\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 3D Alpha Shapes

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FixedWeightedAlphaShapeTraits_3 Concept Reference
Concepts

## Definition

The concept `FixedWeightedAlphaShapeTraits_3` describes the requirements for the geometric traits class of the underlying Regular triangulation of a weighted alpha shape with fixed alpha value.

Refines:
  `RegularTriangulationTraits_3`

In addition to the requirements described in the concept RegularTriangulationTraits_3, the geometric traits class of a Regular triangulation plugged in a weighted alpha shape with fixed alpha value provides the following.

Has Models:
  `CGAL::Regular_triangulation_euclidean_traits_3<K>`

## Types
typedef unspecified_type | Comparison_result
| `CGAL::Comparison_result` or `Uncertain<CGAL::Comparison_result>`
typedef unspecified_type | Compare_weighted_squared_radius_3
| An object constructor able to compare the squared radius of the smallest sphere orthogonal to either four, three, two or one weighted point(s) to a given value of alpha. More...

## Creation
| FixedWeightedAlphaShapeTraits_3 ()
| default constructor.

## Access Functions
Compare_weighted_squared_radius_3 | compare_weighted_squared_radius_3_object ()

## Member Typedef Documentation

typedef unspecified_type FixedWeightedAlphaShapeTraits_3::Compare_weighted_squared_radius_3

An object constructor able to compare the squared radius of the smallest sphere orthogonal to either four, three, two or one weighted point(s) to a given value of alpha.

It provides:

- `Comparison_result operator()(Weighted_point_3 ,Weighted_point_3 ,Weighted_point_3 ,Weighted_point_3 )`
- `Comparison_result operator()(Weighted_point_3 ,Weighted_point_3 ,Weighted_point_3 )`
- `Comparison_result operator()(Weighted_point_3 ,Weighted_point_3 )`
- `Comparison_result operator()(Weighted_point_3 )`