CGAL 6.1 - 2D Generalized Barycentric Coordinates

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CGAL::Barycentric_coordinates::Delaunay_domain_2< VertexRange, GeomTraits, PointMap > Class Template Reference
Reference Manual » Harmonic Coordinates

`#include <CGAL/Barycentric_coordinates_2/Delaunay_domain_2.h>`

## Definition

template<typename VertexRange, typename GeomTraits, typename PointMap = CGAL::Identity_property_map<typename GeomTraits::Point_2>>
class CGAL::Barycentric_coordinates::Delaunay_domain_2< VertexRange, GeomTraits, PointMap >

2D Delaunay domain restricted to a simple polygon.

This class implements a discretized domain restricted to a simple polygon. The interior part of the input polygon is triangulated and refined with respect to the user-specified shape size parameter. The final triangulation is a constrained Delaunay triangulation, where the constraints are the polygon edges.

Internally, the package 2D Conforming Triangulations and Meshes is used. See it for more details.

Template Parameters

  VertexRange | a model of `ConstRange` whose iterator type is `RandomAccessIterator`
  GeomTraits | a model of `BarycentricTraits_2`
  PointMap | a model of `ReadablePropertyMap` whose key type is `VertexRange::value_type` and value type is `Point_2`. The default is `CGAL::Identity_property_map`.

Is model of
  `DiscretizedDomain_2`

Examples
  Barycentric_coordinates_2/harmonic_coordinates.cpp, Barycentric_coordinates_2/shape_deformation.cpp, and Barycentric_coordinates_2/terrain_height_modeling.cpp.

## Types
typedef GeomTraits::FT | FT
| Number type.
typedef GeomTraits::Point_2 | Point_2
| Point type.

## Initialization
| Delaunay_domain_2 (const VertexRange &polygon, const GeomTraits traits=GeomTraits(), const PointMap point_map=PointMap())
| initializes all internal data structures.
template<typename PointRange >
void | create (const FT max_edge_length, const PointRange &seeds)
| creates a refined Delaunay triangulation restricted to the input polygon.

## Access
template<typename OutIterator >
OutIterator | barycenters (OutIterator b_begin) const
| computes barycenters of all generated triangles.
std::size_t | number_of_vertices () const
| returns the number of triangulation vertices.
const Point_2 & | vertex (const std::size_t query_index) const
| returns a const reference to the triangulation vertex with the index `query_index`.
bool | is_on_boundary (const std::size_t query_index) const
| controls if the triangulation vertex with the index `query_index` is on the polygon boundary.
void | operator() (const std::size_t query_index, std::vector< std::size_t > &neighbors) const
| returns the one-ring neighborhood of the triangulation vertex with the index `query_index`.
void | locate (const Point_2 &query, std::vector< std::size_t > &triangle) const
| locates a triangle that contains a given query point.

## Memory Management
void | clear ()
| clears all internal data structures.
void | release_memory ()
| releases all memory that is used internally.

## Constructor & Destructor Documentation

## ◆ Delaunay_domain_2()

template<typename VertexRange , typename GeomTraits , typename PointMap = CGAL::Identity_property_map<typename GeomTraits::Point_2>>

CGAL::Barycentric_coordinates::Delaunay_domain_2< VertexRange, GeomTraits, PointMap >::Delaunay_domain_2 | ( | const VertexRange & | polygon,
|  | const GeomTraits | traits = `GeomTraits()`,
|  | const PointMap | point_map = `PointMap()`
| ) |  |

initializes all internal data structures.

Parameters

  polygon | an instance of `VertexRange` with the vertices of a simple polygon
  traits | a traits class with geometric objects, predicates, and constructions; the default initialization is provided
  point_map | an instance of `PointMap` that maps a vertex from `polygon` to `Point_2`; the default initialization is provided

Precondition
  polygon.size() >= 3
  polygon is simple

## Member Function Documentation

## ◆ barycenters()

template<typename VertexRange , typename GeomTraits , typename PointMap = CGAL::Identity_property_map<typename GeomTraits::Point_2>>
template<typename OutIterator >

OutIterator CGAL::Barycentric_coordinates::Delaunay_domain_2< VertexRange, GeomTraits, PointMap >::barycenters | ( | OutIterator | b_begin | ) | const

computes barycenters of all generated triangles.

Template Parameters

  OutIterator | a model of `OutputIterator` that accepts points of type `Point_2`

Parameters

  b_begin | the beginning of the destination range with the computed barycenters

Returns
  an output iterator to the element in the destination range, one past the last barycenter stored

## ◆ create()

template<typename VertexRange , typename GeomTraits , typename PointMap = CGAL::Identity_property_map<typename GeomTraits::Point_2>>
template<typename PointRange >

void CGAL::Barycentric_coordinates::Delaunay_domain_2< VertexRange, GeomTraits, PointMap >::create | ( | const FT | max_edge_length,
|  | const PointRange & | seeds
| ) |  |

creates a refined Delaunay triangulation restricted to the input polygon.

After the construction is completed, the first n vertices are the polygon vertices, the next m vertices are the vertices generated along the polygon boundary, the last k vertices are the vertices generated in the interior part of the polygon.

Template Parameters

  PointRange | a model of `ConstRange` whose value type is `GeomTraits::Point_2`

Parameters

  max_edge_length | an upper bound on the length of the longest edge; see `Delaunay_mesh_size_criteria_2` for more details
  seeds | contains seed points indicating, which parts of the input polygon should be partitioned and subdivided

## ◆ is_on_boundary()

template<typename VertexRange , typename GeomTraits , typename PointMap = CGAL::Identity_property_map<typename GeomTraits::Point_2>>

bool CGAL::Barycentric_coordinates::Delaunay_domain_2< VertexRange, GeomTraits, PointMap >::is_on_boundary | ( | const std::size_t | query_index | ) | const

controls if the triangulation vertex with the index `query_index` is on the polygon boundary.

This function implements `DiscretizedDomain_2::is_on_boundary()`.

Parameters

  query_index | an index of the query vertex

Precondition
  query_index >= 0 && query_index < number_of_vertices()

## ◆ locate()

template<typename VertexRange , typename GeomTraits , typename PointMap = CGAL::Identity_property_map<typename GeomTraits::Point_2>>

void CGAL::Barycentric_coordinates::Delaunay_domain_2< VertexRange, GeomTraits, PointMap >::locate | ( | const Point_2 & | query,
|  | std::vector< std::size_t > & | triangle
| ) |  | const

locates a triangle that contains a given query point.

If `triangle` is empty, the query point does not belong to the domain.

This function implements `DiscretizedDomain_2::locate()`.

Parameters

  query | a query point
  triangle | stores indices of the vertices, which form a triangle, that contains the query point

## ◆ number_of_vertices()

template<typename VertexRange , typename GeomTraits , typename PointMap = CGAL::Identity_property_map<typename GeomTraits::Point_2>>

std::size_t CGAL::Barycentric_coordinates::Delaunay_domain_2< VertexRange, GeomTraits, PointMap >::number_of_vertices | ( |  | ) | const

returns the number of triangulation vertices.

This function implements `DiscretizedDomain_2::number_of_vertices()`.

## ◆ operator()()

template<typename VertexRange , typename GeomTraits , typename PointMap = CGAL::Identity_property_map<typename GeomTraits::Point_2>>

void CGAL::Barycentric_coordinates::Delaunay_domain_2< VertexRange, GeomTraits, PointMap >::operator() | ( | const std::size_t | query_index,
|  | std::vector< std::size_t > & | neighbors
| ) |  | const

returns the one-ring neighborhood of the triangulation vertex with the index `query_index`.

This function implements `DiscretizedDomain_2::operator()()`.

Parameters

  query_index | an index of the query vertex
  neighbors | stores indices of the vertices, which from the one-ring neighborhood of the query vertex

Precondition
  query_index >= 0 && query_index < number_of_vertices()

## ◆ vertex()

template<typename VertexRange , typename GeomTraits , typename PointMap = CGAL::Identity_property_map<typename GeomTraits::Point_2>>

const Point_2 & CGAL::Barycentric_coordinates::Delaunay_domain_2< VertexRange, GeomTraits, PointMap >::vertex | ( | const std::size_t | query_index | ) | const

returns a const reference to the triangulation vertex with the index `query_index`.

This function implements `DiscretizedDomain_2::vertex()`.

Parameters

  query_index | an index of the requested vertex

Precondition
  query_index >= 0 && query_index < number_of_vertices()