CGAL::Advancing_front_surface_reconstruction< Dt, P > Class Template Reference

#include <CGAL/Advancing_front_surface_reconstruction.h>

Definition

template<class Dt = Default, class P = Default>
class CGAL::Advancing_front_surface_reconstruction< Dt, P >

The class Advancing_front_surface_reconstruction enables advanced users to provide the unstructured point cloud in a 3D Delaunay triangulation.

The reconstruction algorithm then marks vertices and faces in the triangulation as being on the 2D surface embedded in 3D space, and constructs a 2D triangulation data structure that describes the surface. The vertices and facets of the 2D triangulation data structure store handles to the vertices and faces of the 3D triangulation, which enables the user to explore the 2D as well as 3D neighborhood of vertices and facets of the surface.

Template Parameters

Dt	must be a Delaunay_triangulation_3 with Advancing_front_surface_reconstruction_vertex_base_3 and Advancing_front_surface_reconstruction_cell_base_3 blended into the vertex and cell type. The default uses the Exact_predicates_inexact_constructions_kernel as geometric traits class.
P	must be a functor with double operator()(AdvancingFront,Cell_handle,int) returning the priority of the facet (Cell_handle,int). This functor enables the user to choose how candidate triangles are prioritized. If a facet should not appear in the output, infinity() must be returned. It defaults to a functor that returns the smallest_radius_delaunay_sphere().

Examples:

Advancing_front_surface_reconstruction/boundaries.cpp, Advancing_front_surface_reconstruction/reconstruction_class.cpp, and Advancing_front_surface_reconstruction/reconstruction_structured.cpp.

Types
typedef unspecified_type	Triangulation_data_structure_2
	The type of the 2D triangulation data structure describing the reconstructed surface, being a model of TriangulationDataStructure_2. More...
typedef unspecified_type	Triangulation_3
	The type of the 3D triangulation.
typedef unspecified_type	Priority
	The type of the facet priority functor.
typedef Triangulation_3::Point	Point
	The point type.
typedef Triangulation_3::Vertex_handle	Vertex_handle
	The vertex handle type of the 3D triangulation.
typedef Triangulation_3::Cell_handle	Cell_handle
	The cell handle type of the 3D triangulation.
typedef Triangulation_3::Facet	Facet
	The facet type of the 3D triangulation.
typedef unspecified_type	Outlier_range
	A bidirectional iterator range which enables to enumerate all points that were removed from the 3D Delaunay triangulation during the surface reconstruction. More...
typedef unspecified_type	Boundary_range
	A bidirectional iterator range which enables to visit all boundaries. More...
typedef unspecified_type	Vertex_on_boundary_range
	A bidirectional iterator range which enables to visit all vertices on a boundary. More...

Creation
	Advancing_front_surface_reconstruction (Triangulation_3 &dt, Priority priority=Priority())
	Constructor for the unstructured point cloud given as 3D Delaunay triangulation.

Operations
void	run (double radius_ratio_bound=5, double beta=0.52)
	runs the surface reconstruction function. More...
const Triangulation_data_structure_2 &	triangulation_data_structure_2 () const
	returns the reconstructed surface.
Triangulation_3 &	triangulation_3 () const
	returns the underlying 3D Delaunay triangulation.
const Outlier_range &	outliers () const
	returns an iterator range over the outliers.
const Boundary_range &	boundaries () const
	returns an iterator range over the boundaries.

Predicates
bool	has_boundaries () const
	returns true if the reconstructed surface has boundaries.
bool	has_on_surface (Facet f) const
	returns true if the facet is on the surface.
bool	has_on_surface (typename Triangulation_data_structure_2::Face_handle f2) const
	returns true if the facet f2 is on the surface.
bool	has_on_surface (typename Triangulation_data_structure_2::Vertex_handle v2) const
	returns true if the vertex v2 is on the surface.

Priority values
coord_type	smallest_radius_delaunay_sphere (const Cell_handle &c, const int &index) const
	computes the priority of the facet (c,index) such that the facet with the smallest radius of Delaunay sphere has the highest priority. More...
coord_type	infinity () const
	returns the infinite floating value that prevents a facet to be used.

Member Typedef Documentation

template<class Dt = Default, class P = Default>

typedef unspecified_type CGAL::Advancing_front_surface_reconstruction< Dt, P >::Boundary_range

A bidirectional iterator range which enables to visit all boundaries.

The value type of the iterator is Vertex_on_boundary_range.

template<class Dt = Default, class P = Default>

typedef unspecified_type CGAL::Advancing_front_surface_reconstruction< Dt, P >::Outlier_range

A bidirectional iterator range which enables to enumerate all points that were removed from the 3D Delaunay triangulation during the surface reconstruction.

The value type of the iterator is Point.

template<class Dt = Default, class P = Default>

typedef unspecified_type CGAL::Advancing_front_surface_reconstruction< Dt, P >::Triangulation_data_structure_2

The type of the 2D triangulation data structure describing the reconstructed surface, being a model of TriangulationDataStructure_2.

• The type Triangulation_data_structure_2::Vertex is model of the concept TriangulationDataStructure_2::Vertex and has additionally the method vertex_3() that returns a Vertex_handle to the associated 3D vertex.
• The type Triangulation_data_structure_2::Face is model of the concept TriangulationDataStructure_2::Face and has additionally the method facet() that returns the associated Facet, and a method bool is_on_surface() for testing if a face is part of the reconstructed surface or a face incident to a boundary edge.

In case the surface has boundaries, the 2D surface has one vertex which is associated to the infinite vertex of the 3D triangulation.

template<class Dt = Default, class P = Default>

typedef unspecified_type CGAL::Advancing_front_surface_reconstruction< Dt, P >::Vertex_on_boundary_range

A bidirectional iterator range which enables to visit all vertices on a boundary.

The value type of the iterator is Vertex_handle

Member Function Documentation

template<class Dt = Default, class P = Default>

void CGAL::Advancing_front_surface_reconstruction< Dt, P >::run	(	double	radius_ratio_bound = 5,
		double	beta = 0.52
	)

runs the surface reconstruction function.

Parameters

radius_ratio_bound	candidates incident to surface triangles which are not in the beta-wedge are discarded, if the ratio of their radius and the radius of the surface triangle is larger than radius_ratio_bound. Described in Section Dealing with Multiple Components, Boundaries and Sharp Edges
beta	half the angle of the wedge in which only the radius of triangles counts for the plausibility of candidates. Described in Section Plausibility of a Candidate Triangle

template<class Dt = Default, class P = Default>

coord_type CGAL::Advancing_front_surface_reconstruction< Dt, P >::smallest_radius_delaunay_sphere	(	const Cell_handle &	c,
		const int &	index
	)		const

computes the priority of the facet (c,index) such that the facet with the smallest radius of Delaunay sphere has the highest priority.

Parameters

c	handle to the cell containing the facet
index	index of the facet in c