CGAL 6.1.1 - 3D Mesh Generation

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MeshDomain_3 Concept Reference
Reference Manual » Main Concepts

## Definition

The concept `MeshDomain_3` describes the knowledge required on the object to be discretized. The concept `MeshDomain_3` is the concept to be used when the input domain does not have \( 0\) or \( 1\)-dimensional features that need to be accurately approximated by the mesh. In such a case, the queries issued by the meshing process concern only the faces of the input domain with dimension \( 3\) and \( 2\), that are respectively called subdomains and surface patches.

More specifically the concept `MeshDomain_3` provides a method to localize a point with respect to the input domain and its subdomains. Moreover, as the concept `SurfaceMeshTraits_3`, it also provides predicates to test whether a query segment (or a ray, or a line) intersects the boundary of the domain or of the subdomains, and constructors to compute some intersection point if any. It also includes a method able to provide a small set of initial points on the boundary.

In the following we consider only proper intersection with the domain and subdomain boundaries. A segment, ray or line is said to intersect properly the domain boundary (resp. a subdomain boundary) if it includes points which are strictly inside and strictly outside the domain (resp. the subdomain).

Has models
  `CGAL::Polyhedral_mesh_domain_3<Polyhedron,IGT>`
  `CGAL::Labeled_mesh_domain_3<BGT>`

See also
  `MeshVertexBase_3`
  `MeshCellBase_3`
  `CGAL::make_mesh_3()`
  `CGAL::refine_mesh_3()`

## Types
typedef unspecified_type | R
| Geometric traits class.
typedef unspecified_type | Point_3
| Point type.
typedef unspecified_type | Segment_3
| Segment type.
typedef unspecified_type | Ray_3
| Ray type.
typedef unspecified_type | Line_3
| Line type.
typedef CGAL::Tag_false | Has_features
| A type to distinguish `MeshDomain_3` models from `MeshDomainWithFeatures_3` models.
typedef unspecified_type | Subdomain_index
| Type of indices for subdomains of the input domain.
typedef unspecified_type | Surface_patch_index
| Type of indices for surface patches (boundaries and interfaces) of the input domain.
typedef unspecified_type | Index
| Type of indices to be stored at mesh vertices to characterize the lowest dimensional face of the input complex on which the vertex lies.
typedef std::tuple< Point_3, Index, int > | Intersection
| Returns type of `Construct_intersection` queries.
typedef unspecified_type | Construct_initial_points
| A function object to construct a set of initial points on the surface of the domain.
typedef unspecified_type | Is_in_domain
| A function object to query whether a point is in the input domain or not.
typedef unspecified_type | Do_intersect_surface
| A function object which answers intersection queries between the surface patches of the domain and objects of type `Segment_3`, `Ray_3` or `Line_3`.
typedef unspecified_type | Construct_intersection
| A function object to construct the intersection between an object of type `Segment_3`, `Ray_3` or `Line_3` and an interface.

## Bounding box
Since CGAL-4.8, a model of `MeshDomain_3` must provide a function providing a bounding box of the domain.
Bbox_3 | bbox () const
| Returns a bounding box of the domain.

## Operations
The following functions give access to the function objects:
Construct_initial_points | construct_initial_points_object ()
Is_in_domain | is_in_domain_object ()
Do_intersect_surface | do_intersect_surface_object ()
Construct_intersection | construct_intersection_object ()

## Index Conversion
These methods are designed to convert indices:
Index | index_from_surface_patch_index (Surface_patch_index surface_patch_index)
| Returns the index to be stored at a vertex lying on the surface patch identified by `surface_patch_index`.
Index | index_from_subdomain_index (Subdomain_index subdomain_index)
| Returns the index to be stored at a vertex lying in the subdomain identified by `subdomain_index`.
Surface_patch_index | surface_patch_index (Index index)
| Returns the `Surface_patch_index` of the surface patch where lies a vertex with dimension 2 and index `index`.
Subdomain_index | subdomain_index (Index index)
| Returns the index of the subdomain containing a vertex with dimension 3 and index `index`.

## Member Typedef Documentation

## ◆ Construct_initial_points

typedef unspecified_type MeshDomain_3::Construct_initial_points

A function object to construct a set of initial points on the surface of the domain.

Provides the following operators:

`template<typename OutputIterator>`
`OutputIterator operator()(OutputIterator pts)`

`template<typename OutputIterator>`
`OutputIterator operator()(OutputIterator pts, int n)`

Those two operators output a set of (`n`) surface points to the output iterator `pts`, as objects of type `std::pair<Point_3, Index>`. If `n` is not given, the functor must provide enough points to initialize the mesh generation process.

## ◆ Construct_intersection

typedef unspecified_type MeshDomain_3::Construct_intersection

A function object to construct the intersection between an object of type `Segment_3`, `Ray_3` or `Line_3` and an interface.

Provides the operators:

`Intersection operator()(Segment_3 s)`

`Intersection operator()(Ray_3 r)`

`Intersection operator()(Line_3 l)`

Precondition
  do_intersect_surface(s/r/l) == true

## ◆ Do_intersect_surface

typedef unspecified_type MeshDomain_3::Do_intersect_surface

A function object which answers intersection queries between the surface patches of the domain and objects of type `Segment_3`, `Ray_3` or `Line_3`.

Provides the operators:

`std::optional<Surface_patch_index> operator()(Segment_3 s)`

`std::optional<Surface_patch_index> operator()(Ray_3 r)`

`std::optional<Surface_patch_index> operator()(Line_3 l)`

The return type of the operators tell whether or not the query intersects a surface patch. In the positive case, it provides (through operator*()) the `Surface_patch_index` of one of the intersected surface patches.

## ◆ Index

typedef unspecified_type MeshDomain_3::Index

Type of indices to be stored at mesh vertices to characterize the lowest dimensional face of the input complex on which the vertex lies.

Must be a model of CopyConstructible, Assignable, DefaultConstructible and EqualityComparable.

## ◆ Intersection

typedef std::tuple<Point_3, Index, int> MeshDomain_3::Intersection

Returns type of `Construct_intersection` queries.

`int` represents the dimension of the lower dimensional face of the input complex on which the intersection point lies and `Index` is the index of this face.

## ◆ Is_in_domain

typedef unspecified_type MeshDomain_3::Is_in_domain

A function object to query whether a point is in the input domain or not.

In the positive case, it outputs the subdomain which includes the query point. Provides the operator:

`std::optional<Subdomain_index> operator()(Point_3 p)`

## ◆ R

typedef unspecified_type MeshDomain_3::R

Geometric traits class.

This type is defined to ensure compatibility with `CGAL::Kernel_traits<T>`.

## ◆ Subdomain_index

typedef unspecified_type MeshDomain_3::Subdomain_index

Type of indices for subdomains of the input domain.

Must be a model of CopyConstructible, Assignable, DefaultConstructible and EqualityComparable. The default constructed value must match the label of the exterior of the domain (which contains at least the unbounded component).

## ◆ Surface_patch_index

typedef unspecified_type MeshDomain_3::Surface_patch_index

Type of indices for surface patches (boundaries and interfaces) of the input domain.

Must be a model of CopyConstructible, Assignable, DefaultConstructible and EqualityComparable. The default constructed value must be the index value assigned to a non surface facet.