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

CGAL 4.8 - 3D Mesh Generation

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IntersectionGeometricTraits_3 Concept Reference
Secondary Concepts

## Definition

The concept `IntersectionGeometricTraits_3` provides types and functors required to implement a model of `MeshDomain_3`, when the domain is described by a simplicial surface mesh forming its boundary. The concept `IntersectionGeometricTraits_3` mainly provides the detection and construction of intersections between segments and triangles.

Has Models:
  Any `CGAL::Kernel`.

See Also
  `BisectionGeometricTraits_3`
  `CGAL::Polyhedral_mesh_domain_3<Polyhedron,IGT,TriangleAccessor>`

## Types
typedef unspecified_type | Point_3
| Point type.
typedef unspecified_type | Segment_3
| Segment type.
typedef unspecified_type | Triangle_3
| Triangle type.
typedef unspecified_type | Do_intersect_3
| Function object that detects an intersection between a 3D segment and a 3D triangle. More...
typedef unspecified_type | Intersect_3
| Function object that constructs the intersection between a 3D segment and a 3D triangle. More...

## Operations
Do_intersect_3 | do_intersect_3_object ()
| Returns the intersection detection functor.
Intersect_3 | intersect_3_object ()
| Returns the intersection constructor.

## Member Typedef Documentation

typedef unspecified_type IntersectionGeometricTraits_3::Do_intersect_3

Function object that detects an intersection between a 3D segment and a 3D triangle.

Partial model of `Kernel::DoIntersect_3`. Provides the operators:

- `bool operator()(Segment_3 seg, Triangle_3 tr)`
- `bool operator()(Triangle_3 tr, Segment_3 seg)`

which returns `true`, iff the triangle and the segment have a non empty intersection.

typedef unspecified_type IntersectionGeometricTraits_3::Intersect_3

Function object that constructs the intersection between a 3D segment and a 3D triangle.

Partial model of `Kernel::Intersect_3`. Provides the operators:

- `boost::optional< boost::variant< Point_3, Segment_3 > > operator()(Segment_3 seg, Triangle_3 tr)`
- `boost::optional< boost::variant< Point_3, Segment_3 > > operator()(Triangle_3 tr, Segment_3 seg)`

which computes the intersection between the triangle and the segment.