CGAL 5.4 - Polygon Mesh Processing
Polygon Mesh Processing Reference
Sébastien Loriot, Mael Rouxel-Labbé, Jane Tournois, Ilker O. Yaz
This package provides a collection of methods and classes for polygon mesh processing, ranging from basic operations on simplices, to complex geometry processing algorithms.
Introduced in: CGAL 4.7
Depends on: documented for each function; CGAL and Solvers
BibTeX: cgal:lty-pmp-21b
Windows Demo: Polyhedron demo
Common Demo Dlls: dlls

## Parameters

Optional parameters of the functions of this package are implemented as Named Parameters. The page Named Parameters describes their usage.

## Modules

Concepts

Connected Components
Two faces are in the same connected component if there is a path of adjacent faces such that all edges between two consecutive faces of the path are not marked as constrained.

Hole Filling
Functions to fill holes given as a range of halfedges or as range of points.

Meshing
Functions to triangulate faces, and to refine and fair regions of a polygon mesh.

Normal Computation
Functions to compute unit normals for individual/all vertices or faces.

Geometric Measure Functions
Functions to compute lengths of edges and borders, areas of faces and patches, as well as volumes of closed meshes.

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

Intersection Functions
Functions to test if there are self intersections, and to report faces that do intersect.

Combinatorial Repairing
Functions to repair polygon soups and polygon meshes.

Distance Functions
Functions to compute the distance between meshes, between a mesh and a point set and between a point set and a mesh.

Corefinement and Boolean Operations
Functions to corefine triangulated surface meshes and compute triangulated surface meshes of the union, difference and intersection of the bounded volumes.

Feature Detection Functions
Functions to detect sharp edges and surface patches of polygon meshes.

Location Functions
Functions to locate points on a mesh, and manipulate such locations.

Intersection Detection Functions
Functions to detect intersections.

I/O Functions

## Files

file  polygon_mesh_processing.h
Convenience header file including the headers for all the free functions of this package.

## Classes

class  CGAL::Polygon_mesh_slicer< TriangleMesh, Traits, VertexPointMap, AABBTree, UseParallelPlaneOptimization >
Function object that computes the intersection of a plane with a triangulated surface mesh. More...

struct  CGAL::Polyhedral_envelope< GeomTraits >
This class can be used to check if a query point, segment, or triangle is inside or outside a polyhedral envelope of a set of triangles, constructed for a given $$\epsilon$$ distance tolerance. More...

class  CGAL::Side_of_triangle_mesh< TriangleMesh, GeomTraits, VertexPointMap_ >
This class provides an efficient point location functionality with respect to a domain bounded by one or several disjoint closed triangle meshes. More...

## Functions

template<typename PolygonMesh , typename NamedParameters >
CGAL::Bbox_3 CGAL::Polygon_mesh_processing::bbox (const PolygonMesh &pmesh, const NamedParameters &np)
computes a bounding box of a polygon mesh. More...

template<typename PolygonMesh , typename NamedParameters >
CGAL::Bbox_3 CGAL::Polygon_mesh_processing::vertex_bbox (typename boost::graph_traits< PolygonMesh >::vertex_descriptor vd, const PolygonMesh &pmesh, const NamedParameters &np)
computes a bounding box of a vertex of a polygon mesh. More...

template<typename PolygonMesh , typename NamedParameters >
CGAL::Bbox_3 CGAL::Polygon_mesh_processing::edge_bbox (typename boost::graph_traits< PolygonMesh >::edge_descriptor ed, const PolygonMesh &pmesh, const NamedParameters &np)
computes a bounding box of an edge of a polygon mesh. More...

template<typename PolygonMesh , typename NamedParameters >
CGAL::Bbox_3 CGAL::Polygon_mesh_processing::face_bbox (typename boost::graph_traits< PolygonMesh >::face_descriptor fd, const PolygonMesh &pmesh, const NamedParameters &np)
computes a bounding box of a face of a polygon mesh. More...

template<typename PolygonMesh , typename NamedParameters >
CGAL::Bbox_3 CGAL::Polygon_mesh_processing::bbox_3 (const PolygonMesh &pmesh, const NamedParameters &np)

template<typename PolygonMesh , typename FaceRange , typename HalfedgeOutputIterator , typename NamedParameters >
HalfedgeOutputIterator CGAL::Polygon_mesh_processing::border_halfedges (const FaceRange &face_range, const PolygonMesh &pmesh, HalfedgeOutputIterator out, const NamedParameters &np)
collects the border halfedges of a surface patch defined as a face range. More...

template<typename PolygonMesh , typename OutputIterator >
OutputIterator CGAL::Polygon_mesh_processing::extract_boundary_cycles (PolygonMesh &pm, OutputIterator out)
extracts boundary cycles as a list of halfedges, with one halfedge per border. More...

template<class Transformation , class PolygonMesh , class NamedParameters >
void CGAL::Polygon_mesh_processing::transform (const Transformation &transformation, PolygonMesh &mesh, const NamedParameters &np)
applies a transformation to every vertex of a PolygonMesh. More...

## ◆ bbox()

template<typename PolygonMesh , typename NamedParameters >
 CGAL::Bbox_3 CGAL::Polygon_mesh_processing::bbox ( const PolygonMesh & pmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/bbox.h>

computes a bounding box of a polygon mesh.

Template Parameters
 PolygonMesh a model of HalfedgeListGraph NamedParameters a sequence of Named Parameters
Parameters
 pmesh a 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 pmesh 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, 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 providing the functor Construct_bbox_3 and the function Construct_bbox_3 construct_bbox_3_object(). Construct_bbox_3 must provide Bbox_3 operator()(Point_3) where Point_3 is the value type of the vertex point map.
Returns
a bounding box of pmesh

## ◆ bbox_3()

template<typename PolygonMesh , typename NamedParameters >
 CGAL::Bbox_3 CGAL::Polygon_mesh_processing::bbox_3 ( const PolygonMesh & pmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/bbox.h>

Deprecated:
This function is deprecated since CGAL 4.10, CGAL::Polygon_mesh_processing::bbox() should be used instead.

## ◆ border_halfedges()

template<typename PolygonMesh , typename FaceRange , typename HalfedgeOutputIterator , typename NamedParameters >
 HalfedgeOutputIterator CGAL::Polygon_mesh_processing::border_halfedges ( const FaceRange & face_range, const PolygonMesh & pmesh, HalfedgeOutputIterator out, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/border.h>

collects the border halfedges of a surface patch defined as a face range.

For each returned halfedge h, opposite(h, pmesh) belongs to a face of the patch, but face(h, pmesh) does not belong to the patch.

Template Parameters
 PolygonMesh model of HalfedgeGraph FaceRange a model of Range with value type boost::graph_traits::face_descriptor. HalfedgeOutputIterator model of OutputIterator holding boost::graph_traits::halfedge_descriptor for patch border NamedParameters a sequence of Named Parameters
Parameters
 pmesh the polygon mesh to which the faces in face_range belong face_range the range of faces defining the patch whose border halfedges are collected out the output iterator that collects the border halfedges of the patch, seen from outside. np an optional sequence of Named Parameters among the ones listed below
Optional Named Parameters
 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
out
Examples:
Polygon_mesh_processing/isotropic_remeshing_example.cpp.

## ◆ edge_bbox()

template<typename PolygonMesh , typename NamedParameters >
 CGAL::Bbox_3 CGAL::Polygon_mesh_processing::edge_bbox ( typename boost::graph_traits< PolygonMesh >::edge_descriptor ed, const PolygonMesh & pmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/bbox.h>

computes a bounding box of an edge of a polygon mesh.

Template Parameters
 PolygonMesh a model of HalfedgeGraph NamedParameters a sequence of Named Parameters
Parameters
 ed a descriptor of an edge in pmesh pmesh a 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 pmesh 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, 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 providing the functor Construct_bbox_3 and the function Construct_bbox_3 construct_bbox_3_object(). Construct_bbox_3 must provide Bbox_3 operator()(Point_3) where Point_3 is the value type of the vertex point map.
Returns
a bounding box of pmesh

## ◆ extract_boundary_cycles()

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

#include <CGAL/Polygon_mesh_processing/border.h>

extracts boundary cycles as a list of halfedges, with one halfedge per border.

Template Parameters
 PolygonMesh a model of HalfedgeListGraph OutputIterator a model of OutputIterator holding objects of type boost::graph_traits::halfedge_descriptor
Parameters
 pm a polygon mesh out an output iterator where the border halfedges will be put
Examples:
Polygon_mesh_processing/hole_filling_example_SM.cpp.

## ◆ face_bbox()

template<typename PolygonMesh , typename NamedParameters >
 CGAL::Bbox_3 CGAL::Polygon_mesh_processing::face_bbox ( typename boost::graph_traits< PolygonMesh >::face_descriptor fd, const PolygonMesh & pmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/bbox.h>

computes a bounding box of a face of a polygon mesh.

Template Parameters
 PolygonMesh a model of HalfedgeGraph NamedParameters a sequence of Named Parameters
Parameters
 fd a descriptor of a face in pmesh pmesh a 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 pmesh 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, 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 providing the functor Construct_bbox_3 and the function Construct_bbox_3 construct_bbox_3_object(). Construct_bbox_3 must provide Bbox_3 operator()(Point_3) where Point_3 is the value type of the vertex point map. Default: a CGAL Kernel deduced from the point type, using CGAL::Kernel_traits
Returns
a bounding box of pmesh

## ◆ transform()

template<class Transformation , class PolygonMesh , class NamedParameters >
 void CGAL::Polygon_mesh_processing::transform ( const Transformation & transformation, PolygonMesh & mesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/transform.h>

applies a transformation to every vertex of a PolygonMesh.

Template Parameters
 Transformation a functor that has an operator()(Point_3), with Point_3 the value_type of vertex_point_map (see below). Such a functor can be CGAL::Aff_transformation_3 for example. PolygonMesh a model of VertexListGraph NamedParameters a sequence of Named Parameters
Parameters
 transformation the transformation functor to apply to the points of mesh. mesh the PolygonMesh to transform. 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::vertex_descriptor as key type and 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.
Examples:
Polygon_mesh_processing/hausdorff_bounded_error_distance_example.cpp.

## ◆ vertex_bbox()

template<typename PolygonMesh , typename NamedParameters >
 CGAL::Bbox_3 CGAL::Polygon_mesh_processing::vertex_bbox ( typename boost::graph_traits< PolygonMesh >::vertex_descriptor vd, const PolygonMesh & pmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/bbox.h>

computes a bounding box of a vertex of a polygon mesh.

Template Parameters
 PolygonMesh a model of HalfedgeGraph NamedParameters a sequence of Named Parameters
Parameters
 vd a descriptor of a vertex in pmesh pmesh a 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 pmesh 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, 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 providing the functor Construct_bbox_3 and the function Construct_bbox_3 construct_bbox_3_object(). Construct_bbox_3 must provide Bbox_3 operator()(Point_3) where Point_3 is the value type of the vertex point map.
Returns
a bounding box of pmesh