CGAL::HDVF::Duality_cubical_complex_tools< CoefficientType > Class Template Reference

#include <CGAL/HDVF/Geometric_chain_complex_tools.h>

Definition

template<typename CoefficientType>
class CGAL::HDVF::Duality_cubical_complex_tools< CoefficientType >

The class Duality_cubical_complex_tools is dedicated to Alexander duality for 3D binary volumes.

Starting from a Cubical_chain_complex _K, the method cubical_chain_complex_BB builds a Cubical_chain_complex L and Sub_chain_complex_mask K.

• L : complex built of the "full" bounding box of _K
• K (Sub_chain_complex_mask) : Sub_chain_complex_mask identifying _K inside L

Use the frame method from the Cub_object_io class to enlarge the bounding box (via a 1 pixel dilatation) if necessary.

Template Parameters

CoefficientType

a model of the Ring concept providing the ring used to compute homology.

Examples

HDVF/main_dual_hdvf.cpp.

Public Types
typedef Cubical_chain_complex< CoefficientType >	ComplexType
	Type of cubical complexes used for the initial complex and \(L\).
typedef Sub_chain_complex_mask< CoefficientType, ComplexType >	SubCCType
	Type of sub chain complex mask used to encode the sub-complex \(K\).

Public Member Functions
	Duality_cubical_complex_tools ()

Static Public Member Functions
static std::pair< ComplexType &, SubCCType & >	cubical_chain_complex_bb (const ComplexType &_K)
	Generates a subcomplex \(K\)K and a complex \(L\) with \(K\subseteq L\) from a cubical complex _K.

Member Function Documentation

cubical_chain_complex_bb()

template<typename CoefficientType >

static std::pair< ComplexType &, SubCCType & > CGAL::HDVF::Duality_cubical_complex_tools< CoefficientType >::cubical_chain_complex_bb ( const ComplexType &  _K )

static

Generates a subcomplex \(K\)K and a complex \(L\) with \(K\subseteq L\) from a cubical complex _K.

L is the bounding box of _K (homeomorphic to a ball) and \(K\) is a sub chain complex mask encoding _K.

The following figures shows the resulting complex with an initial simple cubical complex (right - sectional view):

Parameters

[in]

_K

Initial cubical chain complex (working mesh).