DGtal  1.5.beta
DGtal::detail::RecursivePConvexity< dim, TInteger > Struct Template Reference

#include <DGtal/geometry/volumes/PConvexity.h>

Inheritance diagram for DGtal::detail::RecursivePConvexity< dim, TInteger >:
[legend]

Public Types

using Integer = TInteger
 
using Point = DGtal::PointVector< dim, Integer >
 
using ProjPoint = DGtal::PointVector< dim-1, Integer >
 
using ProjPConvexity = DGtal::detail::RecursivePConvexity< dim - 1, Integer >
 

Public Member Functions

 BOOST_CONCEPT_ASSERT ((concepts::CInteger< TInteger >))
 Integer must be a model of the concept CInteger. More...
 
 RecursivePConvexity (Dimension bd=dim)
 
void init (Dimension bd=dim)
 
bool isPConvex (const std::vector< Point > &X, bool safe) const
 
double fullConvexityMeasure (const std::vector< Point > &X, bool safe) const
 

Static Public Member Functions

static bool is0Convex (const std::vector< Point > &X, bool safe)
 
static double convexityMeasure (const std::vector< Point > &X, bool safe)
 
static ProjPoint project (const Point &p, Dimension a)
 
static std::vector< ProjPointproject (const std::vector< Point > &p, Dimension a)
 

Data Fields

std::vector< ProjPConvexityprojp
 The array of lower dimensional P-convexities. More...
 

Detailed Description

template<Dimension dim, typename TInteger = DGtal::int32_t>
struct DGtal::detail::RecursivePConvexity< dim, TInteger >

Hidden class to represent the P-convexity in a recursive way. Only used to compute P-convexity, but not exposed to users.

Note
This d-dimensional object builds d (d-1)-dimensional similar objects, but the k-th remembers to build only k lower dimensional ones.
Template Parameters
dimthe dimension of the digital space
TIntegerany model of integer (used to represent digital point coordinates).

Definition at line 66 of file PConvexity.h.

Member Typedef Documentation

◆ Integer

template<Dimension dim, typename TInteger = DGtal::int32_t>
using DGtal::detail::RecursivePConvexity< dim, TInteger >::Integer = TInteger

Definition at line 69 of file PConvexity.h.

◆ Point

template<Dimension dim, typename TInteger = DGtal::int32_t>
using DGtal::detail::RecursivePConvexity< dim, TInteger >::Point = DGtal::PointVector< dim, Integer >

Definition at line 70 of file PConvexity.h.

◆ ProjPConvexity

template<Dimension dim, typename TInteger = DGtal::int32_t>
using DGtal::detail::RecursivePConvexity< dim, TInteger >::ProjPConvexity = DGtal::detail::RecursivePConvexity< dim - 1, Integer >

Definition at line 72 of file PConvexity.h.

◆ ProjPoint

template<Dimension dim, typename TInteger = DGtal::int32_t>
using DGtal::detail::RecursivePConvexity< dim, TInteger >::ProjPoint = DGtal::PointVector< dim-1, Integer >

Definition at line 71 of file PConvexity.h.

Constructor & Destructor Documentation

◆ RecursivePConvexity()

template<Dimension dim, typename TInteger = DGtal::int32_t>
DGtal::detail::RecursivePConvexity< dim, TInteger >::RecursivePConvexity ( Dimension  bd = dim)
inline

Parameter bd is used to build exactly 2^d - 1 PConvexity objects when starting at dimension d.

Parameters
bdthe maximum axis of projection.

Definition at line 77 of file PConvexity.h.

78  {
79  init( bd );
80  }
void init(Dimension bd=dim)
Definition: PConvexity.h:83

References DGtal::detail::RecursivePConvexity< dim, TInteger >::init().

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT()

template<Dimension dim, typename TInteger = DGtal::int32_t>
DGtal::detail::RecursivePConvexity< dim, TInteger >::BOOST_CONCEPT_ASSERT ( (concepts::CInteger< TInteger >)  )

Integer must be a model of the concept CInteger.

◆ convexityMeasure()

template<Dimension dim, typename TInteger = DGtal::int32_t>
static double DGtal::detail::RecursivePConvexity< dim, TInteger >::convexityMeasure ( const std::vector< Point > &  X,
bool  safe 
)
inlinestatic
Parameters
Xany range of lattice points (without duplicates)
safewhen 'true' performs convex hull computations with arbitrary precision integer (if available), otherwise chooses a compromise between speed and precision (int64_t).
Precondition
X must not contain any duplicates.
Returns
a measure that has value 1.0 when X is digitally convex, and less otherwise.

Definition at line 155 of file PConvexity.h.

156  {
157  if ( X.empty() ) return 1.0;
158  // Build polytope according to internal integer type.
159  if ( safe )
160  {
164  computeLatticePolytope( X, false, false );
165  const std::size_t number_lattice_points_in_P = P.count();
166  return double( X.size() ) / double( number_lattice_points_in_P );
167  }
168  else
169  {
173  computeLatticePolytope( X, false, false );
174  const std::size_t number_lattice_points_in_P = P.count();
175  return double( X.size() ) / double( number_lattice_points_in_P );
176  }
177  }
DGtal::int64_t InternalInteger
static LatticePolytope computeLatticePolytope(const PointRange &input_points, bool remove_duplicates=true, bool make_minkowski_summable=false)

References DGtal::ConvexityHelper< dim, TInteger, TInternalInteger >::computeLatticePolytope().

Referenced by DGtal::PConvexity< TSpace >::convexityMeasure(), DGtal::detail::RecursivePConvexity< 1, TInteger >::fullConvexityMeasure(), and DGtal::detail::RecursivePConvexity< dim, TInteger >::fullConvexityMeasure().

◆ fullConvexityMeasure()

template<Dimension dim, typename TInteger = DGtal::int32_t>
double DGtal::detail::RecursivePConvexity< dim, TInteger >::fullConvexityMeasure ( const std::vector< Point > &  X,
bool  safe 
) const
inline
Parameters
Xany range of lattice points (without duplicates)
safewhen 'true' performs convex hull computations with arbitrary precision integer (if available), otherwise chooses a compromise between speed and precision (int64_t).
Precondition
X must not contain any duplicates.
Returns
a measure that has value 1.0 when X is P-convex (or equivalently fully convex), and less otherwise.

Definition at line 189 of file PConvexity.h.

190  {
191  double m = convexityMeasure( X, safe );
192  for ( std::size_t j = 0; j < projp.size(); j++ )
193  {
194  auto pX = project( X, j );
195  m *= projp[ j ].fullConvexityMeasure( pX, safe );
196  }
197  return m;
198  }
static double convexityMeasure(const std::vector< Point > &X, bool safe)
Definition: PConvexity.h:155
std::vector< ProjPConvexity > projp
The array of lower dimensional P-convexities.
Definition: PConvexity.h:237
static ProjPoint project(const Point &p, Dimension a)
Definition: PConvexity.h:206

References DGtal::detail::RecursivePConvexity< dim, TInteger >::convexityMeasure(), DGtal::detail::RecursivePConvexity< dim, TInteger >::project(), and DGtal::detail::RecursivePConvexity< dim, TInteger >::projp.

Referenced by DGtal::PConvexity< TSpace >::fullConvexityMeasure().

◆ init()

template<Dimension dim, typename TInteger = DGtal::int32_t>
void DGtal::detail::RecursivePConvexity< dim, TInteger >::init ( Dimension  bd = dim)
inline
Parameters
bdthe maximum axis of projection.

Definition at line 83 of file PConvexity.h.

84  {
85  for ( Dimension j = 0; j < bd; j++ )
86  projp.push_back( ProjPConvexity( j ) );
87  }
DGtal::uint32_t Dimension
Definition: Common.h:136
DGtal::detail::RecursivePConvexity< dim - 1, Integer > ProjPConvexity
Definition: PConvexity.h:72

References DGtal::detail::RecursivePConvexity< dim, TInteger >::projp.

Referenced by DGtal::detail::RecursivePConvexity< dim, TInteger >::RecursivePConvexity().

◆ is0Convex()

template<Dimension dim, typename TInteger = DGtal::int32_t>
static bool DGtal::detail::RecursivePConvexity< dim, TInteger >::is0Convex ( const std::vector< Point > &  X,
bool  safe 
)
inlinestatic
Parameters
Xany range of lattice points (without duplicates)
safewhen 'true' performs convex hull computations with arbitrary precision integer (if available), otherwise chooses a compromise between speed and precision (int64_t).
Returns
'true' if and only if X is a digitally convex set in the classic sense, i.e. \( Conv(X) \cap Z^d = X \).
Precondition
X must not contain any duplicates.

Definition at line 100 of file PConvexity.h.

101  {
102  if ( X.empty() ) return true;
103  // Build polytope according to internal integer type.
104  if ( safe )
105  {
109  computeLatticePolytope( X, false, false );
110  const std::size_t number_lattice_points_in_P = P.count();
111  return number_lattice_points_in_P == X.size();
112  }
113  else
114  {
118  computeLatticePolytope( X, false, false );
119  const std::size_t number_lattice_points_in_P = P.count();
120  return number_lattice_points_in_P == X.size();
121  }
122  }

References DGtal::ConvexityHelper< dim, TInteger, TInternalInteger >::computeLatticePolytope().

Referenced by DGtal::PConvexity< TSpace >::is0Convex(), DGtal::detail::RecursivePConvexity< 1, TInteger >::isPConvex(), and DGtal::detail::RecursivePConvexity< dim, TInteger >::isPConvex().

◆ isPConvex()

template<Dimension dim, typename TInteger = DGtal::int32_t>
bool DGtal::detail::RecursivePConvexity< dim, TInteger >::isPConvex ( const std::vector< Point > &  X,
bool  safe 
) const
inline
Parameters
Xany range of lattice points (without duplicates)
safewhen 'true' performs convex hull computations with arbitrary precision integer (if available), otherwise chooses a compromise between speed and precision (int64_t).
Returns
'true' if and only if X is a P-convex digital set.
Precondition
X must not contain any duplicates.

Definition at line 133 of file PConvexity.h.

134  {
135  if ( ! is0Convex( X, safe ) ) return false;
136  for ( std::size_t j = 0; j < projp.size(); j++ )
137  {
138  const auto pi_j_X = project( X, j );
139  if ( ! projp[ j ].isPConvex( pi_j_X, safe ) ) return false;
140  }
141  return true;
142  }
bool isPConvex(const std::vector< Point > &X, bool safe) const
Definition: PConvexity.h:133
static bool is0Convex(const std::vector< Point > &X, bool safe)
Definition: PConvexity.h:100

References DGtal::detail::RecursivePConvexity< dim, TInteger >::is0Convex(), DGtal::detail::RecursivePConvexity< dim, TInteger >::project(), and DGtal::detail::RecursivePConvexity< dim, TInteger >::projp.

Referenced by DGtal::PConvexity< TSpace >::isPConvex().

◆ project() [1/2]

template<Dimension dim, typename TInteger = DGtal::int32_t>
static ProjPoint DGtal::detail::RecursivePConvexity< dim, TInteger >::project ( const Point p,
Dimension  a 
)
inlinestatic

Projects a point p along dimension a.

Parameters
[in]pany digital point
[in]aany dimension
Returns
the digital point of dimension (d-1) with omitted a-th coordinate.

Definition at line 206 of file PConvexity.h.

207  {
208  ProjPoint pp;
209  Dimension j = 0;
210  for ( Dimension i = 0; i < Point::dimension; i++ )
211  if ( i != a ) pp[ j++ ] = p[ i ];
212  return pp;
213  }
static const Dimension dimension
Copy of the static dimension of the Point/Vector.
Definition: PointVector.h:626
DGtal::PointVector< dim-1, Integer > ProjPoint
Definition: PConvexity.h:71

References DGtal::PointVector< dim, Integer >::dimension.

Referenced by DGtal::detail::RecursivePConvexity< dim, TInteger >::fullConvexityMeasure(), DGtal::detail::RecursivePConvexity< dim, TInteger >::isPConvex(), and DGtal::detail::RecursivePConvexity< dim, TInteger >::project().

◆ project() [2/2]

template<Dimension dim, typename TInteger = DGtal::int32_t>
static std::vector< ProjPoint > DGtal::detail::RecursivePConvexity< dim, TInteger >::project ( const std::vector< Point > &  p,
Dimension  a 
)
inlinestatic

Projects the range of points p along dimension a.

Parameters
[in]pany range of digital points
[in]aany dimension
Returns
the range of digital points of dimension (d-1) with omitted a-th coordinate.
Postcondition
the returned range has no duplicates.

Definition at line 225 of file PConvexity.h.

226  {
227  std::vector< ProjPoint > pp( p.size() );
228  for ( std::size_t i = 0; i < p.size(); i++ )
229  pp[ i ] = project( p[ i ], a );
230  std::sort( pp.begin(), pp.end() );
231  auto last = std::unique( pp.begin(), pp.end() );
232  pp.erase( last, pp.end() );
233  return pp;
234  }

References DGtal::detail::RecursivePConvexity< dim, TInteger >::project().

Field Documentation

◆ projp

template<Dimension dim, typename TInteger = DGtal::int32_t>
std::vector< ProjPConvexity > DGtal::detail::RecursivePConvexity< dim, TInteger >::projp

The documentation for this struct was generated from the following file: