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

#include <CGAL/HDVF/Geometric_chain_complex_tools.h>

Definition

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

The class Duality_simplicial_complex_tools is dedicated to Alexander duality for 3D surface meshes.

Starting from a simplicial chain complex (encoding a 3D surface mesh), it provides methods to embed the complex into a larger icosphere and generate a 3D constrained Delaunay triangulation.

Technically, starting from a Simplicial_chain_complex _K, the method simp_complex_bb builds a Simplicial_chain_complex L and a Sub_chain_complex_mask K.

• L : complex built out of _K together with a closing icosphere, meshed by tetgen (constrained Delaunay triangulation)
• K (Sub_chain_complex_mask) : Sub_chain_complex_mask identifying _K inside L

Template Parameters

CoefficientType

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

Examples

HDVF/main_dual_hdvf.cpp.

Classes
struct	TripleRes
	Type returned by simp_complex_bb. More...

Public Types
typedef Simplicial_chain_complex< CoefficientType >	ComplexType
	Type of simplicial chain complex encoding L.
typedef Sub_chain_complex_mask< CoefficientType, ComplexType >	SubCCType
	Type of sub chain complex mask encoding the sub complex K.

Public Member Functions
	Duality_simplicial_complex_tools ()
	Default constructor.

Static Public Member Functions
static TripleRes	simplicial_chain_complex_bb (const ComplexType &_K, double BB_ratio=1.5, const string &out_file_prefix="file_K_closed.off")
	Generates a subcomplex \(K\)K and a complex \(L\) with \(K\subseteq L\) from a simplicial complex _K.
static Mesh_object_io &	export_meshObject (const ComplexType &_CC)
	Exports a SimpComplex to a MeshObject

Member Function Documentation

simplicial_chain_complex_bb()

template<typename CoefficientType >

static TripleRes CGAL::HDVF::Duality_simplicial_complex_tools< CoefficientType >::simplicial_chain_complex_bb ( const ComplexType &  _K, double  BB_ratio = 1.5, const string &  out_file_prefix = "file_K_closed.off"  )

static

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

_K is embedded into a larger icosphere and a 3D constrained Delaunay triangulation is generated. Then \(K\), \(L\) and vertices coordinates are extracted and stored in a TripleRes structure.

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

Parameters

[in]	_K	Simplicial chain complex (working mesh).
[in]	BB_ratio	Ratio of the "closing" icosphere diameter with respect to the diameter of the object's bounding box.
[in]	out_file_prefix	Prefix of tetgen intermediate files (default: "file_K_closed.off").