtal/kernel/domains/HyperRectDomain.h"
50 #include "DGtal/arithmetic/IntegerComputer.h"
51 #include "DGtal/arithmetic/ClosedIntegerHalfPlane.h"
53 
54 namespace DGtal
55 {
56 
58  // template class BoundedLatticePolytope
73  template < typename TSpace >
75  {
77 
78  public:
80  typedef TSpace Space;
81  typedef typename Space::Integer Integer;
82  typedef typename Space::Point Point;
83  typedef typename Space::Vector Vector;
84  typedef std::vector<Vector> InequalityMatrix;
85  typedef std::vector<Integer> InequalityVector;
88 #ifdef WITH_BIGINTEGER
90 #else
91  typedef DGtal::int64_t BigInteger;
92 #endif
94 
99  struct UnitSegment {
101  UnitSegment( Dimension d ) : k( d ) {}
102  };
103 
111  };
112 
120  };
121 
127  struct UnitCell {
128  std::vector<Dimension> dims;
129  UnitCell( std::initializer_list<Dimension> l )
130  : dims( l.begin(), l.end() ) {}
131 
138  friend std::ostream&
139  operator<< ( std::ostream & out,
140  const UnitCell & object )
141  {
142  out << "{";
143  for ( Dimension i = 0; i < object.dims.size(); ++i ) out << object.dims[ i ];
144  out << "}";
145  return out;
146  }
147  };
148 
155  std::vector<Dimension> dims;
156  RightStrictUnitCell( std::initializer_list<Dimension> l )
157  : dims( l.begin(), l.end() ) {}
158 
165  friend std::ostream&
166  operator<< ( std::ostream & out,
167  const RightStrictUnitCell & object )
168  {
169  out << "{";
170  for ( Dimension i = 0; i < object.dims.size(); ++i ) out << object.dims[ i ];
171  out << "}";
172  return out;
173  }
174  };
175 
182  std::vector<Dimension> dims;
183  LeftStrictUnitCell( std::initializer_list<Dimension> l )
184  : dims( l.begin(), l.end() ) {}
185 
192  friend std::ostream&
193  operator<< ( std::ostream & out,
194  const LeftStrictUnitCell & object )
195  {
196  out << "{";
197  for ( Dimension i = 0; i < object.dims.size(); ++i ) out << object.dims[ i ];
198  out << "}";
199  return out;
200  }
201  };
202 
205 
209  ~BoundedLatticePolytope() = default;
210 
214  BoundedLatticePolytope() = default;
215 
220  BoundedLatticePolytope ( const Self & other ) = default;
221 
222 
229  BoundedLatticePolytope( std::initializer_list<Point> l );
230 
239  template <typename PointIterator>
240  BoundedLatticePolytope( PointIterator itB, PointIterator itE );
241 
261  template <typename HalfSpaceIterator>
263  HalfSpaceIterator itB, HalfSpaceIterator itE,
264  bool valid_edge_constraints = false,
265  bool check_duplicate_constraints = false );
266 
286  template <typename HalfSpaceIterator>
287  void init( const Domain& domain,
288  HalfSpaceIterator itB, HalfSpaceIterator itE,
289  bool valid_edge_constraints = false,
290  bool check_duplicate_constraints = false );
291 
292 
305  template <typename PointIterator>
306  bool init( PointIterator itB, PointIterator itE );
307 
313  Self & operator= ( const Self & other ) = default;
314 
316  void clear();
317 
319 
320  // ----------------------- Accessor services ------------------------------
321  public:
324 
326  const Domain& getDomain() const;
327 
329  unsigned int nbHalfSpaces() const;
330 
336  const Vector& getA( unsigned int i ) const;
337 
343  Integer getB( unsigned int i ) const;
344 
350  bool isLarge( unsigned int i ) const;
351 
353  const InequalityMatrix& getA() const;
354 
356  const InequalityVector& getB() const;
360  const std::vector<bool>& getI() const;
361 
366  bool canBeSummed() const;
367 
369 
370  // ----------------------- Check point services ------------------------------
371  public:
372 
375 
380  bool isInside( const Point& p ) const;
381 
388  bool isDomainPointInside( const Point& p ) const;
389 
394  bool isInterior( const Point& p ) const;
395 
400  bool isBoundary( const Point& p ) const;
401 
403 
404  // ----------------------- Modification services ------------------------------
405  public:
406 
409 
413 
426  unsigned int cut( Dimension k, bool pos, Integer b, bool large = true );
427 
445  unsigned int cut( const Vector& a, Integer b, bool large = true,
446  bool valid_edge_constraint = false );
447 
464  unsigned int cut( const HalfSpace & hs, bool large = true,
465  bool valid_edge_constraint = false );
466 
471  void swap( BoundedLatticePolytope & other );
472 
473 
479  Self& operator*=( Integer t );
480 
487  Self& operator+=( UnitSegment s );
488 
495  Self& operator+=( UnitCell c );
496 
503  Self& operator+=( RightStrictUnitSegment s );
504 
511  Self& operator+=( RightStrictUnitCell c );
512 
519  Self& operator+=( LeftStrictUnitSegment s );
520 
527  Self& operator+=( LeftStrictUnitCell c );
529 
530  // ----------------------- Enumeration services ------------------------------
531  public:
532 
535 
543  Integer count() const;
544 
555  Integer countInterior() const;
556 
567  Integer countBoundary() const;
568 
579  Integer countWithin( Point low, Point hi ) const;
580 
597  Integer countUpTo( Integer max ) const;
598 
607  void getPoints( std::vector<Point>& pts ) const;
608 
617  void getInteriorPoints( std::vector<Point>& pts ) const;
618 
627  void getBoundaryPoints( std::vector<Point>& pts ) const;
628 
639  template <typename PointSet>
640  void insertPoints( PointSet& pts_set ) const;
641 
643 
644 
645  // ----------------------- Interface --------------------------------------
646  public:
649 
654  void selfDisplay ( std::ostream & out ) const;
655 
662  bool isValid() const;
663 
667  std::string className() const;
668 
670 
671  // ------------------------- Protected Datas ------------------------------
672  protected:
680  std::vector<bool> I;
683 
684  // ------------------------- Private Datas --------------------------------
685  private:
686 
687 
688  // ------------------------- Internals ------------------------------------
689  private:
697 
704 
711 
712  }; // end of class BoundedLatticePolytope
713 
714  namespace detail {
723  template <DGtal::Dimension N, typename TInteger>
725  typedef TInteger Integer;
727  typedef typename Space::Point Point;
728  typedef typename Space::Vector Vector;
731 
744  static void
745  addEdgeConstraint( Polytope& , unsigned int , unsigned int ,
746  const std::vector<Point>& )
747  {
748  trace.error() << "[BoundedLatticePolytopeHelper::addEdgeConstraint]"
749  << " this method is only implemented in 3D." << std::endl;
750  }
751 
754  static
755  Vector crossProduct( const Vector& , const Vector& )
756  {
757  trace.error() << "[BoundedLatticePolytopeHelper::crossProduct]"
758  << " this method is only implemented in 3D." << std::endl;
759  return Vector::zero;
760  }
761  };
762 
770  template <typename TInteger>
771  struct BoundedLatticePolytopeSpecializer<3, TInteger> {
772  typedef TInteger Integer;
774  typedef typename Space::Point Point;
775  typedef typename Space::Vector Vector;
778 
788  static void
789  addEdgeConstraint( Polytope& P, unsigned int i, unsigned int j,
790  const std::vector<Point>& pts )
791  {
792  Vector ab = pts[ i ] - pts[ j ];
793  for ( int s = 0; s < 2; s++ )
794  for ( Dimension k = 0; k < dimension; ++k )
795  {
796  Vector n = ab.crossProduct( Point::base( k, (s == 0) ? 1 : -1 ) );
797  Integer b = n.dot( pts[ i ] );
798  std::size_t nb_in = 0;
799  for ( auto p : pts ) {
800  Integer v = n.dot( p );
801  if ( v < b ) nb_in++;
802  }
803  if ( nb_in == pts.size() - 2 ) {
804  P.cut( n, b, true, true );
805  }
806  }
807  }
812  static
813  Vector crossProduct( const Vector& v1, const Vector& v2 )
814  {
815  return v1.crossProduct( v2 );
816  }
817  };
818  }
819 
822 
829  template <typename TSpace>
830  std::ostream&
831  operator<< ( std::ostream & out,
832  const BoundedLatticePolytope<TSpace> & object );
833 
834 
840  template <typename TSpace>
841  BoundedLatticePolytope<TSpace>
843  const BoundedLatticePolytope<TSpace> & P );
844 
845 
853  template <typename TSpace>
854  BoundedLatticePolytope<TSpace>
855  operator+ ( const BoundedLatticePolytope<TSpace> & P,
856  typename BoundedLatticePolytope<TSpace>::UnitSegment s );
857 
865  template <typename TSpace>
866  BoundedLatticePolytope<TSpace>
867  operator+ ( const BoundedLatticePolytope<TSpace> & P,
868  typename BoundedLatticePolytope<TSpace>::UnitCell c );
869 
877  template <typename TSpace>
878  BoundedLatticePolytope<TSpace>
879  operator+ ( const BoundedLatticePolytope<TSpace> & P,
880  typename BoundedLatticePolytope<TSpace>::RightStrictUnitSegment s );
881 
889  template <typename TSpace>
890  BoundedLatticePolytope<TSpace>
891  operator+ ( const BoundedLatticePolytope<TSpace> & P,
892  typename BoundedLatticePolytope<TSpace>::RightStrictUnitCell c );
893 
901  template <typename TSpace>
902  BoundedLatticePolytope<TSpace>
903  operator+ ( const BoundedLatticePolytope<TSpace> & P,
904  typename BoundedLatticePolytope<TSpace>::LeftStrictUnitSegment s );
905 
913  template <typename TSpace>
914  BoundedLatticePolytope<TSpace>
915  operator+ ( const BoundedLatticePolytope<TSpace> & P,
916  typename BoundedLatticePolytope<TSpace>::LeftStrictUnitCell c );
917 
919 
920 } // namespace DGtal
921 
922 
924 // Includes inline functions.
925 #include "BoundedLatticePolytope.ih"
926 
927 // //
929 
930 #endif // !defined BoundedLatticePolytope_h
931 
932 #undef BoundedLatticePolytope_RECURSES
933 #endif // else defined(BoundedLatticePolytope_RECURSES)
DGtal::BigInteger
mpz_class BigInteger
Multi-precision integer with GMP implementation.
Definition: BasicTypes.h:79
DGtal::BoundedLatticePolytope::UnitCell::UnitCell
UnitCell(std::initializer_list< Dimension > l)
Definition: BoundedLatticePolytope.h:129
DGtal::BoundedLatticePolytope::Point
Space::Point Point
Definition: BoundedLatticePolytope.h:82
DGtal::detail::BoundedLatticePolytopeSpecializer< 3, TInteger >::Polytope
BoundedLatticePolytope< Space > Polytope
Definition: BoundedLatticePolytope.h:776
DGtal::PointVector< dim, Integer >::zero
static Self zero
Static const for zero PointVector.
Definition: PointVector.h:1595
DGtal::detail::BoundedLatticePolytopeSpecializer< 3, TInteger >::addEdgeConstraint
static void addEdgeConstraint(Polytope &P, unsigned int i, unsigned int j, const std::vector< Point > &pts)
Definition: BoundedLatticePolytope.h:789
DGtal::BoundedLatticePolytope::countBoundary
Integer countBoundary() const
DGtal::BoundedLatticePolytope::insertPoints
void insertPoints(PointSet &pts_set) const
DGtal::detail::BoundedLatticePolytopeSpecializer::addEdgeConstraint
static void addEdgeConstraint(Polytope &, unsigned int, unsigned int, const std::vector< Point > &)
Definition: BoundedLatticePolytope.h:745
DGtal::BoundedLatticePolytope::countInterior
Integer countInterior() const
DGtal::HyperRectDomain< Space >
DGtal::detail::BoundedLatticePolytopeSpecializer::Space
SpaceND< N, Integer > Space
Definition: BoundedLatticePolytope.h:726
DGtal::BoundedLatticePolytope::Self
BoundedLatticePolytope< TSpace > Self
Definition: BoundedLatticePolytope.h:79
DGtal::concepts::CSpace
Aim: Defines the concept describing a digital space, ie a cartesian product of integer lines.
Definition: CSpace.h:105
DGtal::BoundedLatticePolytope::isDomainPointInside
bool isDomainPointInside(const Point &p) const
DGtal::detail::BoundedLatticePolytopeSpecializer::dimension
static const Dimension dimension
Definition: BoundedLatticePolytope.h:730
DGtal::BoundedLatticePolytope::canBeSummed
bool canBeSummed() const
max
int max(int a, int b)
Definition: testArithmeticalDSS.cpp:1108
DGtal::BoundedLatticePolytope::HalfSpace
ClosedIntegerHalfPlane< Space > HalfSpace
Definition: BoundedLatticePolytope.h:87
DGtal::BoundedLatticePolytope::myValidEdgeConstraints
bool myValidEdgeConstraints
Indicates if Minkowski sums with segments will be valid.
Definition: BoundedLatticePolytope.h:682
DGtal::Trace::error
std::ostream & error()
DGtal::BoundedLatticePolytope::D
Domain D
Tight bounded box.
Definition: BoundedLatticePolytope.h:678
DGtal::BoundedLatticePolytope::getPoints
void getPoints(std::vector< Point > &pts) const
DGtal::BoundedLatticePolytope::countUpTo
Integer countUpTo(Integer max) const
DGtal::BoundedLatticePolytope::I
std::vector< bool > I
Are inequalities large ?
Definition: BoundedLatticePolytope.h:680
DGtal::BoundedLatticePolytope::UnitSegment
Definition: BoundedLatticePolytope.h:99
DGtal::BoundedLatticePolytope::interiorPolytope
BoundedLatticePolytope interiorPolytope() const
DGtal::BoundedLatticePolytope::RightStrictUnitCell::dims
std::vector< Dimension > dims
Definition: BoundedLatticePolytope.h:155
DGtal::trace
Trace trace
Definition: Common.h:154
DGtal::Dimension
DGtal::uint32_t Dimension
Definition: Common.h:137
DGtal::detail::BoundedLatticePolytopeSpecializer::Integer
TInteger Integer
Definition: BoundedLatticePolytope.h:725
DGtal::BoundedLatticePolytope::LeftStrictUnitCell::operator<<
friend std::ostream & operator<<(std::ostream &out, const LeftStrictUnitCell &object)
Definition: BoundedLatticePolytope.h:193
DGtal::BoundedLatticePolytope::RightStrictUnitCell
Definition: BoundedLatticePolytope.h:154
DGtal::BoundedLatticePolytope::LeftStrictUnitCell
Definition: BoundedLatticePolytope.h:181
DGtal::detail::BoundedLatticePolytopeSpecializer
Aim: It is just a helper class for BoundedLatticePolytope to add dimension specific static methods.
Definition: BoundedLatticePolytope.h:724
DGtal::BoundedLatticePolytope::cut
unsigned int cut(Dimension k, bool pos, Integer b, bool large=true)
DGtal::BoundedLatticePolytope::clear
void clear()
Clears the polytope.
DGtal::BoundedLatticePolytope::getBoundaryPoints
void getBoundaryPoints(std::vector< Point > &pts) const
DGtal::detail::BoundedLatticePolytopeSpecializer< 3, TInteger >::Vector
Space::Vector Vector
Definition: BoundedLatticePolytope.h:775
DGtal::BoundedLatticePolytope::internalInitFromSegment3D
bool internalInitFromSegment3D(Point a, Point b)
DGtal::BoundedLatticePolytope::Vector
Space::Vector Vector
Definition: BoundedLatticePolytope.h:83
DGtal::BoundedLatticePolytope::init
void init(const Domain &domain, HalfSpaceIterator itB, HalfSpaceIterator itE, bool valid_edge_constraints=false, bool check_duplicate_constraints=false)
DGtal::BoundedLatticePolytope::selfDisplay
void selfDisplay(std::ostream &out) const
DGtal::operator<<
std::ostream & operator<<(std::ostream &out, const ATu0v1< TKSpace, TLinearAlgebra > &object)
DGtal::PointVector< dim, Integer >::base
static Self base(Dimension k, Component val=1)
DGtal::SpaceND
Definition: SpaceND.h:95
DGtal::detail::BoundedLatticePolytopeSpecializer< 3, TInteger >::Space
SpaceND< 3, Integer > Space
Definition: BoundedLatticePolytope.h:773
DGtal::PointVector::crossProduct
auto crossProduct(const PointVector< dim, OtherComponent, OtherStorage > &v) const -> decltype(DGtal::crossProduct(*this, v))
Cross product with a PointVector.
DGtal::BoundedLatticePolytope::countWithin
Integer countWithin(Point low, Point hi) const
DGtal::BoundedLatticePolytope::Domain
HyperRectDomain< Space > Domain
Definition: BoundedLatticePolytope.h:86
DGtal::BoundedLatticePolytope::LeftStrictUnitSegment::k
Dimension k
Definition: BoundedLatticePolytope.h:118
DGtal::BoundedLatticePolytope::isInside
bool isInside(const Point &p) const
DGtal::BoundedLatticePolytope::RightStrictUnitSegment::k
Dimension k
Definition: BoundedLatticePolytope.h:109
DGtal::operator+
Circulator< TIterator > operator+(typename IteratorCirculatorTraits< TIterator >::Difference d, Circulator< TIterator > &object)
Definition: Circulator.h:453
DGtal::BoundedLatticePolytope::BigInteger
DGtal::BigInteger BigInteger
Definition: BoundedLatticePolytope.h:89
DGtal::BoundedLatticePolytope::B
InequalityVector B
The vector B in the polytope representation .
Definition: BoundedLatticePolytope.h:676
DGtal::BoundedLatticePolytope::InequalityVector
std::vector< Integer > InequalityVector
Definition: BoundedLatticePolytope.h:85
DGtal::BoundedLatticePolytope::operator*=
Self & operator*=(Integer t)
DGtal
DGtal is the top-level namespace which contains all DGtal functions and types.
DGtal::BoundedLatticePolytope::UnitSegment::k
Dimension k
Definition: BoundedLatticePolytope.h:100
DGtal::BoundedLatticePolytope::dimension
static const Dimension dimension
Definition: BoundedLatticePolytope.h:93
Domain
HyperRectDomain< Space > Domain
Definition: testSimpleRandomAccessRangeFromPoint.cpp:44
DGtal::BoundedLatticePolytope::LeftStrictUnitSegment::LeftStrictUnitSegment
LeftStrictUnitSegment(Dimension d)
Definition: BoundedLatticePolytope.h:119
DGtal::BoundedLatticePolytope::LeftStrictUnitSegment
Definition: BoundedLatticePolytope.h:117
DGtal::BoundedLatticePolytope::internalInitFromTriangle3D
bool internalInitFromTriangle3D(Point a, Point b, Point c)
DGtal::detail::BoundedLatticePolytopeSpecializer::crossProduct
static Vector crossProduct(const Vector &, const Vector &)
Definition: BoundedLatticePolytope.h:755
DGtal::SpaceND::dimension
static const Dimension dimension
static constants to store the dimension.
Definition: SpaceND.h:132
DGtal::BoundedLatticePolytope::~BoundedLatticePolytope
~BoundedLatticePolytope()=default
DGtal::detail::BoundedLatticePolytopeSpecializer< 3, TInteger >::Point
Space::Point Point
Definition: BoundedLatticePolytope.h:774
DGtal::BoundedLatticePolytope::getInteriorPoints
void getInteriorPoints(std::vector< Point > &pts) const
DGtal::detail::BoundedLatticePolytopeSpecializer::Point
Space::Point Point
Definition: BoundedLatticePolytope.h:727
DGtal::BoundedLatticePolytope::operator=
Self & operator=(const Self &other)=default
DGtal::BoundedLatticePolytope::BOOST_CONCEPT_ASSERT
BOOST_CONCEPT_ASSERT((concepts::CSpace< TSpace >))
Vector
FreemanChain< int >::Vector Vector
Definition: testCombinDSS.cpp:60
DGtal::BoundedLatticePolytope::count
Integer count() const
Integer
Point::Coordinate Integer
Definition: examplePlaneProbingParallelepipedEstimator.cpp:44
DGtal::ClosedIntegerHalfPlane
Aim: A half-space specified by a vector N and a constant c. The half-space is the set .
Definition: ClosedIntegerHalfPlane.h:63
DGtal::BoundedLatticePolytope::swap
void swap(BoundedLatticePolytope &other)
DGtal::BoundedLatticePolytope::RightStrictUnitCell::operator<<
friend std::ostream & operator<<(std::ostream &out, const RightStrictUnitCell &object)
Definition: BoundedLatticePolytope.h:166
DGtal::BoundedLatticePolytope::nbHalfSpaces
unsigned int nbHalfSpaces() const
DGtal::BoundedLatticePolytope::isValid
bool isValid() const
DGtal::BoundedLatticePolytope::isInterior
bool isInterior(const Point &p) const
DGtal::detail::BoundedLatticePolytopeSpecializer< 3, TInteger >::crossProduct
static Vector crossProduct(const Vector &v1, const Vector &v2)
Definition: BoundedLatticePolytope.h:813
DGtal::detail::BoundedLatticePolytopeSpecializer::Polytope
BoundedLatticePolytope< Space > Polytope
Definition: BoundedLatticePolytope.h:729
DGtal::BoundedLatticePolytope::isLarge
bool isLarge(unsigned int i) const
domain
Domain domain
Definition: testProjection.cpp:88
DGtal::PointVector< dim, Integer >
DGtal::detail::BoundedLatticePolytopeSpecializer::Vector
Space::Vector Vector
Definition: BoundedLatticePolytope.h:728
DGtal::BoundedLatticePolytope::Space
TSpace Space
Definition: BoundedLatticePolytope.h:80
DGtal::BoundedLatticePolytope::getI
const std::vector< bool > & getI() const
DGtal::BoundedLatticePolytope::getDomain
const Domain & getDomain() const
DGtal::operator*
KForm< Calculus, order, duality > operator*(const typename Calculus::Scalar &scalar, const KForm< Calculus, order, duality > &form)
DGtal::BoundedLatticePolytope::UnitSegment::UnitSegment
UnitSegment(Dimension d)
Definition: BoundedLatticePolytope.h:101
DGtal::BoundedLatticePolytope
Aim: Represents an nD lattice polytope, i.e. a convex polyhedron bounded with vertices with integer c...
Definition: BoundedLatticePolytope.h:74
DGtal::BoundedLatticePolytope::UnitCell
Definition: BoundedLatticePolytope.h:127
DGtal::int64_t
boost::int64_t int64_t
signed 94-bit integer.
Definition: BasicTypes.h:74
DGtal::BoundedLatticePolytope::UnitCell::dims
std::vector< Dimension > dims
Definition: BoundedLatticePolytope.h:128
DGtal::BoundedLatticePolytope::getA
const InequalityMatrix & getA() const
DGtal::BoundedLatticePolytope::A
InequalityMatrix A
The matrix A in the polytope representation .
Definition: BoundedLatticePolytope.h:674
DGtal::BoundedLatticePolytope::internalInitFromSegment2D
bool internalInitFromSegment2D(Point a, Point b)
DGtal::BoundedLatticePolytope::BoundedLatticePolytope
BoundedLatticePolytope()=default
DGtal::BoundedLatticePolytope::className
std::string className() const
DGtal::BoundedLatticePolytope::isBoundary
bool isBoundary(const Point &p) const
DGtal::BoundedLatticePolytope::operator+=
Self & operator+=(UnitSegment s)
DGtal::detail::BoundedLatticePolytopeSpecializer< 3, TInteger >::Integer
TInteger Integer
Definition: BoundedLatticePolytope.h:772
DGtal::BoundedLatticePolytope::RightStrictUnitCell::RightStrictUnitCell
RightStrictUnitCell(std::initializer_list< Dimension > l)
Definition: BoundedLatticePolytope.h:156
DGtal::BoundedLatticePolytope::InequalityMatrix
std::vector< Vector > InequalityMatrix
Definition: BoundedLatticePolytope.h:84
DGtal::BoundedLatticePolytope::getB
const InequalityVector & getB() const
Point
MyPointD Point
Definition: testClone2.cpp:383
DGtal::BoundedLatticePolytope::LeftStrictUnitCell::LeftStrictUnitCell
LeftStrictUnitCell(std::initializer_list< Dimension > l)
Definition: BoundedLatticePolytope.h:183
DGtal::BoundedLatticePolytope::UnitCell::operator<<
friend std::ostream & operator<<(std::ostream &out, const UnitCell &object)
Definition: BoundedLatticePolytope.h:139
DGtal::BoundedLatticePolytope::RightStrictUnitSegment
Definition: BoundedLatticePolytope.h:108
DGtal::SpaceND::Integer
TInteger Integer
Arithmetic ring induced by (+,-,*) and Integer numbers.
Definition: SpaceND.h:102
DGtal::BoundedLatticePolytope::Integer
Space::Integer Integer
Definition: BoundedLatticePolytope.h:81
DGtal::BoundedLatticePolytope::RightStrictUnitSegment::RightStrictUnitSegment
RightStrictUnitSegment(Dimension d)
Definition: BoundedLatticePolytope.h:110
DGtal::BoundedLatticePolytope::LeftStrictUnitCell::dims
std::vector< Dimension > dims
Definition: BoundedLatticePolytope.h:182