CGAL::Barycentric_coordinates::Discrete_harmonic_coordinates_2< VertexRange, GeomTraits, PointMap > Class Template Reference

#include <CGAL/Barycentric_coordinates_2/Discrete_harmonic_coordinates_2.h>

Definition

template<typename VertexRange, typename GeomTraits, typename PointMap = CGAL::Identity_property_map<typename GeomTraits::Point_2>>
class CGAL::Barycentric_coordinates::Discrete_harmonic_coordinates_2< VertexRange, GeomTraits, PointMap >

2D discrete harmonic coordinates.

This class implements 2D discrete harmonic coordinates ( [2], [9], [1] ), which can be computed at any point inside a strictly convex polygon.

Discrete harmonic coordinates are well-defined in the closure of a strictly convex polygon but they are not necessarily positive. The coordinates are computed analytically. See more details in the user manual here.

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.

Examples:

Barycentric_coordinates_2/discrete_harmonic_coordinates.cpp.

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

Initialization
	Discrete_harmonic_coordinates_2 (const VertexRange &polygon, const Computation_policy_2 policy=Computation_policy_2::PRECISE_WITH_EDGE_CASES, const GeomTraits traits=GeomTraits(), const PointMap point_map=PointMap())
	initializes all internal data structures. More...

Access
template<typename OutIterator >
OutIterator	weights (const Point_2 &query, OutIterator w_begin)
	computes 2D discrete harmonic weights. More...
template<typename OutIterator >
OutIterator	operator() (const Point_2 &query, OutIterator c_begin)
	computes 2D discrete harmonic coordinates. More...

Constructor & Destructor Documentation

Discrete_harmonic_coordinates_2()

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

CGAL::Barycentric_coordinates::Discrete_harmonic_coordinates_2< VertexRange, GeomTraits, PointMap >::Discrete_harmonic_coordinates_2	(	const VertexRange &	polygon,
		const Computation_policy_2	policy = Computation_policy_2::PRECISE_WITH_EDGE_CASES,
		const GeomTraits	traits = GeomTraits(),
		const PointMap	point_map = PointMap()
	)

initializes all internal data structures.

This class implements the behavior of discrete harmonic coordinates for 2D query points.

Parameters

polygon	an instance of VertexRange with the vertices of a strictly convex polygon
policy	one of the Computation_policy_2; the default is Computation_policy_2::PRECISE_WITH_EDGE_CASES
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

polygon is strictly convex

Member Function Documentation

operator()()

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

template<typename OutIterator >

OutIterator CGAL::Barycentric_coordinates::Discrete_harmonic_coordinates_2< VertexRange, GeomTraits, PointMap >::operator()	(	const Point_2 &	query,
		OutIterator	c_begin
	)

computes 2D discrete harmonic coordinates.

This function fills c_begin with 2D discrete harmonic coordinates computed at the query point with respect to the vertices of the input polygon.

The number of returned coordinates equals to the number of polygon vertices.

After the coordinates \(b_i\) with \(i = 1\dots n\) are computed, where \(n\) is the number of polygon vertices, the query point \(q\) can be obtained as \(q = \sum_{i = 1}^{n}b_ip_i\), where \(p_i\) are the polygon vertices.

Template Parameters

OutIterator

a model of OutputIterator that accepts values of type FT

Parameters

query	a query point
c_begin	the beginning of the destination range with the computed coordinates

Returns

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

weights()

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

template<typename OutIterator >

OutIterator CGAL::Barycentric_coordinates::Discrete_harmonic_coordinates_2< VertexRange, GeomTraits, PointMap >::weights	(	const Point_2 &	query,
		OutIterator	w_begin
	)

computes 2D discrete harmonic weights.

This function fills weights with 2D discrete harmonic weights computed at the query point with respect to the vertices of the input polygon. If query belongs to the polygon boundary, the returned weights are normalized.

The number of returned weights equals to the number of polygon vertices.

Template Parameters

OutIterator

a model of OutputIterator that accepts values of type FT

Parameters

query	a query point
w_begin	the beginning of the destination range with the computed weights

Returns

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