CGAL 5.5 - Polygon Mesh Processing
Combinatorial Repairing

Functions to repair polygon soups and polygon meshes.

## Functions

template<typename PolygonMesh >
bool CGAL::Polygon_mesh_processing::is_non_manifold_vertex (typename boost::graph_traits< PolygonMesh >::vertex_descriptor v, const PolygonMesh &pm)
returns whether a vertex of a polygon mesh is non-manifold. More...

template<typename PolygonMesh , typename OutputIterator >
OutputIterator CGAL::Polygon_mesh_processing::non_manifold_vertices (const PolygonMesh &pm, OutputIterator out)
collects the non-manifold vertices (if any) present in the mesh. More...

template<typename PolygonMesh , typename NamedParameters = parameters::Default_named_parameters>
std::size_t CGAL::Polygon_mesh_processing::duplicate_non_manifold_vertices (PolygonMesh &pm, const NamedParameters &np=parameters::default_values())
duplicates all the non-manifold vertices of the input mesh. More...

template<class PolygonMesh , class NamedParameters = parameters::Default_named_parameters>
void CGAL::Polygon_mesh_processing::merge_duplicated_vertices_in_boundary_cycle (typename boost::graph_traits< PolygonMesh >::halfedge_descriptor h, PolygonMesh &pm, const NamedParameters &np=parameters::default_values())
merges identical vertices around a cycle of boundary edges. More...

template<class PolygonMesh , class NamedParameters = parameters::Default_named_parameters>
void CGAL::Polygon_mesh_processing::merge_duplicated_vertices_in_boundary_cycles (PolygonMesh &pm, const NamedParameters &np=parameters::default_values())
extracts boundary cycles and merges the duplicated vertices of each cycle. More...

template<typename PolygonMesh , typename PointRange , typename PolygonRange , typename NamedParameters = parameters::Default_named_parameters>
void CGAL::Polygon_mesh_processing::polygon_mesh_to_polygon_soup (const PolygonMesh &mesh, PointRange &points, PolygonRange &polygons, const NamedParameters &np=parameters::default_values())
adds the vertices and faces of a mesh into a (possibly non-empty) polygon soup. More...

template<typename PolygonRange >
bool CGAL::Polygon_mesh_processing::is_polygon_soup_a_polygon_mesh (const PolygonRange &polygons)
returns true if the soup of polygons defines a valid polygon mesh that can be handled by CGAL::Polygon_mesh_processing::polygon_soup_to_polygon_mesh(). More...

template<typename PolygonMesh , typename PointRange , typename PolygonRange , typename NamedParameters_PS = parameters::Default_named_parameters, typename NamedParameters_PM = parameters::Default_named_parameters>
void CGAL::Polygon_mesh_processing::polygon_soup_to_polygon_mesh (const PointRange &points, const PolygonRange &polygons, PolygonMesh &out, const NamedParameters_PS &np_ps=parameters::default_values(), const NamedParameters_PM &np_pm=parameters::default_values())
builds a polygon mesh from a soup of polygons. More...

template<class PolygonMesh >
std::size_t CGAL::Polygon_mesh_processing::remove_isolated_vertices (PolygonMesh &pmesh)
removes the isolated vertices from any polygon mesh. More...

template<typename TriangleMesh , typename NamedParameters = parameters::Default_named_parameters>
std::size_t CGAL::Polygon_mesh_processing::remove_connected_components_of_negligible_size (TriangleMesh &tmesh, const NamedParameters &np=parameters::default_values())
removes connected components whose area or volume is under a certain threshold value. More...

template<typename PointRange , typename PolygonRange >
std::size_t CGAL::Polygon_mesh_processing::remove_isolated_points_in_polygon_soup (PointRange &points, PolygonRange &polygons)
removes the isolated points from a polygon soup. More...

template<typename PointRange , typename PolygonRange , typename NamedParameters = parameters::Default_named_parameters>
std::size_t CGAL::Polygon_mesh_processing::merge_duplicate_points_in_polygon_soup (PointRange &points, PolygonRange &polygons, const NamedParameters &np=parameters::default_values())
merges the duplicate points in a polygon soup. More...

template<typename PointRange , typename PolygonRange , typename NamedParameters = parameters::Default_named_parameters>
std::size_t CGAL::Polygon_mesh_processing::merge_duplicate_polygons_in_polygon_soup (const PointRange &points, PolygonRange &polygons, const NamedParameters &np=parameters::default_values())
merges the duplicate polygons in a polygon soup. More...

template<typename PointRange , typename PolygonRange , typename NamedParameters = parameters::Default_named_parameters>
void CGAL::Polygon_mesh_processing::repair_polygon_soup (PointRange &points, PolygonRange &polygons, const NamedParameters &np=parameters::default_values())
cleans a given polygon soup through various repairing operations. More...

template<typename PolygonMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
std::size_t CGAL::Polygon_mesh_processing::stitch_boundary_cycle (const typename boost::graph_traits< PolygonMesh >::halfedge_descriptor h, PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
stitches together, whenever possible, two halfedges belonging to the boundary cycle described by the halfedge h. More...

template<typename BorderHalfedgeRange , typename PolygonMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
std::size_t CGAL::Polygon_mesh_processing::stitch_boundary_cycles (const BorderHalfedgeRange &boundary_cycle_representatives, PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
stitches together, whenever possible, two halfedges belonging to the same boundary cycle. More...

template<typename PolygonMesh , typename HalfedgePairsRange , typename NamedParameters = CGAL::parameters::Default_named_parameters>
std::size_t CGAL::Polygon_mesh_processing::stitch_borders (PolygonMesh &pmesh, const HalfedgePairsRange &hedge_pairs_to_stitch, const NamedParameters &np=parameters::default_values(), typename boost::enable_if< typename boost::has_range_iterator< HalfedgePairsRange > >::type *=0)
stitches together border halfedges in a polygon mesh. More...

template<typename PolygonMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
std::size_t CGAL::Polygon_mesh_processing::stitch_borders (PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
Same as the other overload, but the pairs of halfedges to be stitched are automatically found amongst all border halfedges. More...

template<typename BorderHalfedgeRange , typename PolygonMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
std::size_t CGAL::Polygon_mesh_processing::stitch_borders (const BorderHalfedgeRange &boundary_cycle_representatives, PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
Same as the other overload, but the pairs of halfedges to be stitched are automatically found amongst halfedges in cycles described by boundary_cycle_representatives. More...

## ◆ duplicate_non_manifold_vertices()

template<typename PolygonMesh , typename NamedParameters = parameters::Default_named_parameters>
 std::size_t CGAL::Polygon_mesh_processing::duplicate_non_manifold_vertices ( PolygonMesh & pm, const NamedParameters & np = parameters::default_values() )

#include <CGAL/Polygon_mesh_processing/manifoldness.h>

duplicates all the non-manifold vertices of the input mesh.

Template Parameters
 PolygonMesh a model of HalfedgeListGraph and MutableHalfedgeGraph NamedParameters a sequence of Named Parameters
Parameters
 pm the surface mesh to be repaired 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 ReadWritePropertyMap with boost::graph_traits::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 must be available in PolygonMesh. a property map containing the constrained-or-not status of each vertex of pm. Type: a class model of ReadWritePropertyMap with boost::graph_traits::vertex_descriptor as key type and bool as value type. It must be default constructible. Default: a default property map where no vertex is constrained Extra: put(vcm, v, true) will be called for each duplicated vertices, as well as the original non-manifold vertex in the input mesh. an output iterator to collect the duplicated vertices Type: a model of OutputIterator with value type std::vector Default: unused Extra: The first vertex of each vector is a non-manifold vertex of the input mesh, followed by the new vertices that were created to fix the given non-manifold configuration.
Returns
the number of vertices created
non_manifold_vertices()
Examples:
Polygon_mesh_processing/manifoldness_repair_example.cpp.

## ◆ is_non_manifold_vertex()

template<typename PolygonMesh >
 bool CGAL::Polygon_mesh_processing::is_non_manifold_vertex ( typename boost::graph_traits< PolygonMesh >::vertex_descriptor v, const PolygonMesh & pm )

#include <CGAL/Polygon_mesh_processing/manifoldness.h>

returns whether a vertex of a polygon mesh is non-manifold.

Warning
This function has linear runtime with respect to the size of the mesh. The function non_manifold_vertices() should be used when gathering all non manifold vertices.
Template Parameters
 PolygonMesh a model of HalfedgeListGraph
Parameters
 v a vertex of pm pm a triangle mesh containing v
Returns
true if the vertex is non-manifold, false otherwise
duplicate_non_manifold_vertices()
Examples:
Polygon_mesh_processing/manifoldness_repair_example.cpp.

## ◆ is_polygon_soup_a_polygon_mesh()

template<typename PolygonRange >
 bool CGAL::Polygon_mesh_processing::is_polygon_soup_a_polygon_mesh ( const PolygonRange & polygons )

#include <CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h>

returns true if the soup of polygons defines a valid polygon mesh that can be handled by CGAL::Polygon_mesh_processing::polygon_soup_to_polygon_mesh().

It checks that each edge has at most two incident faces and such an edge is visited in opposite direction along the two face boundaries, no polygon has twice the same vertex, and the polygon soup describes a manifold surface. This function does not require a range of points as an argument since the check is purely topological. To each vertex of the mesh is associated an index that is used in the description of the boundaries of the polygons provided in polygons.

Template Parameters
 PolygonRange a model of the concept RandomAccessContainer whose value_type is a model of the concept RandomAccessContainer whose value_type is std::size_t.
Parameters
 polygons each element in the range describes a polygon using the indices of the vertices.
CGAL::Polygon_mesh_processing::orient_polygon_soup()
Examples:
Polygon_mesh_processing/orientation_pipeline_example.cpp.

## ◆ merge_duplicate_points_in_polygon_soup()

template<typename PointRange , typename PolygonRange , typename NamedParameters = parameters::Default_named_parameters>
 std::size_t CGAL::Polygon_mesh_processing::merge_duplicate_points_in_polygon_soup ( PointRange & points, PolygonRange & polygons, const NamedParameters & np = parameters::default_values() )

#include <CGAL/Polygon_mesh_processing/repair_polygon_soup.h>

merges the duplicate points in a polygon soup.

Note that the index of a point that is merged with another point will thus change in all the polygons that the point appears in.

Template Parameters
 PointRange a model of the concepts SequenceContainer and Swappable whose value type is the point type. PolygonRange a model of the concept RandomAccessContainer whose value_type is itself 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 polygons a vector of polygons. Each element in the vector describes a polygon using the indices of the points in points. np an optional sequence of Named Parameters among the ones listed below
Optional Named Parameters
 an instance of a geometric traits class Type: The traits class must provide the nested functor Less_xyz_3 to compare lexicographically two points a function Less_xyz_3 less_xyz_3_object(). 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.
Returns
the number of removed points
repair_polygon_soup()

## ◆ merge_duplicate_polygons_in_polygon_soup()

template<typename PointRange , typename PolygonRange , typename NamedParameters = parameters::Default_named_parameters>
 std::size_t CGAL::Polygon_mesh_processing::merge_duplicate_polygons_in_polygon_soup ( const PointRange & points, PolygonRange & polygons, const NamedParameters & np = parameters::default_values() )

#include <CGAL/Polygon_mesh_processing/repair_polygon_soup.h>

merges the duplicate polygons in a polygon soup.

Two polygons are duplicate if they share the same vertices in the same order. Note that the first vertex of the polygon does not matter, that is the triangle 0,1,2 is a duplicate of the triangle 2,0,1.

Template Parameters
 PointRange a model of the concept RandomAccessContainer whose value type is the point type. PolygonRange a model of the concept SequenceContainer whose value_type is itself a model of the concepts RandomAccessContainer and ReversibleContainer whose value_type is std::size_t. NamedParameters a sequence of Named Parameters
Parameters
 points points of the soup of polygons polygons a vector of polygons. Each element in the vector describes a polygon using the indices of the points in points. np an optional sequence of Named Parameters among the ones listed below
Optional Named Parameters
 an instance of a geometric traits class Type: The traits class must provide the nested functor Less_xyz_3 to compare lexicographically two points a function Less_xyz_3 less_xyz_3_object(). 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. Parameter to indicate, when multiple polygons are duplicates, whether all the duplicate polygons should be removed or if one (arbitrarily chosen) face should be kept. Type: Boolean Default: false Parameter to indicate if polygon orientation should be taken into account when determining whether two polygons are duplicates, that is, whether e.g. the triangles 0,1,2 and 0,2,1 are duplicates. Type: Boolean Default: false
Returns
the number of removed polygons
repair_polygon_soup()

## ◆ merge_duplicated_vertices_in_boundary_cycle()

template<class PolygonMesh , class NamedParameters = parameters::Default_named_parameters>
 void CGAL::Polygon_mesh_processing::merge_duplicated_vertices_in_boundary_cycle ( typename boost::graph_traits< PolygonMesh >::halfedge_descriptor h, PolygonMesh & pm, const NamedParameters & np = parameters::default_values() )

#include <CGAL/Polygon_mesh_processing/merge_border_vertices.h>

merges identical vertices around a cycle of boundary edges.

Template Parameters
 PolygonMesh a model of FaceListGraph and MutableFaceGraph. NamedParameters a sequence of Named Parameters.
Parameters
 h a halfedge that belongs to a boundary cycle. pm the polygon mesh which contains the boundary cycle. 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 ReadWritePropertyMap with boost::graph_traits::vertex_descriptor as key type and Point_3 as value type Default: boost::get(CGAL::vertex_point, pm)
merge_duplicated_vertices_in_boundary_cycles()

## ◆ merge_duplicated_vertices_in_boundary_cycles()

template<class PolygonMesh , class NamedParameters = parameters::Default_named_parameters>
 void CGAL::Polygon_mesh_processing::merge_duplicated_vertices_in_boundary_cycles ( PolygonMesh & pm, const NamedParameters & np = parameters::default_values() )

#include <CGAL/Polygon_mesh_processing/merge_border_vertices.h>

extracts boundary cycles and merges the duplicated vertices of each cycle.

Template Parameters
 PolygonMesh a model of FaceListGraph and MutableFaceGraph. NamedParameters a sequence of Named Parameters.
Parameters
 pm the polygon mesh which contains the cycles. 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 ReadWritePropertyMap with boost::graph_traits::vertex_descriptor as key type and Point_3 as value type Default: boost::get(CGAL::vertex_point, pm)
merge_duplicated_vertices_in_boundary_cycle()

## ◆ non_manifold_vertices()

template<typename PolygonMesh , typename OutputIterator >
 OutputIterator CGAL::Polygon_mesh_processing::non_manifold_vertices ( const PolygonMesh & pm, OutputIterator out )

#include <CGAL/Polygon_mesh_processing/manifoldness.h>

collects the non-manifold vertices (if any) present in the mesh.

A non-manifold vertex v is returned via one incident halfedge h such that target(h, pm) = v for all the umbrellas that v appears in (an umbrella being the set of faces incident to all the halfedges reachable by walking around v using hnext = prev(opposite(h, pm), pm), starting from h).

Template Parameters
 PolygonMesh a model of HalfedgeListGraph OutputIterator a model of OutputIterator holding objects of type boost::graph_traits::halfedge_descriptor
Parameters
 pm a triangle mesh out the output iterator that collects halfedges incident to v
Returns
the output iterator
is_non_manifold_vertex()
duplicate_non_manifold_vertices()

## ◆ polygon_mesh_to_polygon_soup()

template<typename PolygonMesh , typename PointRange , typename PolygonRange , typename NamedParameters = parameters::Default_named_parameters>
 void CGAL::Polygon_mesh_processing::polygon_mesh_to_polygon_soup ( const PolygonMesh & mesh, PointRange & points, PolygonRange & polygons, const NamedParameters & np = parameters::default_values() )

#include <CGAL/Polygon_mesh_processing/polygon_mesh_to_polygon_soup.h>

adds the vertices and faces of a mesh into a (possibly non-empty) polygon soup.

Template Parameters
 PolygonMesh a model of FaceListGraph PointRange a model of the concepts RandomAccessContainer and BackInsertionSequence whose value type can be constructed from the point type of the polygon mesh PolygonRange a model of the concepts RandomAccessContainer and BackInsertionSequence whose value type is itself a model of the concepts RandomAccessContainer and BackInsertionSequence whose value type is std::size_t NamedParameters a sequence of Named Parameters
Parameters
 mesh the mesh whose faces are being put in the polygon soup points points making the polygons of the soup polygons each element in the vector describes a polygon using the indices of the points in points 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 ReadablePropertyMap with boost::graph_traits::vertex_descriptor as key type and Point_3 as value type Default: boost::get(CGAL::vertex_point, mesh)

PolygonRange can also be a model of the concepts RandomAccessContainer and BackInsertionSequence whose value type is an array, but it is the user's responsability to ensure that all faces have the same number of vertices, and that this number is equal to the size of the array.

CGAL::Polygon_mesh_processing::orient_polygon_soup()
CGAL::Polygon_mesh_processing::is_polygon_soup_a_polygon_mesh()
CGAL::Polygon_mesh_processing::polygon_soup_to_polygon_mesh()

## ◆ polygon_soup_to_polygon_mesh()

template<typename PolygonMesh , typename PointRange , typename PolygonRange , typename NamedParameters_PS = parameters::Default_named_parameters, typename NamedParameters_PM = parameters::Default_named_parameters>
 void CGAL::Polygon_mesh_processing::polygon_soup_to_polygon_mesh ( const PointRange & points, const PolygonRange & polygons, PolygonMesh & out, const NamedParameters_PS & np_ps = parameters::default_values(), const NamedParameters_PM & np_pm = parameters::default_values() )

#include <CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h>

builds a polygon mesh from a soup of polygons.

Precondition
the input polygon soup describes a consistently oriented polygon mesh. This can be checked using the function CGAL::Polygon_mesh_processing::is_polygon_soup_a_polygon_mesh(polygons) .
Template Parameters
 PolygonMesh a model of MutableFaceGraph PointRange a model of the concept RandomAccessContainer 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_PS a sequence of Named Parameters NamedParameters_PM a sequence of Named Parameters
Parameters
 points points of the soup of polygons polygons each element in the range describes a polygon using the indices of the points in points out the polygon mesh to be built np_ps 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 value type is a point type convertible to the point type of the vertex point map associated to the polygon mesh Default: CGAL::Identity_property_map
Parameters
 np_pm an optional sequence of Named Parameters among the ones listed below
Optional Named Parameters
 a property map associating points to the vertices of out Type: a class model of ReadWritePropertyMap with boost::graph_traits::vertex_descriptor as key type and Point_3 as value type Default: boost::get(CGAL::vertex_point, out) Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh.
CGAL::Polygon_mesh_processing::orient_polygon_soup()
CGAL::Polygon_mesh_processing::is_polygon_soup_a_polygon_mesh()
CGAL::Polygon_mesh_processing::polygon_mesh_to_polygon_soup()
Examples:
Polygon_mesh_processing/cc_compatible_orientations.cpp, Polygon_mesh_processing/orient_polygon_soup_example.cpp, Polygon_mesh_processing/orientation_pipeline_example.cpp, and Polygon_mesh_processing/repair_polygon_soup_example.cpp.

## ◆ remove_connected_components_of_negligible_size()

template<typename TriangleMesh , typename NamedParameters = parameters::Default_named_parameters>
 std::size_t CGAL::Polygon_mesh_processing::remove_connected_components_of_negligible_size ( TriangleMesh & tmesh, const NamedParameters & np = parameters::default_values() )

#include <CGAL/Polygon_mesh_processing/repair.h>

removes connected components whose area or volume is under a certain threshold value.

Thresholds are provided via Named Parameters. (see below). If thresholds are not provided by the user, default values are computed as follows:

• the area threshold is taken as the square of one percent of the length of the diagonal of the bounding box of the mesh.
• the volume threshold is taken as the third power of one percent of the length of the diagonal of the bounding box of the mesh.

The area and volume of a connected component will always be positive values (regardless of the orientation of the mesh).

As a consequence of the last sentence, the area or volume criteria can be disabled by passing zero (0) as threshold value.

Template Parameters
 TriangleMesh a model of FaceListGraph and MutableFaceGraph NamedParameters a sequence of Named Parameters
Parameters
 tmesh the triangulated polygon 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 tmesh Type: a class model of ReadWritePropertyMap with boost::graph_traits::vertex_descriptor as key type and Point_3 as value type Default: boost::get(CGAL::vertex_point, tmesh) Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in TriangleMesh. 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. Extra: Exact constructions kernels are not supported by this function. a property map associating to each face of tmesh a unique index between 0 and num_faces(tmesh) - 1 Type: a class model of ReadablePropertyMap with boost::graph_traits::face_descriptor as key type and std::size_t as value type Default: an automatically indexed internal map a fixed value such that only connected components whose area is larger than this value are kept Type: geom_traits::FT Default: 1% of the length of the diagonal of the axis-aligned bounding box of the mesh, squared a fixed value such that only connected components whose volume is larger than this value are kept (only applies to closed connected components) Type: geom_traits::FT Default: 1% of the length of the diagonal of the axis-aligned bounding box of the mesh, cubed Extra: The mesh must be closed. a property map containing the constrained-or-not status of each edge of tmesh Type: a class model of ReadablePropertyMap with boost::graph_traits::edge_descriptor as key type and bool as value type. It must be default constructible. Default: a default property map where no edge is constrained Extra: A constrained edge can be split or collapsed, but not flipped, nor its endpoints moved by smoothing. If true, the mesh will not be altered, but the number of components that would be removed is returned. Type: Boolean Default: false An output iterator to collect the faces that would be removed by the algorithm, when using the "dry run" mode (see parameter dry_run) Type: a model of OutputIterator with value type face_descriptor Default: unused
Returns
the number of connected components removed (ignoring isolated vertices).
keep_connected_components()
remove_connected_components()

## ◆ remove_isolated_points_in_polygon_soup()

template<typename PointRange , typename PolygonRange >
 std::size_t CGAL::Polygon_mesh_processing::remove_isolated_points_in_polygon_soup ( PointRange & points, PolygonRange & polygons )

#include <CGAL/Polygon_mesh_processing/repair_polygon_soup.h>

removes the isolated points from a polygon soup.

A point is considered isolated if it does not appear in any polygon of the soup.

Template Parameters
 PointRange a model of the concept SequenceContainer whose value type is the point type. PolygonRange a model of the concept RandomAccessContainer whose value_type is itself a model of the concept RandomAccessContainer whose value_type is std::size_t.
Parameters
 points points of the soup of polygons polygons a vector of polygons. Each element in the vector describes a polygon using the indices of the points in points.
Returns
the number of removed isolated points
repair_polygon_soup()

## ◆ remove_isolated_vertices()

template<class PolygonMesh >
 std::size_t CGAL::Polygon_mesh_processing::remove_isolated_vertices ( PolygonMesh & pmesh )

#include <CGAL/Polygon_mesh_processing/repair.h>

removes the isolated vertices from any polygon mesh.

A vertex is considered isolated if it is not incident to a simplex of higher dimension.

Template Parameters
 PolygonMesh a model of FaceListGraph and MutableFaceGraph
Parameters
 pmesh the polygon mesh to be repaired
Returns
the number of removed isolated vertices

## ◆ repair_polygon_soup()

template<typename PointRange , typename PolygonRange , typename NamedParameters = parameters::Default_named_parameters>
 void CGAL::Polygon_mesh_processing::repair_polygon_soup ( PointRange & points, PolygonRange & polygons, const NamedParameters & np = parameters::default_values() )

#include <CGAL/Polygon_mesh_processing/repair_polygon_soup.h>

cleans a given polygon soup through various repairing operations.

More precisely, this function carries out the following tasks, in the same order as they are listed:

• merging of duplicate points, using the function CGAL::Polygon_mesh_processing::merge_duplicate_points_in_polygon_soup();
• simplification of polygons to remove geometrically identical consecutive vertices;
• splitting of "pinched" polygons, that is polygons in which a geometric position appears more than once. The splitting process results in multiple non-pinched polygons;
• removal of invalid polygons, that is polygons with fewer than 2 vertices;
• removal of duplicate polygons, using the function CGAL::Polygon_mesh_processing::merge_duplicate_polygons_in_polygon_soup();
• removal of isolated points, using the function CGAL::Polygon_mesh_processing::remove_isolated_points_in_polygon_soup().

Note that the point and polygon containers will be modified by the repairing operations, and thus the indexing of the polygons will also be changed.

Template Parameters
 PointRange a model of the concepts SequenceContainer and Swappable and whose value type is the point type. PolygonRange a model of the concept SequenceContainer. whose value_type is itself a model of the concepts SequenceContainer, Swappable, and ReversibleContainer whose value_type is std::size_t. NamedParameters a sequence of Named Parameters
Parameters
 points points of the soup of polygons polygons a vector of polygons. Each element in the vector describes a polygon using the indices of the points in points. np an optional sequence of Named Parameters among the ones listed below
Optional Named Parameters
 an instance of a geometric traits class Type: The traits class must provide the nested functors Less_xyz_3 and Equal_3 to respectivelycompare lexicographically two points and to check if two points are identical. For each functor Foo, a function Foo foo_object() must be provided. 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. Parameter to indicate, when multiple polygons are duplicates, whether all the duplicate polygons should be removed or if one (arbitrarily chosen) face should be kept. Type: Boolean Default: false Parameter to indicate if polygon orientation should be taken into account when determining whether two polygons are duplicates, that is, whether e.g. the triangles 0,1,2 and 0,2,1 are duplicates. Type: Boolean Default: false
Examples:
Polygon_mesh_processing/repair_polygon_soup_example.cpp.

## ◆ stitch_borders() [1/3]

template<typename PolygonMesh , typename HalfedgePairsRange , typename NamedParameters = CGAL::parameters::Default_named_parameters>
 std::size_t CGAL::Polygon_mesh_processing::stitch_borders ( PolygonMesh & pmesh, const HalfedgePairsRange & hedge_pairs_to_stitch, const NamedParameters & np = parameters::default_values(), typename boost::enable_if< typename boost::has_range_iterator< HalfedgePairsRange > >::type * = 0 )

#include <CGAL/Polygon_mesh_processing/stitch_borders.h>

stitches together border halfedges in a polygon mesh.

The halfedges to be stitched are provided in hedge_pairs_to_stitch. For each pair p in this vector, p.second and its opposite will be removed from pmesh.

Template Parameters
 PolygonMesh a model of MutableFaceGraph HalfedgePairsRange a range of std::pair::halfedge_descriptor, boost::graph_traits::halfedge_descriptor>, model of Range. Its iterator type is InputIterator.
Parameters
 pmesh the polygon mesh to be modified by stitching hedge_pairs_to_stitch a range of std::pair of halfedges to be stitched together 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 ReadWritePropertyMap with boost::graph_traits::vertex_descriptor as key type and Point_3 as value type Default: boost::get(CGAL::vertex_point, pmesh) Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh.
Returns
the number of pairs of halfedges that were stitched.
stitch_boundary_cycle()
stitch_boundary_cycles()
Examples:
Polygon_mesh_processing/cc_compatible_orientations.cpp, and Polygon_mesh_processing/stitch_borders_example.cpp.

## ◆ stitch_borders() [2/3]

template<typename PolygonMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
 std::size_t CGAL::Polygon_mesh_processing::stitch_borders ( PolygonMesh & pmesh, const NamedParameters & np = parameters::default_values() )

#include <CGAL/Polygon_mesh_processing/stitch_borders.h>

Same as the other overload, but the pairs of halfedges to be stitched are automatically found amongst all border halfedges.

Two border halfedges h1 and h2 are set to be stitched if the points associated to the source and target vertices of h1 are the same as those of the target and source vertices of h2, respectively.

Template Parameters
 BorderHalfedgeRange a model of Range with value type boost::graph_traits::halfedge_descriptor PolygonMesh a model of FaceListGraph and MutableFaceGraph NamedParameters a sequence of Named Parameters
Parameters
 pmesh the polygon mesh to be modified by the stitching procedure np optional sequence of Named Parameters among the ones listed below
Optional Named Parameters
 a property map associating points to the vertices of pmesh Type: a class model of ReadWritePropertyMap with boost::graph_traits::vertex_descriptor as key type and Point_3 as value type Default: boost::get(CGAL::vertex_point, pmesh) Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh. specifies if the borders should only be stitched only within their own connected component. Type: Boolean Default: false a property map associating to each face of pmesh a unique index between 0 and num_faces(pmesh) - 1 Type: a class model of ReadablePropertyMap with boost::graph_traits::face_descriptor as key type and std::size_t as value type Default: an automatically indexed internal map
Returns
the number of pairs of halfedges that were stitched.
stitch_boundary_cycle()
stitch_boundary_cycles()

## ◆ stitch_borders() [3/3]

template<typename BorderHalfedgeRange , typename PolygonMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
 std::size_t CGAL::Polygon_mesh_processing::stitch_borders ( const BorderHalfedgeRange & boundary_cycle_representatives, PolygonMesh & pmesh, const NamedParameters & np = parameters::default_values() )

#include <CGAL/Polygon_mesh_processing/stitch_borders.h>

Same as the other overload, but the pairs of halfedges to be stitched are automatically found amongst halfedges in cycles described by boundary_cycle_representatives.

Two border halfedges h1 and h2 are set to be stitched if the points associated to the source and target vertices of h1 are the same as those of the target and source vertices of h2, respectively.

Template Parameters
 BorderHalfedgeRange a model of Range with value type boost::graph_traits::halfedge_descriptor PolygonMesh a model of FaceListGraph and MutableFaceGraph NamedParameters a sequence of Named Parameters
Parameters
 boundary_cycle_representatives a range of border halfedges, each describing a boundary cycle whose halfedges will be considered for stitching pmesh the polygon mesh to be modified by the stitching procedure np optional sequence of Named Parameters among the ones listed below
Optional Named Parameters
 specifies if the borders should only be stitched only within their own connected component. Type: Boolean Default: false a property map associating to each face of pmesh a unique index between 0 and num_faces(pmesh) - 1 Type: a class model of ReadablePropertyMap with boost::graph_traits::face_descriptor as key type and std::size_t as value type Default: an automatically indexed internal map a property map associating points to the vertices of pmesh Type: a class model of ReadWritePropertyMap with boost::graph_traits::vertex_descriptor as key type and Point_3 as value type Default: boost::get(CGAL::vertex_point, pmesh) Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh. an instance of a geometric traits class Type: The traits class must provide the nested type Point_3, and the nested functors: Less_xyz_3 to compare lexicographically two points Equal_3 to check whether two points are identical. For each functor Foo, a function Foo foo_object() must be provided. 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.
Returns
the number of pairs of halfedges that were stitched.
stitch_boundary_cycle()
stitch_boundary_cycles()

## ◆ stitch_boundary_cycle()

template<typename PolygonMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
 std::size_t CGAL::Polygon_mesh_processing::stitch_boundary_cycle ( const typename boost::graph_traits< PolygonMesh >::halfedge_descriptor h, PolygonMesh & pmesh, const NamedParameters & np = parameters::default_values() )

#include <CGAL/Polygon_mesh_processing/stitch_borders.h>

stitches together, whenever possible, two halfedges belonging to the boundary cycle described by the halfedge h.

Two border halfedges h1 and h2 can be stitched if the points associated to the source and target vertices of h1 are the same as those of the target and source vertices of h2, respectively.

Template Parameters
 PolygonMesh a model of MutableFaceGraph NamedParameters a sequence of Named Parameters
Parameters
 h a border halfedge of the polygon mesh pmesh pmesh the polygon mesh to be stitched 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 ReadWritePropertyMap with boost::graph_traits::vertex_descriptor as key type and Point_3 as value type Default: boost::get(CGAL::vertex_point, pmesh) Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh. an instance of a geometric traits class Type: The traits class must provide the nested type Point_3, and the nested functors: Less_xyz_3 to compare lexicographically two points Equal_3 to check whether two points are identical. For each functor Foo, a function Foo foo_object() must be provided. 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.
Returns
the number of pairs of halfedges that were stitched.
stitch_boundary_cycles()
stitch_borders()

## ◆ stitch_boundary_cycles()

template<typename BorderHalfedgeRange , typename PolygonMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
 std::size_t CGAL::Polygon_mesh_processing::stitch_boundary_cycles ( const BorderHalfedgeRange & boundary_cycle_representatives, PolygonMesh & pmesh, const NamedParameters & np = parameters::default_values() )

#include <CGAL/Polygon_mesh_processing/stitch_borders.h>

stitches together, whenever possible, two halfedges belonging to the same boundary cycle.

Two border halfedges h1 and h2 can be stitched if the points associated to the source and target vertices of h1 are the same as those of the target and source vertices of h2, respectively.

Template Parameters
 BorderHalfedgeRange a model of Range with value type boost::graph_traits::halfedge_descriptor PolygonMesh a model of MutableFaceGraph NamedParameters a sequence of Named Parameters
Parameters
 boundary_cycle_representatives a range of border halfedges, each describing a boundary cycle of the mesh pmesh pmesh the polygon mesh to be modified by stitching 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 ReadWritePropertyMap with boost::graph_traits::vertex_descriptor as key type and Point_3 as value type Default: boost::get(CGAL::vertex_point, pmesh) Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh. an instance of a geometric traits class Type: The traits class must provide the nested type Point_3, and the nested functors: Less_xyz_3 to compare lexicographically two points Equal_3 to check whether two points are identical. For each functor Foo, a function Foo foo_object() must be provided. 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.
Returns
the number of pairs of halfedges that were stitched.
stitch_boundary_cycle()
stitch_borders()