CGAL 6.1.2 - Weights: Wachspress Weights

CGAL 6.1.2 - Weights

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Classes | Functions
Wachspress Weights
Reference Manual » Barycentric Weights

##

`#include<CGAL/Weights/wachspress_weights.h>`

Wachspress weights which can be computed for a query point with respect to the vertices of a strictly convex polygon.

## Classes
class | CGAL::Weights::Wachspress_weights_2< VertexRange, GeomTraits, PointMap >
| 2D Wachspress weights for polygons. More...

## Functions
template<typename PointRange , typename OutIterator , typename GeomTraits >
OutIterator | CGAL::Weights::wachspress_weights_2 (const PointRange &polygon, const typename GeomTraits::Point_2 &query, OutIterator w_begin, const GeomTraits &traits)
| computes 2D Wachspress weights for polygons.

## Function Documentation

## ◆ wachspress_weights_2()

template<typename PointRange , typename OutIterator , typename GeomTraits >

OutIterator CGAL::Weights::wachspress_weights_2 | ( | const PointRange & | polygon,
|  | const typename GeomTraits::Point_2 & | query,
|  | OutIterator | w_begin,
|  | const GeomTraits & | traits
| ) |  |

`#include <CGAL/Weights/wachspress_weights.h>`

computes 2D Wachspress weights for polygons.

This function computes 2D Wachspress weights at a given `query` point with respect to the vertices of a strictly convex `polygon`, that is one weight per vertex. The weights are stored in a destination range beginning at `w_begin`.

Internally, the class `Wachspress_weights_2` is used. If one wants to process multiple query points, it is better to use that class. When using the free function, internal memory is allocated for each query point, while when using the class, it is allocated only once which is much more efficient. However, for a few query points, it is easier to use this function. It can also be used when the processing time is not a concern.

Template Parameters

  PointRange | a model of `ConstRange` whose iterator type is `RandomAccessIterator` and value type is `GeomTraits::Point_2`
  OutIterator | a model of `OutputIterator` whose value type is `GeomTraits::FT`
  GeomTraits | a model of `AnalyticWeightTraits_2`

Parameters

  polygon | an instance of `PointRange` with 2D points which form a strictly convex polygon
  query | a query point
  w_begin | the beginning of the destination range with the computed weights
  traits | a traits class with geometric objects, predicates, and constructions; this parameter can be omitted if the traits class can be deduced from the point type

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

Precondition
  `polygon.size() >= 3`
  `polygon` is simple
  `polygon` is strictly convex