#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. More...

template<typename PointRange >
void	create (const FT max_edge_length, const PointRange &seeds)
	creates a refined Delaunay triangulation restricted to the input polygon. More...

Access
template<typename OutIterator >
OutIterator	barycenters (OutIterator b_begin) const
	computes barycenters of all generated triangles. More...

std::size_t	number_of_vertices () const
	returns the number of triangulation vertices. More...

const Point_2 &	vertex (const std::size_t query_index) const
	returns a const reference to the triangulation vertex with the index `query_index`. More...

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. More...

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`. More...

void	locate (const Point_2 &query, std::vector< std::size_t > &triangle) const
	locates a triangle that contains a given query point. More...

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()

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 >

Types

Initialization

Access

Memory Management

Constructor & Destructor Documentation

◆ Delaunay_domain_2()

Member Function Documentation

◆ barycenters()

◆ create()

◆ is_on_boundary()

◆ locate()

◆ number_of_vertices()

◆ operator()()

◆ vertex()

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 >