CGAL 4.7 - 3D Alpha Shapes: WeightedAlphaShapeTraits_3 Concept Reference

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

CGAL 4.7 - 3D Alpha Shapes

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WeightedAlphaShapeTraits_3 Concept Reference
Concepts

## Definition

The concept `WeightedAlphaShapeTraits_3` describes the requirements for the geometric traits class of the underlying Regular triangulation of a weighted alpha shape.

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 basic alpha shapes provides the following.

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

## Types

typedef unspecified_type | FT
| A number type compatible with the type used for the points coordinates.
typedef unspecified_type | Compute_squared_radius_smallest_orthogonal_sphere_3

An object constructor able to compute the squared radius of the smallest sphere orthogonal to four weighted points `p0, p1, p2, p3`, and the squared radius of the smallest sphere orthogonal to three weighted points `p0, p1, p2`, and the squared radius of smallest sphere orthogonal to two weighted points `p0, p1`, and the squared radius of the smallest sphere orthogonal to a single point `p0`.

## Creation

| WeightedAlphaShapeTraits_3 ()
| default constructor.

## Access Functions

Compute_squared_radius_smallest_orthogonal_sphere_3 | compute_squared_radius_smallest_orthogonal_sphere_3_object ()