CGAL 6.1.1 - 3D Constrained Triangulations

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Functions
Free Functions for Creating Conforming Constrained Delaunay Triangulations
Reference Manual

##

# Free Functions Template for Creating Conforming Constrained Delaunay Triangulations

The following functions create a 3D conforming constrained Delaunay triangulation from either a polygon soup or a polygon mesh.

## Input Data

The input data (polygon mesh or polygon soup) represents the polygonal constraints enforced during the triangulation process.

By default, each face of the input is considered a polygonal constraint for the triangulation. The named parameter `plc_face_id` can be used to describe larger polygonal constraints, possibly with holes. If used, this parameter must be a property map that associates each face of the input with a PLC face identifier. Faces with the same face identifier are considered part of the same surface patch. Each of these surface patches (defined as the union of the input faces with a given patch identifier) is expected to be a polygon or a polygon with holes, with coplanar vertices (or nearly coplanar up to the precision of the number type used).

The generated triangulation will conform to the faces of the input, or to the surface patches described by the `plc_face_id` property map if provided.

In the case where the input contains a non-planar PLC face, building the triangulation may fail with an exception of type `CGAL::Non_planar_plc_facet_exception`.

Precondition
  The input data must not be coplanar.
  The input data must not have self-intersections.

## Template Parameters

For both function templates, the template arguments can be deduced from the function arguments, or defaulted.

- The first template argument `Triangulation` defaults to `CGAL::Default`, and in that case the triangulation type is deduced from the input type and the named parameters (see below).
- The following one or two template arguments are deduced from the input data: either a polygon mesh type, or a polygon soup defined by two types (a sequence of points and a sequence of sequences of indices).
- The last template argument is the named parameters class, deduced from the function arguments.

## Returned Triangulation Type

For both functions, the template parameter `Triangulation` defines the type of the triangulation that is created and returned by the function.

- If `Triangulation` is `CGAL::Default`, the geometric traits class type is deduced from the input data and the named parameters. If the named parameter `geom_traits` is provided, the traits class is deduced from it. Otherwise, the point type of the input data is used to deduce the traits class. Let's call it `Traits`. The returned triangulation type is then `CGAL::Conforming_constrained_Delaunay_triangulation_3<Traits>`.
- Otherwise, `Triangulation` must be a specialization of the `CGAL::Conforming_constrained_Delaunay_triangulation_3` class template, with the following requirements:
  - its `Vertex` type must be a model of `ConformingConstrainedDelaunayTriangulationVertexBase_3`, and
  - its `Cell` type must be a model of `ConformingConstrainedDelaunayTriangulationCellBase_3`.

In both cases, the traits class `Traits` must fulfill the following requirements:

- It must be a model of the concept `ConformingConstrainedDelaunayTriangulationTraits_3`.
- It must have a `Point_3` type that is constructible from the point type of the input data.

## Functions
template<typename Triangulation = CGAL::Default, typename PolygonMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
auto | CGAL::make_conforming_constrained_Delaunay_triangulation_3 (const PolygonMesh &mesh, const NamedParameters &np=parameters::default_values())
| creates a 3D constrained Delaunay triangulation conforming to the faces of a polygon mesh.
template<typename Triangulation = CGAL::Default, typename PointRange , typename PolygonRange , typename NamedParameters = parameters::Default_named_parameters>
auto | CGAL::make_conforming_constrained_Delaunay_triangulation_3 (const PointRange &points, const PolygonRange &polygons, const NamedParameters &np=parameters::default_values())
| creates a 3D constrained Delaunay triangulation conforming to the faces of a polygon soup.

## Function Documentation

## ◆ make_conforming_constrained_Delaunay_triangulation_3() [1/2]

template<typename Triangulation = CGAL::Default, typename PointRange , typename PolygonRange , typename NamedParameters = parameters::Default_named_parameters>

auto CGAL::make_conforming_constrained_Delaunay_triangulation_3 | ( | const PointRange & | points,
|  | const PolygonRange & | polygons,
|  | const NamedParameters & | np = `parameters::default_values()`
| ) |  |

`#include <CGAL/make_conforming_constrained_Delaunay_triangulation_3.h>`

creates a 3D constrained Delaunay triangulation conforming to the faces of a polygon soup.

Template Parameters

  PointRange | a model of the concept `RandomAccessContainer` whose value type is the point type of the polygon soup
  PolygonRange | a model of the concept `RandomAccessContainer` whose value type is a model of the concept `RandomAccessContainer` whose value type is `std::size_t`
  Triangulation | an instance of the `CGAL::Conforming_constrained_Delaunay_triangulation_3` class template, or `CGAL::Default`
  NamedParameters | a sequence of Named Parameters

Parameters

  points | a range of points representing the vertices of the polygon soup
  polygons | a range of ranges of indices representing the faces of the polygon soup
  np | an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

  a property map associating points to the elements of the range `points` Type: a model of `ReadablePropertyMap` whose key type is the value type of `PointRange`, and value type is convertible to the point type of the geometric traits class Default: `CGAL::Identity_property_map` |
  a property map associating a patch identifier to each facet of `soup`. Each identifier corresponds to a planar surface patch. Each surface patch can be composed of several faces of `soup`, forming a planar polygon. Type: a class model of `ReadablePropertyMap` with `std::size_t` as key type and with any value type that is a regular type (model of `Regular`) Extra: If this parameter is omitted, each facet of the polygon soup is considered a separate PLC face. Extra: Otherwise facets with the same patch identifier are considered part of the same PLC face. |
  an instance of a geometric traits class Type: `Traits` as defined above in the section Returned Triangulation Type Default: the default constructed traits object `Traits{}` |

Returns
  a 3D constrained Delaunay triangulation conforming to the faces of the polygon soup, of a type described in the section Returned Triangulation Type above.

Precondition
  The polygon soup must be free of self-intersections. If the polygon soup is a triangle soup, this is equivalent to: `CGAL::Polygon_mesh_processing::does_triangle_soup_self_intersect(points, polygons, np) == false` .

## ◆ make_conforming_constrained_Delaunay_triangulation_3() [2/2]

template<typename Triangulation = CGAL::Default, typename PolygonMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>

auto CGAL::make_conforming_constrained_Delaunay_triangulation_3 | ( | const PolygonMesh & | mesh,
|  | const NamedParameters & | np = `parameters::default_values()`
| ) |  |

`#include <CGAL/make_conforming_constrained_Delaunay_triangulation_3.h>`

creates a 3D constrained Delaunay triangulation conforming to the faces of a polygon mesh.

Template Parameters

  PolygonMesh | a model of `FaceListGraph`
  Triangulation | an instance of the `CGAL::Conforming_constrained_Delaunay_triangulation_3` class template, or `CGAL::Default`
  NamedParameters | a sequence of Named Parameters

Parameters

  mesh | the polygon mesh representing the constraints
  np | an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

  a property map associating points to the vertices of `mesh` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMesh>::vertex_descriptor` as key type and `Traits::Point_3` as value type Default: `boost::get(CGAL::vertex_point, mesh)` Extra: If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` must be available in `PolygonMesh`. |
  a property map associating a patch identifier to each facet of `mesh`. Each identifier corresponds to a planar surface patch. Each surface patch can be composed of several facets of `mesh`, forming a planar polygon. Type: a class model of `ReadablePropertyMap` with `boost::graph_traits<PolygonMesh>::face_descriptor` as key type and with any value type that is a regular type (model of `Regular`) Extra: If this parameter is omitted, each facet of `mesh` is considered a separate PLC face. Faces of `mesh` with the same patch identifier are considered part of the same PLC face. |
  an instance of a geometric traits class Type: `Traits` as defined above in the section Returned Triangulation Type Default: the default constructed traits object `Traits{}` |

Returns
  a 3D constrained Delaunay triangulation conforming to the faces of the polygon mesh, of a type described in the section Returned Triangulation Type above.

Precondition
  `mesh` must not have self-intersections. For triangulated surfaces, it can be checked using the function `CGAL::Polygon_mesh_processing::does_self_intersect(mesh, np) == false`

Examples
  Constrained_triangulation_3/ccdt_3_after_autorefinement.cpp, Constrained_triangulation_3/ccdt_3_check_preconditions.cpp, Constrained_triangulation_3/ccdt_3_fimap_region_growing.cpp, Constrained_triangulation_3/ccdt_3_from_soup.cpp, Constrained_triangulation_3/ccdt_3_from_soup_fimap.cpp, Constrained_triangulation_3/ccdt_3_preprocessing.cpp, Constrained_triangulation_3/conforming_constrained_Delaunay_triangulation_3.cpp, and Constrained_triangulation_3/conforming_constrained_Delaunay_triangulation_3_fimap.cpp.