CGAL::Weights::Wachspress_weights_2< VertexRange, GeomTraits, PointMap > Class Template Reference

#include <CGAL/Weights/wachspress_weights.h>

Definition

template<typename VertexRange, typename GeomTraits, typename PointMap = CGAL::Identity_property_map<typename GeomTraits::Point_2>>
class CGAL::Weights::Wachspress_weights_2< VertexRange, GeomTraits, PointMap >

2D Wachspress weights for polygons.

This class implements 2D Wachspress weights ( [2], [5], [7] ) which can be computed at any point inside a strictly convex polygon.

Wachspress weights are well-defined and non-negative inside a strictly convex polygon. The weights are computed analytically using the formulation from the wachspress_weight().

Template Parameters

VertexRange	a model of ConstRange whose iterator type is RandomAccessIterator
GeomTraits	a model of AnalyticWeightTraits_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

BarycentricWeights_2

Examples

Weights/coordinates_multiple_queries.cpp.

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

Initialization
	Wachspress_weights_2 (const VertexRange &polygon, const GeomTraits traits=GeomTraits(), const PointMap point_map=PointMap())
	initializes all internal data structures.

Access
template<typename OutIterator >
OutIterator	operator() (const Point_2 &query, OutIterator w_begin)
	computes 2D Wachspress weights.

Constructor & Destructor Documentation

Wachspress_weights_2()

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

CGAL::Weights::Wachspress_weights_2< VertexRange, GeomTraits, PointMap >::Wachspress_weights_2	(	const VertexRange &	polygon,
		const GeomTraits	traits = GeomTraits(),
		const PointMap	point_map = PointMap()
	)

initializes all internal data structures.

This class implements the behavior of Wachspress weights for 2D query points inside strictly convex polygons.

Parameters

polygon	an instance of VertexRange with the vertices of a strictly convex 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

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::Weights::Wachspress_weights_2< VertexRange, GeomTraits, PointMap >::operator()	(	const Point_2 &	query,
		OutIterator	w_begin
	)

computes 2D Wachspress weights.

This function fills a destination range with 2D Wachspress weights computed at the query point with respect to the vertices of the input polygon.

The number of computed weights is equal to the number of polygon vertices.

Template Parameters

OutIterator

a model of OutputIterator whose value type is 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