CGAL 5.6 - Polygon Mesh Processing
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Polygon Mesh Processing Reference

Sébastien Loriot, Mael Rouxel-Labbé, Jane Tournois, and 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 such as Boolean operations, remeshing, repairing, collision and intersection detection, and more.
Introduced in: CGAL 4.7
Depends on: documented for each function; CGAL and Solvers
BibTeX: cgal:lty-pmp-23a
License: GPL
Windows Demo: Polyhedron demo
Common Demo Dlls: dlls

Classified Reference Pages

Parameters

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

Corefinement and Boolean Operation Functions

Meshing Functions

Orientation Functions

Hole Filling Functions

Intersection Functions

Collision Detection

Predicate Functions

Combinatorial Repair Functions

Geometric Repair Functions

Connected Components

Location Functions

Normal Computation Functions

Distance Functions

Geometric Measure Functions

Feature Detection Functions

Miscellaneous

I/O Functions

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 Repair
 Functions to repair polygon soups and polygon meshes.
 
 Geometric Repair
 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.
 
 Predicates
 Classes and functions that answer queries about a polygon mesh or its elements.
 
 I/O Functions
 
 Deprecated 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::Rigid_triangle_mesh_collision_detection< TriangleMesh, VertexPointMap, Kernel, AABBTree, Has_rotation >
 This class provides methods to perform some intersection tests between triangle meshes that undergo affine transformations (rotation, translation, and scaling). More...
 

Functions

template<typename PolygonMesh , typename NamedParameters = parameters::Default_named_parameters>
CGAL::Bbox_3 CGAL::Polygon_mesh_processing::bbox (const PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
 computes a bounding box of a polygon mesh.
 
template<typename PolygonMesh , typename NamedParameters = parameters::Default_named_parameters>
CGAL::Bbox_3 CGAL::Polygon_mesh_processing::vertex_bbox (typename boost::graph_traits< PolygonMesh >::vertex_descriptor vd, const PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
 computes a bounding box of the vertex of a polygon mesh.
 
template<typename PolygonMesh , typename NamedParameters = parameters::Default_named_parameters>
CGAL::Bbox_3 CGAL::Polygon_mesh_processing::edge_bbox (typename boost::graph_traits< PolygonMesh >::edge_descriptor ed, const PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
 computes a bounding box of an edge of a polygon mesh.
 
template<typename PolygonMesh , typename NamedParameters = parameters::Default_named_parameters>
CGAL::Bbox_3 CGAL::Polygon_mesh_processing::face_bbox (typename boost::graph_traits< PolygonMesh >::face_descriptor fd, const PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
 computes a bounding box of a face of a polygon mesh.
 
template<typename PolygonMesh , typename FaceRange , typename HalfedgeOutputIterator , typename NamedParameters = parameters::Default_named_parameters>
HalfedgeOutputIterator CGAL::Polygon_mesh_processing::border_halfedges (const FaceRange &face_range, const PolygonMesh &pmesh, HalfedgeOutputIterator out, const NamedParameters &np=parameters::default_values())
 collects the border halfedges of a surface patch defined as a face range.
 
template<typename PolygonMesh , typename OutputIterator >
OutputIterator CGAL::Polygon_mesh_processing::extract_boundary_cycles (const PolygonMesh &pm, OutputIterator out)
 extracts boundary cycles as a list of halfedges, with one halfedge per border.
 
template<class Transformation , class PolygonMesh , class NamedParameters = parameters::Default_named_parameters>
void CGAL::Polygon_mesh_processing::transform (const Transformation &transformation, PolygonMesh &mesh, const NamedParameters &np=parameters::default_values())
 applies a transformation to every vertex of a PolygonMesh.
 
template<typename TriangleMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
Triangle_3 CGAL::Polygon_mesh_processing::triangle (typename boost::graph_traits< TriangleMesh >::face_descriptor fd, const TriangleMesh &tmesh, const NamedParameters &np=parameters::default_values())
 computes a triangle for a face descriptor of a triangle mesh.
 
template<typename PolygonMesh , typename RegionMap , typename NamedParameters = parameters::Default_named_parameters>
std::size_t CGAL::Polygon_mesh_processing::region_growing_of_planes_on_faces (const PolygonMesh &mesh, RegionMap region_map, const NamedParameters &np=parameters::default_values())
 applies a region growing algorithm to fit planes on faces of a mesh.
 
template<typename PolygonMesh , typename RegionMap , typename CornerIdMap , typename NamedParameters = parameters::Default_named_parameters>
std::size_t CGAL::Polygon_mesh_processing::detect_corners_of_regions (const PolygonMesh &mesh, RegionMap region_map, std::size_t nb_regions, CornerIdMap corner_id_map, const NamedParameters &np=parameters::default_values())
 detects the corners on the boundary of almost planar regions by applying the region growing algorithm fitting lines on segment edges of a partition of a mesh.
 

Function Documentation

◆ bbox()

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

#include <CGAL/Polygon_mesh_processing/bbox.h>

computes a bounding box of a polygon mesh.

Template Parameters
PolygonMesha model of VertexListGraph
NamedParametersa sequence of Named Parameters
Parameters
pmesha polygon mesh
npan 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<PolygonMesh>::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 the functor Bbox_3 operator()(Point_3) where Point_3 is the value type of the vertex point map.
See also
vertex_bbox()
edge_bbox()
face_bbox()

◆ border_halfedges()

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

#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
PolygonMeshmodel of HalfedgeGraph
FaceRangea model of Range with value type boost::graph_traits<PolygonMesh>::face_descriptor.
HalfedgeOutputIteratormodel of OutputIterator holding boost::graph_traits<PolygonMesh>::halfedge_descriptor for patch border
NamedParametersa sequence of Named Parameters
Parameters
pmeshthe polygon mesh to which the faces in face_range belong
face_rangethe range of faces defining the patch whose border halfedges are collected
outthe output iterator that collects the border halfedges of the patch, seen from outside.
npan 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<PolygonMesh>::face_descriptor as key type and std::size_t as value type
  • Default: an automatically indexed internal map
Returns
out
See also
extract_boundary_cycles()

◆ detect_corners_of_regions()

template<typename PolygonMesh , typename RegionMap , typename CornerIdMap , typename NamedParameters = parameters::Default_named_parameters>
std::size_t CGAL::Polygon_mesh_processing::detect_corners_of_regions ( const PolygonMesh &  mesh,
RegionMap  region_map,
std::size_t  nb_regions,
CornerIdMap  corner_id_map,
const NamedParameters &  np = parameters::default_values() 
)

#include <CGAL/Polygon_mesh_processing/region_growing.h>

detects the corners on the boundary of almost planar regions by applying the region growing algorithm fitting lines on segment edges of a partition of a mesh.

More precisely, a corner on the boundary of a region is a vertex that is either shared by at least three regions (two if it is also a vertex on the boundary of the mesh), or that is incident to two segments edges assigned to different lines. See Section Region Growing for more details on the method.

Template Parameters
PolygonMesha model of FaceListGraph and EdgeListGraph
RegionMapa model of ReadablePropertyMap with boost::graph_traits<PolygonMesh>::face_descriptor as key type and std::size_t as value type.
CornerIdMapa model of WritablePropertyMap with boost::graph_traits<PolygonMesh>::vertex_descriptor as key type and std::size_t as value type.
NamedParametersa sequence of Named Parameters
Parameters
meshpolygon mesh for region growing.
region_mapproperty map providing the region index of each face, values must be in [0, nb_regions-1].
corner_id_mapproperty map storing the corner index of each vertex. Values start at 0 up to the value returned minus 1. std::size_t(-1) is put for vertices that are not corners.
nb_regionsthe number of patches in the partition of mesh defined by region_map
npan optional sequence of Named Parameters among the ones listed below
Returns
the number of corners detected
Optional Named Parameters
  • a property map filled by this function such that an edge is marked as constrained if it is at the interface of two different regions or on the boundary of the mesh
  • Type: a class model of ReadWritePropertyMap with boost::graph_traits<PolygonMesh>::edge_descriptor as key type and bool as value type
  • Default: Unused if not provided
  • Extra: The value for each edge must be initialized to false.
  • the maximum distance from a segment to a line such that it is considered part of the region of the line
  • Type: GeomTraits::FT with GeomTraits being the type of the parameter geom_traits
  • Default: 1
  • the maximum angle in degrees between two adjacent segments such that they are considered part of the same region
  • Type: GeomTraits::FT with GeomTraits being the type of the parameter geom_traits
  • Default: 25 degrees
  • Extra: this parameter and cosine_of_maximum_angle are exclusive
  • The maximum angle, given as a cosine, for the smallest angle between the supporting line of a segment and an adjacent segment such that they are considered part of the same region
  • Type: GeomTraits::FT with GeomTraits being the type of the parameter geom_traits
  • Default: cos(25 * PI / 180)
  • Extra: this parameter and maximum_angle are exclusive
  • a property map associating points to the vertices of mesh
  • 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, mesh)
  • 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: 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.

◆ edge_bbox()

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

#include <CGAL/Polygon_mesh_processing/bbox.h>

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

Template Parameters
PolygonMesha model of Graph
NamedParametersa sequence of Named Parameters
Parameters
eda descriptor of an edge in pmesh
pmesha polygon mesh
npan 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<PolygonMesh>::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.
See also
vertex_bbox()
face_bbox()
bbox()

◆ extract_boundary_cycles()

template<typename PolygonMesh , typename OutputIterator >
OutputIterator CGAL::Polygon_mesh_processing::extract_boundary_cycles ( const 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
PolygonMesha model of HalfedgeListGraph
OutputIteratora model of OutputIterator holding objects of type boost::graph_traits<PolygonMesh>::halfedge_descriptor
Parameters
pma polygon mesh
outan output iterator where the border halfedges will be put
See also
border_halfedges()

◆ face_bbox()

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

#include <CGAL/Polygon_mesh_processing/bbox.h>

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

Template Parameters
PolygonMesha model of Graph
NamedParametersa sequence of Named Parameters
Parameters
fda descriptor of a face in pmesh
pmesha polygon mesh
npan 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<PolygonMesh>::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
See also
vertex_bbox()
edge_bbox()
bbox()

◆ region_growing_of_planes_on_faces()

template<typename PolygonMesh , typename RegionMap , typename NamedParameters = parameters::Default_named_parameters>
std::size_t CGAL::Polygon_mesh_processing::region_growing_of_planes_on_faces ( const PolygonMesh &  mesh,
RegionMap  region_map,
const NamedParameters &  np = parameters::default_values() 
)

#include <CGAL/Polygon_mesh_processing/region_growing.h>

applies a region growing algorithm to fit planes on faces of a mesh.

See Section Region Growing for more details on the method.

Template Parameters
PolygonMesha model of FaceListGraph
RegionMapa model of WritablePropertyMap with boost::graph_traits<PolygonMesh>::face_descriptor as key type and std::size_t as value type.
NamedParametersa sequence of Named Parameters
Parameters
meshthe polygon mesh whose faces are used for region growing
region_mapa property map storing the region index of each face. Values start at 0 up to the value returned minus 1. std::size_t(-1) is put for faces with no region assigned (can only happen if minimum_region_size > 1).
npan optional sequence of Named Parameters among the ones listed below
Returns
the number of regions detected
Optional Named Parameters
  • the maximum distance from a face to a plane such that it is considered part of the region of the plane
  • Type: GeomTraits::FT with GeomTraits being the type of the parameter geom_traits
  • Default: 1
  • the maximum angle (in degrees) between the normals of the supporting planes of two adjacent faces such that they are considered part of the same region
  • Type: GeomTraits::FT with GeomTraits being the type of the parameter geom_traits
  • Default: 25 degrees
  • Extra: this parameter and cosine_of_maximum_angle are exclusive
  • Apply a post-processing step to the output of the region growing algorithm.
  • Type: bool
  • Default: false
  • The maximum angle, given as a cosine, between the normals of the supporting planes of adjacent faces such that they are considered part of the same region
  • Type: GeomTraits::FT with GeomTraits being the type of the parameter geom_traits
  • Default: cos(25 * PI / 180)
  • Extra: this parameter and maximum_angle are exclusive
  • the minimum number of faces such that a new region can be created from a set of faces
  • Type: std::size_t
  • Default: 1
  • a property map associating points to the vertices of mesh
  • 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, mesh)
  • 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: 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 filled by this function and that will contain for each region the plane (or only its orthognonal vector) estimated that approximates it.
  • Type: a class model of WritablePropertyMap with the value type of RegionMap as key and GeomTraits::Plane_3 or GeomTraits::Vector_3 as value type, GeomTraits being the type of the parameter geom_traits
  • Default: None

◆ transform()

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

#include <CGAL/Polygon_mesh_processing/transform.h>

applies a transformation to every vertex of a PolygonMesh.

Template Parameters
Transformationa 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.
PolygonMesha model of VertexListGraph
NamedParametersa sequence of Named Parameters
Parameters
transformationthe transformation functor to apply to the points of mesh.
meshthe PolygonMesh to transform.
npan optional sequence of Named Parameters among the ones listed below
Optional Named Parameters
  • a property map associating points to the vertices of mesh
  • Type: a class model of ReadWritePropertyMap with boost::graph_traits<PolygonMesh>::vertex_descriptor as key type and 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.

◆ triangle()

template<typename TriangleMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
Triangle_3 CGAL::Polygon_mesh_processing::triangle ( typename boost::graph_traits< TriangleMesh >::face_descriptor  fd,
const TriangleMesh &  tmesh,
const NamedParameters &  np = parameters::default_values() 
)

#include <CGAL/Polygon_mesh_processing/triangle.h>

computes a triangle for a face descriptor of a triangle mesh.

Template Parameters
TriangleMesha model of FaceGraph
NamedParametersa sequence of Named Parameters
Parameters
tmeshthe triangulated surface mesh
fdthe descriptor of the face to construct the triangle from
npan 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 ReadablePropertyMap with boost::graph_traits<TriangleMesh>::vertex_descriptor as key type and Point_3 as value type
  • Default: boost::get(CGAL::vertex_point, tmesh)

  • 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.

◆ vertex_bbox()

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

#include <CGAL/Polygon_mesh_processing/bbox.h>

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

Template Parameters
PolygonMesha model of Graph
NamedParametersa sequence of Named Parameters
Parameters
vda descriptor of a vertex in pmesh
pmesha polygon mesh
npan 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<PolygonMesh>::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.
See also
edge_bbox()
face_bbox()
bbox()