CGAL 5.0 - Advancing Front Surface Reconstruction
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:

## 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

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_2triangulation_data_structure_2 () const
returns the reconstructed surface.

Triangulation_3triangulation_3 () const
returns the underlying 3D Delaunay triangulation.

const Outlier_rangeoutliers () const
returns an iterator range over the outliers.

const Boundary_rangeboundaries () 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.

## ◆ Boundary_range

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.

## ◆ Outlier_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.

## ◆ Triangulation_data_structure_2

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

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.

## ◆ Vertex_on_boundary_range

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

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

The value type of the iterator is Vertex_handle

## ◆ run()

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

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