CGAL 5.3 - Scale-Space Surface Reconstruction
CGAL::Scale_space_reconstruction_3::Alpha_shape_mesher< Geom_traits, FixedSurface > Class Template Reference

#include <CGAL/Scale_space_reconstruction_3/Alpha_shape_mesher.h>

## Definition

### template<typename Geom_traits, typename FixedSurface = Tag_true> class CGAL::Scale_space_reconstruction_3::Alpha_shape_mesher< Geom_traits, FixedSurface >

Surface mesher for scale space reconstruction based on CGAL::Alpha_shape_3.

The surface can be constructed either for a fixed neighborhood radius, or for a dynamic radius. When constructing the surface for exactly one neighborhood radius, it is faster to set FixedSurface to Tag_true. If the correct neighborhood radius should be changed or estimated multiple times, it is faster to set FixedSurface to Tag_false.

It is undefined whether a surface with fixed radius may have its radius changed, but if so, this will likely require more computation time than changing the radius of a dynamic surface. In either case, it is possible to change the point set while maintaining the same radius.

The surface can be stored either as an unordered collection of triangles, or as a collection ordered by shells. A shell is a maximally connected component of the surface where connected facets are locally oriented towards the same side of the surface.

Is Model Of:
CGAL::Scale_space_reconstruction_3::Mesher
Template Parameters
 Geom_traits is the geometric traits class. It must be a model of DelaunayTriangulationTraits_3. It must have a RealEmbeddable field number type. Generally, Exact_predicates_inexact_constructions_kernel is preferred. FixedSurface determines whether the surface is expected to be constructed for a fixed neighborhood radius. It must be a Boolean_tag type. The default value is Tag_true. Note that the value of this parameter does not change the result but only has an impact on the run-time.
Examples:
Scale_space_reconstruction_3/scale_space_incremental.cpp, and Scale_space_reconstruction_3/scale_space_manifold.cpp.

## Public Types

typedef Geom_traits::Point_3 Point
defines the point type.

typedef std::array< unsigned int, 3 > Facet
defines a triple of point indices indicating a triangle of the surface.

typedef unspecified_type Facet_iterator
defines an iterator over the triples.

## Public Member Functions

Alpha_shape_mesher (FT squared_radius, bool separate_shells=false, bool force_manifold=false, FT border_angle=45.)
Constructs an alpha shape mesher. More...

std::size_t number_of_triangles () const
gives the number of triangles of the surface.

Facet_const_iterator surface_begin () const
gives an iterator to the first triple in the surface.

Facet_iterator surface_begin ()
gives an iterator to the first triple in the surface. More...

Facet_const_iterator surface_end () const
gives a past-the-end iterator of the triples in the surface.

Facet_iterator surface_end ()
gives a past-the-end iterator of the triples in the surface. More...

std::size_t number_of_shells () const
gives the number of shells of the surface.

Facet_const_iterator shell_begin (std::size_t shell) const
gives an iterator to the first triple in a given shell. More...

Facet_iterator shell_begin (std::size_t shell)
gives an iterator to the first triple in a given shell. More...

Facet_const_iterator shell_end (std::size_t shell) const
gives a past-the-end iterator of the triples in a given shell. More...

Facet_iterator shell_end (std::size_t shell)
gives a past-the-end iterator of the triples in a given shell. More...

Facet_const_iterator garbage_begin () const
gives an iterator to the first triple of the garbage facets that may be discarded if 2-manifold output is required. More...

Facet_iterator garbage_begin ()
gives an iterator to the first triple of the garbage facets that may be discarded if 2-manifold output is required. More...

Facet_const_iterator garbage_end () const
gives a past-the-end iterator of the triples of the garbage facets that may be discarded if 2-manifold output is required. More...

Facet_iterator garbage_end ()
gives a past-the-end iterator of the triples of the garbage facets that may be discarded if 2-manifold output is required. More...

## Public Attributes

const typedef unspecified_type Facet_const_iterator
defines a constant iterator over the triples.

## ◆ Alpha_shape_mesher()

template<typename Geom_traits , typename FixedSurface = Tag_true>
 CGAL::Scale_space_reconstruction_3::Alpha_shape_mesher< Geom_traits, FixedSurface >::Alpha_shape_mesher ( FT squared_radius, bool separate_shells = false, bool force_manifold = false, FT border_angle = 45. )

Constructs an alpha shape mesher.

Parameters
 squared_radius $$\alpha$$ parameter of the alpha shape algorithm. separate_shells determines whether to collect the surface per shell. force_manifold determines if the surface is forced to be 2-manifold. border_angle sets the maximal angle between two facets such that the edge is seen as a border.

If the output is forced to be 2-manifold, some almost flat volume bubbles are detected. To do so, border edges must be estimated.

An edge adjacent to 2 regular facets is considered as a border if it is also adjacent to a singular facet or if the angle between the two regular facets is lower than this parameter (set to 45° by default).

Note
border_angle is not used if force_manifold is set to false.

## ◆ garbage_begin() [1/2]

template<typename Geom_traits , typename FixedSurface = Tag_true>
 Facet_const_iterator CGAL::Scale_space_reconstruction_3::Alpha_shape_mesher< Geom_traits, FixedSurface >::garbage_begin ( ) const

gives an iterator to the first triple of the garbage facets that may be discarded if 2-manifold output is required.

## ◆ garbage_begin() [2/2]

template<typename Geom_traits , typename FixedSurface = Tag_true>
 Facet_iterator CGAL::Scale_space_reconstruction_3::Alpha_shape_mesher< Geom_traits, FixedSurface >::garbage_begin ( )

gives an iterator to the first triple of the garbage facets that may be discarded if 2-manifold output is required.

## ◆ garbage_end() [1/2]

template<typename Geom_traits , typename FixedSurface = Tag_true>
 Facet_const_iterator CGAL::Scale_space_reconstruction_3::Alpha_shape_mesher< Geom_traits, FixedSurface >::garbage_end ( ) const

gives a past-the-end iterator of the triples of the garbage facets that may be discarded if 2-manifold output is required.

## ◆ garbage_end() [2/2]

template<typename Geom_traits , typename FixedSurface = Tag_true>
 Facet_iterator CGAL::Scale_space_reconstruction_3::Alpha_shape_mesher< Geom_traits, FixedSurface >::garbage_end ( )

gives a past-the-end iterator of the triples of the garbage facets that may be discarded if 2-manifold output is required.

## ◆ shell_begin() [1/2]

template<typename Geom_traits , typename FixedSurface = Tag_true>
 Facet_const_iterator CGAL::Scale_space_reconstruction_3::Alpha_shape_mesher< Geom_traits, FixedSurface >::shell_begin ( std::size_t shell ) const

gives an iterator to the first triple in a given shell.

Parameters
 shell is the index of the shell to access.
Precondition
shell is in the range [ 0, number_of_shells() ).

## ◆ shell_begin() [2/2]

template<typename Geom_traits , typename FixedSurface = Tag_true>
 Facet_iterator CGAL::Scale_space_reconstruction_3::Alpha_shape_mesher< Geom_traits, FixedSurface >::shell_begin ( std::size_t shell )

gives an iterator to the first triple in a given shell.

Parameters
 shell is the index of the shell to access.
Precondition
shell is in the range [ 0, number_of_shells() ).
Warning
Changes to a shell may invalidate the topology of the surface.

## ◆ shell_end() [1/2]

template<typename Geom_traits , typename FixedSurface = Tag_true>
 Facet_const_iterator CGAL::Scale_space_reconstruction_3::Alpha_shape_mesher< Geom_traits, FixedSurface >::shell_end ( std::size_t shell ) const

gives a past-the-end iterator of the triples in a given shell.

Parameters
 shell is the index of the shell to access.
Precondition
shell is in the range [ 0, number_of_shells() ).

## ◆ shell_end() [2/2]

template<typename Geom_traits , typename FixedSurface = Tag_true>
 Facet_iterator CGAL::Scale_space_reconstruction_3::Alpha_shape_mesher< Geom_traits, FixedSurface >::shell_end ( std::size_t shell )

gives a past-the-end iterator of the triples in a given shell.

Parameters
 shell is the index of the shell to access.
Precondition
shell is in the range [ 0, number_of_shells() ).
Warning
Changes to a shell may invalidate the topology of the surface.

## ◆ surface_begin()

template<typename Geom_traits , typename FixedSurface = Tag_true>
 Facet_iterator CGAL::Scale_space_reconstruction_3::Alpha_shape_mesher< Geom_traits, FixedSurface >::surface_begin ( )

gives an iterator to the first triple in the surface.

Warning
Changes to the surface may change its topology.

## ◆ surface_end()

template<typename Geom_traits , typename FixedSurface = Tag_true>
 Facet_iterator CGAL::Scale_space_reconstruction_3::Alpha_shape_mesher< Geom_traits, FixedSurface >::surface_end ( )

gives a past-the-end iterator of the triples in the surface.

Warning
Changes to the surface may change its topology.