CGAL 4.7 - 3D Polyhedral Surface: PolyhedronTraits_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 Polyhedral Surface

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PolyhedronTraits_3 Concept Reference
Concepts

## Definition

Required types and member functions for the `PolyhedronTraits_3` concept. This geometric traits concept is used in the polyhedral surface data structure `CGAL::Polyhedron_3<Traits>`. Any CGAL kernel is a model of this concept and can be used directly as template argument.

Refines:

  `CopyConstructible`

  `Assignable`

Has Models:

  `CGAL::Polyhedron_traits_3<Kernel>`

  `CGAL::Polyhedron_traits_with_normals_3<Kernel>`

  All models of the `CGAL::Kernel` concept, e.g., `CGAL::Simple_cartesian<FieldNumberType>`

See Also
  `CGAL::Polyhedron_3<Traits>`

## Types

typedef unspecified_type | Point_3
| point type.
typedef unspecified_type | Plane_3
| plane equation. More...
typedef unspecified_type | Construct_opposite_plane_3
| is an unary function object that reverses the plane orientation. More...

## Creation

| PolyhedronTraits_3 (const PolyhedronTraits_3 &traits2)
| copy constructor.
PolyhedronTraits_3 & | operator= (const PolyhedronTraits_3 &traits2)
| assignment.

## Operations

Construct_opposite_plane_3 | construct_opposite_plane_3_object ()
| returns an instance of this function object.

## Member Typedef Documentation

typedef unspecified_type PolyhedronTraits_3::Construct_opposite_plane_3

is an unary function object that reverses the plane orientation.

Must provide `Plane_3 operator()(Plane_3 plane)` that returns the reversed plane. Required only if plane equations are supported and the `inside_out()` method is used to reverse the polyhedral surface orientation.

typedef unspecified_type PolyhedronTraits_3::Plane_3

plane equation.

Even if plane equations are not supported with a particular polyhedral surface this type has to be defined (some dummy type).