CGAL 5.6.3 - Scale-Space Surface Reconstruction

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List of all members | Public Types
CGAL::Scale_space_surface_reconstruction_3< Geom_traits > Class Template Reference
Scale-Space Surface Reconstruction Reference » Classes

`#include <CGAL/Scale_space_surface_reconstruction_3.h>`

## Definition

template<typename Geom_traits>
class CGAL::Scale_space_surface_reconstruction_3< Geom_traits >

computes a triangulated surface mesh interpolating a point set.

Scale space reconstruction consists in combining a smoothing algorithm (see `Scale_space_reconstruction_3::Smoother`) that is used to generate a user-specified number of scales with a meshing algorithm (see `Scale_space_reconstruction_3::Mesher`).

The class stores the point set at the current scale and the reconstructed surface. User can either use the reconstructed surface at the current scale (smoothed version) or propagate the connectivity of the facets back to the original point set. This latest option makes it possible to reconstruct an interpolative surface on a noisy point set.

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.

Examples
  Scale_space_reconstruction_3/scale_space.cpp, Scale_space_reconstruction_3/scale_space_advancing_front.cpp, Scale_space_reconstruction_3/scale_space_incremental.cpp, Scale_space_reconstruction_3/scale_space_manifold.cpp, and Scale_space_reconstruction_3/scale_space_sm.cpp.

## Public Types
typedef Geom_traits::FT | FT
| defines the field number type.
typedef Geom_traits::Point_3 | Point
| defines the point type.
typedef std::array< std::size_t, 3 > | Facet
| defines a facet of the surface (triple of point indices).
typedef unspecified_type | Point_range
| defines a range points.
typedef unspecified_type | Point_iterator
| defines an iterator over the points.
typedef const unspecified_type | Point_const_iterator
| defines a constant iterator over the points.
typedef unspecified_type | Facet_range
| defines a range of facets
typedef unspecified_type | Facet_iterator
| defines an iterator over the facets.
typedef const unspecified_type | Facet_const_iterator
| defines a constant iterator over the facets.

## Initialization
| Scale_space_surface_reconstruction_3 ()
| Empty constructor.
template<typename InputIterator >
| Scale_space_surface_reconstruction_3 (InputIterator begin, InputIterator end)
| Constructs a reconstruction object with the given point range.
void | insert (const Point &p)
| inserts a point into the scale-space at the current scale.
template<typename InputIterator >
void | insert (InputIterator begin, InputIterator end)
| inserts a collection of points into the scale-space at the current scale.

## Algorithms
template<typename Smoother >
void | increase_scale (std::size_t iterations=1, const Smoother &smoother=Smoother())
| increases the scale by a number of iterations.
template<typename Mesher >
void | reconstruct_surface (const Mesher &mesher=Mesher())
| constructs a triangle mesh from the point set at a fixed scale.

## Output
std::size_t | number_of_points () const
| gives the number of points of the surface.
const Point_range & | points () const
| gives the range of points
Point_iterator | points_begin ()
| gives an iterator to the first point at the current scale.
Point_iterator | points_end ()
| gives a past-the-end iterator of the points at the current scale.
Point_const_iterator | points_begin () const
| gives an iterator to the first point at the current scale.
Point_const_iterator | points_end () const
| gives a past-the-end iterator of the points at the current scale.
std::size_t | number_of_facets () const
| gives the number of facets of the surface.
const Facet_range & | facets () const
| gives the range of facets
Facet_iterator | facets_begin ()
| gives an iterator to the first triple in the surface.
Facet_iterator | facets_end ()
| gives a past-the-end iterator of the triples in the surface.
Facet_const_iterator | facets_begin () const
| gives an iterator to the first triple in the surface.
Facet_const_iterator | facets_end () const
| gives a past-the-end iterator of the triples in the surface.

## Constructor & Destructor Documentation

## ◆ Scale_space_surface_reconstruction_3()

template<typename Geom_traits >
template<typename InputIterator >

CGAL::Scale_space_surface_reconstruction_3< Geom_traits >::Scale_space_surface_reconstruction_3 | ( | InputIterator | begin,
|  | InputIterator | end
| ) |  |

Constructs a reconstruction object with the given point range.

Note
  This constructor is equivalent to constructing an empty object and then calling `insert(begin, end)`.

Template Parameters

  InputIterator | is an iterator over the point collection. The value type of the iterator must be a `Point`.

Parameters

  begin | is an iterator to the first point of the collection.
  end | is a past-the-end iterator for the point collection.

## Member Function Documentation

## ◆ facets_begin()

template<typename Geom_traits >

Facet_iterator CGAL::Scale_space_surface_reconstruction_3< Geom_traits >::facets_begin | ( |  | ) |

gives an iterator to the first triple in the surface.

Warning
  Changes to the surface may change its topology.

## ◆ facets_end()

template<typename Geom_traits >

Facet_iterator CGAL::Scale_space_surface_reconstruction_3< Geom_traits >::facets_end | ( |  | ) |

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

Warning
  Changes to the surface may change its topology.

## ◆ increase_scale()

template<typename Geom_traits >
template<typename Smoother >

void CGAL::Scale_space_surface_reconstruction_3< Geom_traits >::increase_scale | ( | std::size_t | iterations = `1`,
|  | const Smoother & | smoother = `Smoother()`
| ) |  |

increases the scale by a number of iterations.

Each iteration the scale is increased, the points set at a higher scale is computed. At a higher scale, the points set is smoother.

Note
  If no smoothing algorithm is specified, the default `Weighted_PCA_smoother` is used.

Template Parameters

  Smoother | model of `Scale_space_reconstruction_3::Smoother`.

Parameters

  iterations | is the number of iterations to perform. If `iterations` is 0, nothing happens.
  smoother | the smoother object.

Note
  This method processes the point set at the current scale. The points can be set with `insert(begin, end)`.
  If the surface was already constructed, increasing the scale will not automatically adjust the surface.

See also
  `reconstruct_surface()`.

## ◆ insert() [1/2]

template<typename Geom_traits >

void CGAL::Scale_space_surface_reconstruction_3< Geom_traits >::insert | ( | const Point & | p | ) |

inserts a point into the scale-space at the current scale.

Parameters

  p | is the point to insert.

Note
  Inserting the point does not automatically construct or update the surface.
  In order to construct the surface, call `#reconstruct_surface()`.

See also
  `insert(InputIterator begin, InputIterator end)`.

## ◆ insert() [2/2]

template<typename Geom_traits >
template<typename InputIterator >

void CGAL::Scale_space_surface_reconstruction_3< Geom_traits >::insert | ( | InputIterator | begin,
|  | InputIterator | end
| ) |  |

inserts a collection of points into the scale-space at the current scale.

Template Parameters

  InputIterator | is an iterator over the point collection. The value type of the iterator must be a `Point`.

Parameters

  begin | is an iterator to the first point of the collection.
  end | is a past-the-end iterator for the point collection.

Note
  Inserting the points does not automatically construct or update the surface.
  In order to construct the surface, call `reconstruct_surface()` after inserting the points.

See also
  `insert(const Point& p)`.

## ◆ points_begin()

template<typename Geom_traits >

Point_iterator CGAL::Scale_space_surface_reconstruction_3< Geom_traits >::points_begin | ( |  | ) |

gives an iterator to the first point at the current scale.

Warning
  Changes to the scale-space do not cause an automatic update to the surface.

## ◆ points_end()

template<typename Geom_traits >

Point_iterator CGAL::Scale_space_surface_reconstruction_3< Geom_traits >::points_end | ( |  | ) |

gives a past-the-end iterator of the points at the current scale.

Warning
  Changes to the scale-space do not cause an automatic update to the surface.

## ◆ reconstruct_surface()

template<typename Geom_traits >
template<typename Mesher >

void CGAL::Scale_space_surface_reconstruction_3< Geom_traits >::reconstruct_surface | ( | const Mesher & | mesher = `Mesher()` | ) |

constructs a triangle mesh from the point set at a fixed scale.

The order of the points at the current scale is the same as the order at the original scale, meaning that the surface can interpolate the point set at the original scale by applying the indices of the surface triangles to the original point set.

After construction, the facets of the surface can be iterated using `facets_begin()` and `facets_end()`.

Note
  If no meshing algorithm is specified, the default `Alpha_shape_mesher` is used.

Template Parameters

  Mesher | model of `Scale_space_reconstruction_3::Mesher`.

Parameters

  mesher | the mesher object.

Note
  This method processes the point set at the current scale. The points can be set with `insert(begin, end)`.

See also
  `increase_scale()`.