CGAL 6.1 - Polygon Mesh Processing

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Classes | Enumerations | Functions
Orientation Functions
Reference Manual

##

Functions to compute or change the orientation of faces and surfaces.

## Classes
struct | CGAL::Polygon_mesh_processing::Default_orientation_visitor
| Default visitor model of `PMPPolygonSoupOrientationVisitor`. More...

## Enumerations
enum | CGAL::Polygon_mesh_processing::Volume_error_code { CGAL::Polygon_mesh_processing::VALID_VOLUME , CGAL::Polygon_mesh_processing::SURFACE_WITH_SELF_INTERSECTIONS , CGAL::Polygon_mesh_processing::VOLUME_INTERSECTION , CGAL::Polygon_mesh_processing::INCOMPATIBLE_ORIENTATION }
| Enumeration type used to indicate the status of a set of faces classified by the function `volume_connected_components()`. More...

## Functions
template<class PointRange , class PolygonRange , class NamedParameters = parameters::Default_named_parameters>
bool | CGAL::Polygon_mesh_processing::orient_polygon_soup (PointRange &points, PolygonRange &polygons, const NamedParameters &np=parameters::default_values())
| tries to consistently orient a soup of polygons in 3D space.
template<class PointRange , class PolygonRange >
bool | CGAL::Polygon_mesh_processing::duplicate_non_manifold_edges_in_polygon_soup (PointRange &points, PolygonRange &polygons)
| duplicates each point p at which the intersection of an infinitesimally small ball centered at p with the polygons incident to it is not a topological disk.
template<class Concurrency_tag = CGAL::Sequential_tag, class ReferencePointRange , class ReferenceFaceRange , class PointRange , class FaceRange , class NamedParameters1 = parameters::Default_named_parameters, class NamedParameters2 = parameters::Default_named_parameters>
void | CGAL::Polygon_mesh_processing::orient_triangle_soup_with_reference_triangle_soup (const ReferencePointRange &ref_points, const ReferenceFaceRange &ref_faces, const PointRange &points, FaceRange &faces, const NamedParameters1 &np1=parameters::default_values(), const NamedParameters2 &np2=parameters::default_values())
| orients each triangle of a triangle soup using the orientation of its closest non degenerate triangle in a triangle soup.
template<class Concurrency_tag = Sequential_tag, class PointRange , class TriangleRange , class TriangleMesh , class NamedParameters1 = parameters::Default_named_parameters, class NamedParameters2 = parameters::Default_named_parameters>
void | CGAL::Polygon_mesh_processing::orient_triangle_soup_with_reference_triangle_mesh (const TriangleMesh &tm_ref, const PointRange &points, TriangleRange &triangles, const NamedParameters1 &np1=parameters::default_values(), const NamedParameters2 &np2=parameters::default_values())
| orients each triangle of a triangle soup using the orientation of its closest non degenerate triangle in `tm_ref`.
template<typename TriangleMesh , typename NamedParameters = parameters::Default_named_parameters>
bool | CGAL::Polygon_mesh_processing::is_outward_oriented (const TriangleMesh &tm, const NamedParameters &np=parameters::default_values())
| tests whether a closed triangle mesh has a positive orientation.
template<typename PolygonMesh >
void | CGAL::Polygon_mesh_processing::reverse_face_orientations (PolygonMesh &pmesh)
| reverses for each face the order of the vertices along the face boundary.
template<typename PolygonMesh , typename FaceRange >
void | CGAL::Polygon_mesh_processing::reverse_face_orientations (const FaceRange &face_range, PolygonMesh &pmesh)
| reverses for each face in `face_range` the order of the vertices along the face boundary.
template<class TriangleMesh , class NamedParameters = parameters::Default_named_parameters>
void | CGAL::Polygon_mesh_processing::orient (TriangleMesh &tm, const NamedParameters &np=parameters::default_values())
| makes each closed connected component of a triangulated surface mesh inward or outward oriented.
template<class TriangleMesh , class VolumeFaceIndexMap , class NamedParameters = parameters::Default_named_parameters>
std::size_t | CGAL::Polygon_mesh_processing::volume_connected_components (const TriangleMesh &tm, VolumeFaceIndexMap volume_id_map, const NamedParameters &np=parameters::default_values())
| assigns to each face of `tm` an id corresponding to the volume connected component it contributes to.
template<class TriangleMesh , class NamedParameters = parameters::Default_named_parameters>
bool | CGAL::Polygon_mesh_processing::does_bound_a_volume (const TriangleMesh &tm, const NamedParameters &np=parameters::default_values())
| indicates if `tm` bounds a volume.
template<class TriangleMesh , class NamedParameters = parameters::Default_named_parameters>
void | CGAL::Polygon_mesh_processing::orient_to_bound_a_volume (TriangleMesh &tm, const NamedParameters &np=parameters::default_values())
| orients the connected components of `tm` to make it bound a volume.
template<class PolygonMesh , class NamedParameters = parameters::Default_named_parameters>
void | CGAL::Polygon_mesh_processing::merge_reversible_connected_components (PolygonMesh &pm, const NamedParameters &np=parameters::default_values())
| reverses the connected components of `tm` having compatible boundary cycles that could be merged if their orientation were made compatible, and stitches them.
template<class PolygonMesh , class FaceBitMap , class NamedParameters = parameters::Default_named_parameters>
bool | CGAL::Polygon_mesh_processing::compatible_orientations (const PolygonMesh &pm, FaceBitMap fbm, const NamedParameters &np=parameters::default_values())
| identifies faces whose orientation must be reversed in order to enable stitching of connected components.

## Enumeration Type Documentation

## ◆ Volume_error_code

enum CGAL::Polygon_mesh_processing::Volume_error_code

`#include <CGAL/Polygon_mesh_processing/orientation.h>`

Enumeration type used to indicate the status of a set of faces classified by the function `volume_connected_components()`.

The set of faces defines either a volume connected connected component in the case of `VALID_VOLUME` or a surface connected component otherwise.

Enumerator
VALID_VOLUME | The set of faces bounds a volume.
SURFACE_WITH_SELF_INTERSECTIONS | The set of faces is self-intersecting.
VOLUME_INTERSECTION | The set of faces intersects another surface connected component.
INCOMPATIBLE_ORIENTATION | The set of faces is included in a volume but has an incompatible orientation.

## Function Documentation

## ◆ compatible_orientations()

template<class PolygonMesh , class FaceBitMap , class NamedParameters = parameters::Default_named_parameters>

bool CGAL::Polygon_mesh_processing::compatible_orientations | ( | const PolygonMesh & | pm,
|  | FaceBitMap | fbm,
|  | const NamedParameters & | np = `parameters::default_values()`
| ) |  |

`#include <CGAL/Polygon_mesh_processing/orientation.h>`

identifies faces whose orientation must be reversed in order to enable stitching of connected components.

Each face is assigned a bit (`false` or `true`) such that two faces have compatible orientations iff they are assigned the same bits. If `pm` features several connected components (ignoring edge orientations), the property map passed to the named parameter `face_partition_id_map` will indicate for each face to which connected component it belongs. Note that two faces in different connected components are not impacting each others' orientations, so comparing their associated bits in `face_bit_map` is irrelevant.

Template Parameters

  PolygonMesh | a model of `HalfedgeListGraph`, `FaceGraph`.
  FaceBitMap | a model of `WritablePropertyMap` with `face_descriptor` as key and `bool` as value_type
  NamedParameters | a sequence of Named Parameters

Parameters

  pm | a surface mesh
  fbm | face bit map indicating if a face orientation should be reversed to be stitchable (see `CGAL::Polygon_mesh_processing::stitch_borders()`) with another face. If `false` is returned, the map will not be filled.
  np | an optional sequence of Named Parameters among the ones listed below

Returns
  `true` if `pm` can be reoriented and `false` otherwise.

Optional Named Parameters

  a property map associating points to the vertices of `pm` Type: a class model of `ReadablePropertyMap` with `boost::graph_traits<PolygonMesh>::vertex_descriptor` as key type and `Point_3` as value type Default: `boost::get(CGAL::vertex_point, pm)` Extra: If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` should be available for the vertices of `pm`. |
  a property map filled by this function and that will contain for each face the id of its surface component after reversal and stitching in the range `[0, n - 1]`, with `n` the number of such components. Type: a class model of `WritablePropertyMap` with `boost::graph_traits<PolygonMesh>::face_descriptor` as key type and `std::size_t` as value type |

See also
  reverse_face_orientations()
  stitch_borders()

## ◆ does_bound_a_volume()

template<class TriangleMesh , class NamedParameters = parameters::Default_named_parameters>

bool CGAL::Polygon_mesh_processing::does_bound_a_volume | ( | const TriangleMesh & | tm,
|  | const NamedParameters & | np = `parameters::default_values()`
| ) |  |

`#include <CGAL/Polygon_mesh_processing/orientation.h>`

indicates if `tm` bounds a volume.

See Definitions for details.

Template Parameters

  TriangleMesh | a model of `HalfedgeListGraph`, `FaceListGraph`, and `MutableFaceGraph`.
  NamedParameters | a sequence of Named Parameters

Parameters

  tm | a closed triangulated surface mesh
  np | an optional sequence of Named Parameters among the ones listed below

Precondition
  `CGAL::is_closed(tm)`

Attention
  if `tm` is self-intersecting the behavior of this function is undefined.

Optional Named Parameters

  a property map associating points to the vertices of `tm` Type: a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::vertex_descriptor` as key type and `Point_3` as value type Default: `boost::get(CGAL::vertex_point, tm)` |
  a property map associating to each face of `tm` a unique index between `0` and `num_faces(tm) - 1` Type: a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::face_descriptor` as key type and `std::size_t` as value type Default: an automatically indexed internal map |
  For each connected component identified using its id `ccid`, the output of `is_outward_oriented()` called on the triangle mesh corresponding to this connected component is the value at the position `ccid` in the container. The size of the container is exactly the number of connected components. Type: a `reference_wrapper` (either from `boost` or the standard library) containing a reference to a container that must be a model of the `BackInsertionSequence` concept, with value type `bool` Default: unused |

See also
  `CGAL::Polygon_mesh_processing::orient_to_bound_a_volume()`

## ◆ duplicate_non_manifold_edges_in_polygon_soup()

template<class PointRange , class PolygonRange >

bool CGAL::Polygon_mesh_processing::duplicate_non_manifold_edges_in_polygon_soup | ( | PointRange & | points,
|  | PolygonRange & | polygons
| ) |  |

`#include <CGAL/Polygon_mesh_processing/orient_polygon_soup_extension.h>`

duplicates each point p at which the intersection of an infinitesimally small ball centered at p with the polygons incident to it is not a topological disk.

Template Parameters

  PointRange | a model of the concepts `RandomAccessContainer` and `BackInsertionSequence` whose `value_type` is the point type
  PolygonRange | a model of the concept `RandomAccessContainer` whose `value_type` is a model of the concept `RandomAccessContainer` whose `value_type` is `std::size_t`, and is also a model of `BackInsertionSequence`

Parameters

  points | points of the soup of polygons. Some additional points might be pushed back to resolve non-manifoldness or non-orientability issues.
  polygons | each element in the vector describes a polygon using the indices of the points in `points`. If needed the order of the indices of a polygon might be reversed.

Returns
  `false` if some points were duplicated, thus producing a self-intersecting surface mesh.
  `true` otherwise.

See also
  `orient_polygon_soup()`
  `duplicate_non_manifold_vertices()`

## ◆ is_outward_oriented()

template<typename TriangleMesh , typename NamedParameters = parameters::Default_named_parameters>

bool CGAL::Polygon_mesh_processing::is_outward_oriented | ( | const TriangleMesh & | tm,
|  | const NamedParameters & | np = `parameters::default_values()`
| ) |  |

`#include <CGAL/Polygon_mesh_processing/orientation.h>`

tests whether a closed triangle mesh has a positive orientation.

A closed triangle mesh is considered to have a positive orientation if the normal vectors to all its faces point outside the domain bounded by the triangle mesh. The normal vector to each face is chosen pointing on the side of the face where its sequence of vertices is seen counterclockwise.

Precondition
  `CGAL::is_closed(tm)`
  `CGAL::is_triangle_mesh(tm)`
  If `tm` contains several connected components, they are oriented consistently. In other words, the answer to this predicate would be the same for each isolated connected component.

Template Parameters

  TriangleMesh | a model of `FaceListGraph`
  NamedParameters | a sequence of Named Parameters

Parameters

  tm | the closed triangle mesh free from self-intersections to be tested
  np | an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

  a property map associating points to the vertices of `tm` Type: a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::vertex_descriptor` as key type and `Point_3` as value type Default: `boost::get(CGAL::vertex_point, tm)` |
  an instance of a geometric traits class Type: a class model of `Kernel` Default: a CGAL Kernel deduced from the point type, using `CGAL::Kernel_traits` Extra: The geometric traits class must be compatible with the vertex point type. |

Note
  This function is only doing an orientation test for one connected component of `tm`. For performance reasons, it is left to the user to call the function `does_bound_a_volume()` on a triangulated version of `tm` to ensure the result returned is relevant. For advanced usages, the function `volume_connected_components()` should be used instead.

See also
  `CGAL::Polygon_mesh_processing::reverse_face_orientations()`

## ◆ merge_reversible_connected_components()

template<class PolygonMesh , class NamedParameters = parameters::Default_named_parameters>

void CGAL::Polygon_mesh_processing::merge_reversible_connected_components | ( | PolygonMesh & | pm,
|  | const NamedParameters & | np = `parameters::default_values()`
| ) |  |

`#include <CGAL/Polygon_mesh_processing/orientation.h>`

reverses the connected components of `tm` having compatible boundary cycles that could be merged if their orientation were made compatible, and stitches them.

Connected components are examined by increasing number of faces.

Template Parameters

  PolygonMesh | a model of `HalfedgeListGraph`, `FaceListGraph`, and `MutableFaceGraph`.
  NamedParameters | a sequence of Named Parameters

Parameters

  pm | a surface mesh
  np | an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

  a property map associating points to the vertices of `pm` Type: a class model of `ReadablePropertyMap` with `boost::graph_traits<PolygonMesh>::vertex_descriptor` as key type and `Point_3` as value type Default: `boost::get(CGAL::vertex_point, pm)` Extra: If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` should be available for the vertices of `pm`. |
  a property map associating to each face of `pm` a unique index between `0` and `num_faces(pm) - 1`) Type: a class model of `ReadablePropertyMap` with `boost::graph_traits<PolygonMesh>::face_descriptor` as key type and `std::size_t` as value type Default: an automatically indexed internal map |
  If not `0`, a connected component is considered reversible only if it has no more faces than the value given. Otherwise, it is always considered reversible. Type: `std::size_t` Default: `0` |

## ◆ orient()

template<class TriangleMesh , class NamedParameters = parameters::Default_named_parameters>

void CGAL::Polygon_mesh_processing::orient | ( | TriangleMesh & | tm,
|  | const NamedParameters & | np = `parameters::default_values()`
| ) |  |

`#include <CGAL/Polygon_mesh_processing/orientation.h>`

makes each closed connected component of a triangulated surface mesh inward or outward oriented.

If a connected component is not closed, the orientation may or may not be changed or not is not guaranteed.

Template Parameters

  TriangleMesh | a model of `FaceListGraph` and `MutableFaceGraph`
  NamedParameters | a sequence of Named Parameters

Parameters

  tm | a closed triangulated surface mesh
  np | an optional sequence of Named Parameters among the ones listed below

Precondition
  `CGAL::is_closed(tm)`

Optional Named Parameters

  a property map associating points to the vertices of `tm` Type: a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::vertex_descriptor` as key type and `Point_3` as value type Default: `boost::get(CGAL::vertex_point, tm)` |
  an instance of a geometric traits class Type: a class model of `Kernel` Default: a CGAL Kernel deduced from the point type, using `CGAL::Kernel_traits` Extra: The geometric traits class must be compatible with the vertex point type. |
  a property map associating to each face of `tm` a unique index between `0` and `num_faces(tm) - 1` Type: a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::face_descriptor` as key type and `std::size_t` as value type Default: an automatically indexed internal map |
  If `true`, each connected component will be outward oriented (and inward oriented if `false`). Type: Boolean Default: `true` |

## ◆ orient_polygon_soup()

template<class PointRange , class PolygonRange , class NamedParameters = parameters::Default_named_parameters>

bool CGAL::Polygon_mesh_processing::orient_polygon_soup | ( | PointRange & | points,
|  | PolygonRange & | polygons,
|  | const NamedParameters & | np = `parameters::default_values()`
| ) |  |

`#include <CGAL/Polygon_mesh_processing/orient_polygon_soup.h>`

tries to consistently orient a soup of polygons in 3D space.

The algorithm re-orients polygons such that the orientation of adjacent polygons is consistent. Note that the adjacency is defined in a combinatorial sense, i.e. two polygons are sharing an edge if and only if the endpoints of this edge are represented by the same point indices in both faces (possibly in a different order); it is not sufficient for the points to be geometrically identical. One may use `CGAL::Polygon_mesh_processing::merge_duplicate_points_in_polygon_soup()` to convert geometrical point equality into combinatorial point equality.

When it is not possible to produce a combinatorial manifold surface (for example, if the polygon soup makes up a Möbius strip), some points are duplicated. Because a polygon soup does not have any connectivity (each point has as many occurrences as the number of polygons it belongs to), duplicating one point (or a pair of points) amounts to duplicating the polygon to which it belongs.

These points are either an endpoint of an edge incident to more than two polygons, an endpoint of an edge between two polygons with incompatible orientations (during the re-orientation process), or more generally a point p at which the intersection of an infinitesimally small ball centered at p with the polygons incident to it is not a topological disk.

The algorithm is described in [1].

Template Parameters

  PointRange | a model of the concepts `RandomAccessContainer` and `BackInsertionSequence` whose value type is the point type.
  PolygonRange | a model of the concept `RandomAccessContainer` whose `value_type` is a model of the concept `RandomAccessContainer` whose `value_type` is `std::size_t`.
  NamedParameters | a sequence of named parameters

Parameters

  points | points of the soup of polygons. Some additional points might be pushed back to resolve non-manifoldness or non-orientability issues.
  polygons | each element in the vector describes a polygon using the index of the points in `points`. If needed the order of the indices of a polygon might be reversed.
  np | optional sequence of named parameters among the ones listed below

Optional Named Parameters

  a visitor used to be notified of the presence of non-manifold simplices and of the modifications done to polygons during orientation. Type: a class model of `PMPPolygonSoupOrientationVisitor` Default: `Default_orientation_visitor` |

Returns
  `true` if the orientation operation succeeded.
  `false` if some points were duplicated, thus producing a combinatorially manifold but self-intersecting polyhedron.

See also
  `orient_triangle_soup_with_reference_triangle_mesh()`

Examples
  Polygon_mesh_processing/orient_polygon_soup_example.cpp.

## ◆ orient_to_bound_a_volume()

template<class TriangleMesh , class NamedParameters = parameters::Default_named_parameters>

void CGAL::Polygon_mesh_processing::orient_to_bound_a_volume | ( | TriangleMesh & | tm,
|  | const NamedParameters & | np = `parameters::default_values()`
| ) |  |

`#include <CGAL/Polygon_mesh_processing/orientation.h>`

orients the connected components of `tm` to make it bound a volume.

See Definitions for a precise definition.

Template Parameters

  TriangleMesh | a model of `HalfedgeListGraph`, `FaceListGraph`, and `MutableFaceGraph`.
  NamedParameters | a sequence of Named Parameters

Parameters

  tm | a closed triangulated surface mesh
  np | an optional sequence of Named Parameters among the ones listed below

Precondition
  `CGAL::is_closed(tm)`

Optional Named Parameters

  If `true`, each connected component will be outward oriented (and inward oriented if `false`). Type: Boolean Default: `true` Extra: If the outer connected components are inward oriented, it means that the infinity will be considered as part of the volume bounded by `tm`. |
  a property map associating points to the vertices of `tm` Type: a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::vertex_descriptor` as key type and `Point_3` as value type Default: `boost::get(CGAL::vertex_point, tm)` |
  an instance of a geometric traits class Type: a class model of `Kernel` Default: a CGAL Kernel deduced from the point type, using `CGAL::Kernel_traits` Extra: The geometric traits class must be compatible with the vertex point type. |
  a property map associating to each face of `tm` a unique index between `0` and `num_faces(tm) - 1` Type: a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::face_descriptor` as key type and `std::size_t` as value type Default: an automatically indexed internal map |

See also
  `CGAL::Polygon_mesh_processing::does_bound_a_volume()`

Examples
  Polygon_mesh_processing/orient_polygon_soup_example.cpp.

## ◆ orient_triangle_soup_with_reference_triangle_mesh()

template<class Concurrency_tag = Sequential_tag, class PointRange , class TriangleRange , class TriangleMesh , class NamedParameters1 = parameters::Default_named_parameters, class NamedParameters2 = parameters::Default_named_parameters>

void CGAL::Polygon_mesh_processing::orient_triangle_soup_with_reference_triangle_mesh | ( | const TriangleMesh & | tm_ref,
|  | const PointRange & | points,
|  | TriangleRange & | triangles,
|  | const NamedParameters1 & | np1 = `parameters::default_values()`,
|  | const NamedParameters2 & | np2 = `parameters::default_values()`
| ) |  |

`#include <CGAL/Polygon_mesh_processing/orient_polygon_soup_extension.h>`

orients each triangle of a triangle soup using the orientation of its closest non degenerate triangle in `tm_ref`.

Template Parameters

  Concurrency_tag | enables sequential versus parallel orientation. Possible values are `Sequential_tag` (the default), `Parallel_if_available_tag`, and `Parallel_tag`.
  PointRange | a model of the concept `RandomAccessContainer` whose value type is the point type
  TriangleRange | a model of the concept `RandomAccessContainer` whose `value_type` is a model of the concept `RandomAccessContainer` whose `value_type` is `std::size_t`and of size 3
  TriangleMesh | a model of `FaceListGraph`

Parameters

  tm_ref | the reference triangle_mesh
  points | the points of the soup
  triangles | the triangles of the soup
  np1 | an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

  a property map associating points to the vertices of `tm_ref` Type: a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::vertex_descriptor` as key type and `Point_3` as value type Default: `boost::get(CGAL::vertex_point, tm_ref)` |
  an instance of a geometric traits class Type: a class model of `Kernel` Default: a CGAL Kernel deduced from the point type, using `CGAL::Kernel_traits` |

Parameters

  np2 | an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

  a property map associating points to the elements of the point set `points` Type: a model of `ReadablePropertyMap` whose key type is the value type of the iterator of `PointRange` and whose value type is `geom_traits::Point_3` Default: `CGAL::Identity_property_map<geom_traits::Point_3>` |

Attention
  The types of points in `PointRange`, `geom_traits`, and `vertex_point_map` must be the same.

See also
  `orient_polygon_soup()`

## ◆ orient_triangle_soup_with_reference_triangle_soup()

template<class Concurrency_tag = CGAL::Sequential_tag, class ReferencePointRange , class ReferenceFaceRange , class PointRange , class FaceRange , class NamedParameters1 = parameters::Default_named_parameters, class NamedParameters2 = parameters::Default_named_parameters>

void CGAL::Polygon_mesh_processing::orient_triangle_soup_with_reference_triangle_soup | ( | const ReferencePointRange & | ref_points,
|  | const ReferenceFaceRange & | ref_faces,
|  | const PointRange & | points,
|  | FaceRange & | faces,
|  | const NamedParameters1 & | np1 = `parameters::default_values()`,
|  | const NamedParameters2 & | np2 = `parameters::default_values()`
| ) |  |

`#include <CGAL/Polygon_mesh_processing/orient_polygon_soup_extension.h>`

orients each triangle of a triangle soup using the orientation of its closest non degenerate triangle in a triangle soup.

Template Parameters

  Concurrency_tag | enables sequential versus parallel orientation. Possible values are `Sequential_tag` (the default), `Parallel_if_available_tag`, and `Parallel_tag`.
  ReferencePointRange | a model of the concept `RandomAccessContainer` whose `value_type` is the point type
  ReferenceTriangleRange | a model of the concept `RandomAccessContainer` whose `value_type` is a model of the concept `RandomAccessContainer` whose `value_type` is `std::size_t` and is of size 3
  PointRange | a model of the concept `RandomAccessContainer` whose `value_type` is the point type
  TriangleRange | a model of the concept `RandomAccessContainer` whose `value_type` is a model of the concept `RandomAccessContainer` whose `value_type` is `std::size_t`and is of size 3.
  NamedParameters1 | a sequence of Named Parameters
  NamedParameters2 | a sequence of Named Parameters

Parameters

  ref_points | the points of the reference soup
  ref_faces | triples of indices of points in `ref_points` defining the triangles of the reference soup
  points | the points of the soup to be oriented
  faces | triples of indices of points in `points` defining the triangles of the soup
  np1 | an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

  a property map associating points to the elements of the point set `ref_points` Type: a model of `ReadablePropertyMap` whose key type is the value type of the iterator of `ReferencePointRange` and whose value type is `geom_traits::Point_3` Default: `CGAL::Identity_property_map<geom_traits::Point_3>` |
  an instance of a geometric traits class Type: a class model of `Kernel` Default: a CGAL Kernel deduced from the point type, using `CGAL::Kernel_traits` |

Parameters

  np2 | an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

  a property map associating points to the elements of the point set `points` Type: a model of `ReadablePropertyMap` whose key type is the value type of the iterator of `PointRange` and whose value type is `geom_traits::Point_3` Default: `CGAL::Identity_property_map<geom_traits::Point_3>` |

Attention
  The types of points in `ReferencePointRange`, `PointRange`, and `geom_traits` must be the same.

## ◆ reverse_face_orientations() [1/2]

template<typename PolygonMesh , typename FaceRange >

void CGAL::Polygon_mesh_processing::reverse_face_orientations | ( | const FaceRange & | face_range,
|  | PolygonMesh & | pmesh
| ) |  |

`#include <CGAL/Polygon_mesh_processing/orientation.h>`

reverses for each face in `face_range` the order of the vertices along the face boundary.

The function does not perform any control and if the change of orientation of the faces makes the polygon mesh invalid, the behavior is undefined.

Template Parameters

  PolygonMesh | a model of `FaceListGraph` and `MutableFaceGraph`
  FaceRange | range of face descriptors, model of `Range`. Its iterator type is `InputIterator`.

See also
  `is_outward_oriented()`

## ◆ reverse_face_orientations() [2/2]

template<typename PolygonMesh >

void CGAL::Polygon_mesh_processing::reverse_face_orientations | ( | PolygonMesh & | pmesh | ) |

`#include <CGAL/Polygon_mesh_processing/orientation.h>`

reverses for each face the order of the vertices along the face boundary.

Template Parameters

  PolygonMesh | a model of `FaceListGraph` and `MutableFaceGraph`

See also
  `is_outward_oriented()`

Examples
  Polygon_mesh_processing/orient_polygon_soup_example.cpp.

## ◆ volume_connected_components()

template<class TriangleMesh , class VolumeFaceIndexMap , class NamedParameters = parameters::Default_named_parameters>

std::size_t CGAL::Polygon_mesh_processing::volume_connected_components | ( | const TriangleMesh & | tm,
|  | VolumeFaceIndexMap | volume_id_map,
|  | const NamedParameters & | np = `parameters::default_values()`
| ) |  |

`#include <CGAL/Polygon_mesh_processing/orientation.h>`

assigns to each face of `tm` an id corresponding to the volume connected component it contributes to.

Using the adjacency relation of two faces along an edge, a triangle mesh can be split into connected components (surface components in the following). A surface component without boundary separates the 3D space into an infinite and a finite volume. We say that the finite volume is enclosed by this surface component.

The volume connected components (volume components in the following) are defined as follows: Each surface component `S` that is outside any volume enclosed by another surface component defines the outer boundary of a volume component. Each surface component that is inside the volume enclosed by `S` defines a hole if it is included in no other volume enclosed by a surface component but `S`. Ignoring the identified volume component, the same procedure is recursively repeated for all surface components in each hole.

There are some special cases:

- a non-closed surface component is reported as a volume component ignoring any inclusion test
- a self-intersecting surface component is reported as a volume component ignoring any inclusion test
- a surface component intersecting another surface component is reported as a volume component, and so are all the surface components inside its enclosed volume
- if `do_orientation_tests` is set to `true`, if the holes are not all equally oriented (all inward or all outward) or if the holes and the outer boundary are equally oriented, each surface component is reported as a volume component, and so are all the surface components inside the corresponding enclosed volumes
- If `do_orientation_tests` is set to `true` and the surface components that are outside all enclosed volumes are inward oriented, they are then considered as holes of the unbounded volume (that has no outer boundary)

A property map for `CGAL::vertex_point_t` must be either available as an internal property map of `tm` or provided as one of the Named Parameters.

Template Parameters

  TriangleMesh | a model of `FaceListGraph`
  VolumeFaceIndexMap | a model of `WritablePropertyMap` with `boost::graph_traits<TriangleMesh>::face_descriptor` as key type and `boost::graph_traits<TriangleMesh>::faces_size_type` as value type.
  NamedParameters | a sequence of Named Parameters

Parameters

  tm | the input triangle mesh
  volume_id_map | the property map filled by this function with indices of volume components associated to the faces of `tm`
  np | an optional sequence of Named Parameters among the ones listed below

Precondition
  `CGAL::is_closed(tm)`

Optional Named Parameters

  a property map associating points to the vertices of `tm` Type: a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::vertex_descriptor` as key type and `Point_3` as value type Default: `boost::get(CGAL::vertex_point, tm)` |
  an instance of a geometric traits class Type: a class model of `Kernel` Default: a CGAL Kernel deduced from the point type, using `CGAL::Kernel_traits` Extra: The geometric traits class must be compatible with the vertex point type. |
  a property map associating to each face of `tm` a unique index between `0` and `num_faces(tm) - 1` Type: a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::face_descriptor` as key type and `std::size_t` as value type Default: an automatically indexed internal map |
  a property map filled by this function and that will contain for each face the id of its surface component in the range `[0, number of surface components - 1]` Type: a class model of `WritablePropertyMap` with `boost::graph_traits<TriangleMesh>::face_descriptor` as key type and `std::size_t` as value type Default: an automatically indexed internal map |
  a container, which contains at position `k` the ids of all the surface components that are the first intersected by any ray with source on the surface component `k` and directed outside the volume enclosed by the surface component `k`. There is only one such id but when some surface components intersect. The size of the container is exactly the number of surface components of `tm`. Type: a `reference_wrapper` (either from `boost` or the standard library) containing a reference to an object that must be a model of the `BackInsertionSequence` concept, with a value type being a model of `BackInsertionSequence` of `std::size_t`, both types having the functions `reserve()` and `push_back()` Default: unused |
  If `true`, the orientation of the faces of each surface components will be taken into account for the definition of the volume. If `false`, the face orientation is ignored and the volumes are defined only by the nesting of surface components. Type: Boolean Default: `true` |
  a container which indicates the status of a volume assigned to a set of faces. The description of the value type is given in the documentation of the enumeration type. The size of the container is exactly the number of volume components. Type: a `reference_wrapper` (either from `boost` or the standard library) containing a reference to a container that must be a model of the `BackInsertionSequence` concept, with value type `Volume_error_code` Default: unused |
  If `false`, it is assumed that `tm` does not contains any self-intersections. If `true`, the input might contain some self-intersections and a test is done prior to the volume decomposition. Type: Boolean Default: `false` |
  For each connected component identified using its id `ccid`, the id of the volume it contributes to describe is the value at the position `ccid` in the container. The size of the container is exactly the number of connected components. Type: a `reference_wrapper` (either from `boost` or the standard library) containing a reference to a container that must be a model of the `BackInsertionSequence` concept, with value type `std::size_t` Default: unused |
  For each connected component identified using its id `ccid`, the container contains the number of connected components containing on its bounded side this component. The size of the container is exactly the number of connected components. Type: a `reference_wrapper` (either from `boost` or the standard library) containing a reference to a container that must be a model of the `BackInsertionSequence` concept, with value type `std::size_t` Default: unused |
  For each connected component identified using its id `ccid`, the output of `is_outward_oriented()` called on the triangle mesh corresponding to this connected component is the value at the position `ccid` in the container. The size of the container is exactly the number of connected components. Type: a `reference_wrapper` (either from `boost` or the standard library) containing a reference to a container that must be a model of the `BackInsertionSequence` concept, with value type `bool` Default: unused |
  Output iterator into which pairs of ids (id must be convertible to `std::size_t`) can be put. Each pair of connected components intersecting will be reported using their ids. If `do_self_intersection_tests` named parameter is set to `false`, nothing will be reported. Type: a model of `OutputIterator` Default: unused |

Returns
  the number of volume components defined by `tm`