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

Classes
class	CGAL::Polygon_mesh_processing::Adaptive_sizing_field< PolygonMesh, VPMap >
	a sizing field describing variable target mesh edge lengths for `CGAL::Polygon_mesh_processing::isotropic_remeshing()`. More...

class	CGAL::Polygon_mesh_processing::Uniform_sizing_field< PolygonMesh, VPMap >
	a sizing field describing a uniform target edge length for `CGAL::Polygon_mesh_processing::isotropic_remeshing()`. More...

struct	CGAL::Polygon_mesh_processing::Triangulate_faces::Default_visitor< PolygonMesh >
	Default new face visitor model of `PMPTriangulateFaceVisitor`. More...

struct	CGAL::Polygon_mesh_processing::Triangulate_polygons::Default_visitor
	Default new polygon visitor model of `PMPTriangulateFaceVisitor`. More...

Functions
template<typename TriangleMesh , typename FaceRange , typename NamedParameters = parameters::Default_named_parameters>
void	CGAL::Polygon_mesh_processing::angle_and_area_smoothing (const FaceRange &faces, TriangleMesh &tmesh, const NamedParameters &np=parameters::default_values())
	smooths a triangulated region of a polygon mesh.

template<typename TriangleMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
void	CGAL::Polygon_mesh_processing::angle_and_area_smoothing (TriangleMesh &tmesh, const NamedParameters &np=parameters::default_values())
	smooths a polygon mesh.

template<class InputMesh , class OutputMesh , class BottomFunctor , class TopFunctor , class NamedParameters1 = CGAL::parameters::Default_named_parameter, class NamedParameters2 = CGAL::parameters::Default_named_parameter>
void	CGAL::Polygon_mesh_processing::extrude_mesh (const InputMesh &input, OutputMesh &output, const BottomFunctor &bot, const TopFunctor &top, const NamedParameters1 &np_in=parameters::default_values(), const NamedParameters2 &np_out=parameters::default_values())
	performs a generalized extrusion of `input` and puts it in `output`.

template<class InputMesh , class OutputMesh , class NamedParameters1 = CGAL::parameters::Default_named_parameter, class NamedParameters2 = CGAL::parameters::Default_named_parameter>
void	CGAL::Polygon_mesh_processing::extrude_mesh (const InputMesh &input, OutputMesh &output, Vector_3 v, const NamedParameters1 &np_in=parameters::default_values(), const NamedParameters2 &np_out=parameters::default_values())
	fills `output` with a closed mesh bounding the volume swept by `input` when translating its vertices by `v`.

template<typename TriangleMesh , typename VertexRange , typename NamedParameters = parameters::Default_named_parameters>
bool	CGAL::Polygon_mesh_processing::fair (TriangleMesh &tmesh, const VertexRange &vertices, const NamedParameters &np=parameters::default_values())
	fairs a region on a triangle mesh.

template<typename VertexRange , typename TriangleMesh , typename NamedParameters = parameters::Default_named_parameters>
void	CGAL::Polygon_mesh_processing::random_perturbation (VertexRange vertices, TriangleMesh &tmesh, const double &perturbation_max_size, const NamedParameters &np=parameters::default_values())
	randomly perturbs the locations of non-border vertices of a triangulated surface mesh.

template<typename TriangleMesh , typename NamedParameters = parameters::Default_named_parameters>
void	CGAL::Polygon_mesh_processing::random_perturbation (TriangleMesh &tmesh, const double &perturbation_max_size, const NamedParameters &np=parameters::default_values())
	randomly perturbs the locations of all non-border vertices of a triangulated surface mesh.

template<typename TriangleMesh , typename FaceRange , typename FaceOutputIterator , typename VertexOutputIterator , typename NamedParameters = parameters::Default_named_parameters>
std::pair< FaceOutputIterator, VertexOutputIterator >	CGAL::Polygon_mesh_processing::refine (TriangleMesh &tmesh, const FaceRange &faces, FaceOutputIterator faces_out, VertexOutputIterator vertices_out, const NamedParameters &np=parameters::default_values())
	refines a region of a triangle mesh.

template<typename PolygonMesh , typename FaceRange , typename SizingFunction , typename NamedParameters = parameters::Default_named_parameters, typename = typename std::enable_if_t<!std::is_convertible_v<SizingFunction, double>>>
void	CGAL::Polygon_mesh_processing::isotropic_remeshing (const FaceRange &faces, SizingFunction &sizing, PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
	remeshes a triangulated region of a polygon mesh.

template<typename PolygonMesh , typename EdgeRange , typename SizingFunction , typename NamedParameters = parameters::Default_named_parameters, typename = typename std::enable_if_t<!std::is_convertible_v<SizingFunction, double>>>
void	CGAL::Polygon_mesh_processing::split_long_edges (const EdgeRange &edges, SizingFunction &sizing, PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
	splits the edges listed in `edges` into sub-edges that are not longer than the given threshold `max_length`.

template<typename TriangleMeshIn , typename PolygonMeshOut , typename NamedParametersIn = parameters::Default_named_parameters, typename NamedParametersOut = parameters::Default_named_parameters>
void	CGAL::Polygon_mesh_processing::remesh_planar_patches (const TriangleMeshIn &tm_in, PolygonMeshOut &pm_out, const NamedParametersIn &np_in=parameters::default_values(), const NamedParametersOut &np_out=parameters::default_values())
	generates a new triangle mesh `pm_out` with the minimal number of triangles while preserving the shape of `tm_in`.

template<typename TriangleMeshIn , typename PolygonMeshOut , typename FacePatchMap , typename EdgeIsConstrainedMap , typename VertexCornerMap , typename NamedParametersIn = parameters::Default_named_parameters, typename NamedParametersOut = parameters::Default_named_parameters>
bool	CGAL::Polygon_mesh_processing::remesh_almost_planar_patches (const TriangleMeshIn &tm_in, PolygonMeshOut &pm_out, std::size_t nb_patches, std::size_t nb_corners, FacePatchMap face_patch_map, VertexCornerMap vertex_corner_map, EdgeIsConstrainedMap ecm, const NamedParametersIn &np_in=parameters::default_values(), const NamedParametersOut &np_out=parameters::default_values())
	generates a new triangle mesh `pm_out` with the minimal number of triangles from a partition of `tm_in`.

template<typename TriangleMesh , typename FaceRange , typename NamedParameters = parameters::Default_named_parameters>
void	CGAL::Polygon_mesh_processing::smooth_shape (const FaceRange &faces, TriangleMesh &tmesh, const double time, const NamedParameters &np=parameters::default_values())
	smooths the overall shape of the mesh by using the mean curvature flow.

template<typename VertexRange , class TriangleMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
void	CGAL::Polygon_mesh_processing::tangential_relaxation (const VertexRange &vertices, TriangleMesh &tm, const NamedParameters &np=parameters::default_values())
	applies an iterative area-based tangential smoothing to the given range of vertices.

template<class TriangleMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
void	CGAL::Polygon_mesh_processing::tangential_relaxation (TriangleMesh &tm, const NamedParameters &np=parameters::default_values())
	applies `tangential_relaxation()` to all the vertices of `tm`.

template<typename PolygonMesh , typename NamedParameters = parameters::Default_named_parameters>
bool	CGAL::Polygon_mesh_processing::triangulate_face (typename boost::graph_traits< PolygonMesh >::face_descriptor f, PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
	triangulates a single face of a polygon mesh.

template<typename FaceRange , typename PolygonMesh , typename NamedParameters = parameters::Default_named_parameters>
bool	CGAL::Polygon_mesh_processing::triangulate_faces (FaceRange face_range, PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
	triangulates given faces of a polygon mesh.

template<typename PolygonMesh , typename NamedParameters = parameters::Default_named_parameters>
bool	CGAL::Polygon_mesh_processing::triangulate_faces (PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
	triangulates all faces of a polygon mesh.

template<typename PointRange , typename PolygonRange , typename NamedParameters = parameters::Default_named_parameters>
bool	CGAL::Polygon_mesh_processing::triangulate_polygons (const PointRange &points, PolygonRange &polygons, const NamedParameters &np=parameters::default_values())
	triangulates all polygons of a polygon soup.

template<typename TriangleMesh , typename TriangleMeshOut = TriangleMesh, typename NamedParameters = parameters::Default_named_parameters>
TriangleMeshOut	CGAL::Polygon_mesh_processing::surface_Delaunay_remeshing (const TriangleMesh &tmesh, const NamedParameters &np=parameters::default_values())
	remeshes a surface triangle mesh following the Delaunay refinement algorithm described in the 3D Mesh Generation package.

Function Documentation

◆ angle_and_area_smoothing() [1/2]

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

void CGAL::Polygon_mesh_processing::angle_and_area_smoothing	(	const FaceRange &	faces,
		TriangleMesh &	tmesh,
		const NamedParameters &	np = `parameters::default_values()`
	)

#include <CGAL/Polygon_mesh_processing/angle_and_area_smoothing.h>

smooths a triangulated region of a polygon mesh.

This function aims to make the triangle angle and area distributions as uniform as possible by moving (non-constrained) vertices.

Angle-based smoothing does not change the combinatorial information of the mesh. Area-based smoothing might change the combinatorial information, unless specified otherwise. It is also possible to make the smoothing algorithm "safer" by rejecting moves that, when applied, would worsen the quality of the mesh, e.g. that would decrease the value of the smallest angle around a vertex or create self-intersections.

Optionally, the points are reprojected after each iteration.

Template Parameters

TriangleMesh	model of `MutableFaceGraph`.
FaceRange	range of `boost::graph_traits<TriangleMesh>::face_descriptor`, model of `Range`. Its iterator type is `ForwardIterator`.
NamedParameters	a sequence of Named Parameters

Parameters

tmesh	a polygon mesh with triangulated surface patches to be smoothed.
faces	the range of triangular faces defining one or several surface patches to be smoothed.
np	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

the number of iterations for the sequence of the smoothing iterations performed Type: unsigned int Default: `1`
value to indicate whether angle-based smoothing should be used Type: Boolean Default: `true`
value to indicate whether area-based smoothing should be used Type: Boolean Default: `true`
a property map associating points to the vertices of `tmesh` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMesh>::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.
If `true`, vertex moves that would worsen the mesh are ignored. Type: Boolean Default: `false`
If `true`, area-based smoothing will be completed by a phase of Delaunay-based edge-flips to prevent the creation of elongated triangles. Type: Boolean Default: `true`
If `true`, points are projected onto the initial surface after each iteration. Type: Boolean Default: `true`
a property map containing the constrained-or-not status of each vertex of `tmesh`. Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMesh>::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: A constrained vertex cannot be modified at all during smoothing.
a property map containing the constrained-or-not status of each edge of `tmesh`. Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMesh>::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 cannot be modified at all during smoothing.

Warning: The third party library Ceres is required to use area-based smoothing.

Precondition: tmesh does not contain any degenerate faces.

◆ angle_and_area_smoothing() [2/2]

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

void CGAL::Polygon_mesh_processing::angle_and_area_smoothing	(	TriangleMesh &	tmesh,
		const NamedParameters &	np = `parameters::default_values()`
	)

#include <CGAL/Polygon_mesh_processing/angle_and_area_smoothing.h>

smooths a polygon mesh.

This function aims to make the triangle angle and area distributions as uniform as possible by moving (non-constrained) vertices.

Angle-based smoothing does not change the combinatorial information of the mesh. Area-based smoothing might change the combinatorial information, unless specified otherwise. It is also possible to make the smoothing algorithm "safer" by rejecting moves that, when applied, would worsen the quality of the mesh, e.g. that would decrease the value of the smallest angle around a vertex or create self-intersections.

Optionally, the points are reprojected after each iteration.

See the overload which takes a face range as additional parameter for a comprehensive description of the parameters.

◆ extrude_mesh() [1/2]

template<class InputMesh , class OutputMesh , class BottomFunctor , class TopFunctor , class NamedParameters1 = CGAL::parameters::Default_named_parameter, class NamedParameters2 = CGAL::parameters::Default_named_parameter>

void CGAL::Polygon_mesh_processing::extrude_mesh	(	const InputMesh &	input,
		OutputMesh &	output,
		const BottomFunctor &	bot,
		const TopFunctor &	top,
		const NamedParameters1 &	np_in = `parameters::default_values()`,
		const NamedParameters2 &	np_out = `parameters::default_values()`
	)

#include <CGAL/Polygon_mesh_processing/extrude.h>

performs a generalized extrusion of input and puts it in output.

This function extrudes the open surface mesh input and puts the result in output. The mesh generated is a closed surface mesh with a bottom and top part, both having the same graph combinatorics as input (except that the orientation of the faces of the bottom part is reversed). The bottom and the top parts are connected by a triangle strip between boundary cycles. The coordinates of the points associated to the vertices of the bottom and top part are first initialized to the same value as the corresponding vertices of input. Then for each vertex, a call to bot and top is done for the vertices of the bottom part and the top part, respectively.

Attention: output may be self intersecting.

Template Parameters

InputMesh	a model of `FaceListGraph`
OutputMesh	a model of `FaceListGraph` and `MutableFaceGraph`
NamedParameters1	a sequence of Named Parameters for `InputMesh`
NamedParameters2	a sequence of Named Parameters for `OutputMesh`
BottomFunctor	a functor providing void operator()(boost::graph_traits<InputMesh>::vertex_descriptor input_v,boost::graph_traits<OutputMesh>::vertex_descriptor output_v) where `output_v` is the copy of `input_v` from `input` into the bottom part of `output`.
TopFunctor	a functor providing a similar `operator()` as `BottomFunctor`.

Parameters

input	an open surface mesh to extrude.
output	a surface mesh that will contain the result of the extrusion.
bot	functor that will transform all points copied from `input` in order to shape the bottom part of the extrusion.
top	functor that will transform all points copied from `input` in order to shape the top part of the extrusion.
np_in	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

a property map associating points to the vertices of input
Type: a class model of ReadablePropertyMap with boost::graph_traits<InputMesh>::vertex_descriptor as key type and Point_3 as value type
Default: boost::get(CGAL::vertex_point, input)
Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t should be available for the vertices of input.

Parameters

np_out an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

a property map associating points to the vertices of output
Type: a class model of ReadWritePropertyMap with boost::graph_traits<OutputMesh>::vertex_descriptor as key type and Point_3 as value type
Default: boost::get(CGAL::vertex_point, output)
Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t should be available for the vertices of output.

Examples: Polygon_mesh_processing/extrude.cpp.

◆ extrude_mesh() [2/2]

template<class InputMesh , class OutputMesh , class NamedParameters1 = CGAL::parameters::Default_named_parameter, class NamedParameters2 = CGAL::parameters::Default_named_parameter>

void CGAL::Polygon_mesh_processing::extrude_mesh	(	const InputMesh &	input,
		OutputMesh &	output,
		Vector_3	v,
		const NamedParameters1 &	np_in = `parameters::default_values()`,
		const NamedParameters2 &	np_out = `parameters::default_values()`
	)

#include <CGAL/Polygon_mesh_processing/extrude.h>

fills output with a closed mesh bounding the volume swept by input when translating its vertices by v.

The mesh is oriented so that the faces corresponding to input in output have the same orientation.

Attention: output may be self intersecting.

Template Parameters

InputMesh	a model of the concept `FaceListGraph`
OutputMesh	a model of the concept `FaceListGraph` and `MutableFaceGraph`
Vector_3	vector type from the same CGAL kernel as the point of the vertex point map used for `OutputMesh`.
NamedParameters1	a sequence of Named Parameters for `InputMesh`
NamedParameters2	a sequence of Named Parameters for `OutputMesh`

Parameters

input	an open surface mesh to extrude
output	a surface mesh that will contain the result of the extrusion
v	the vector defining the direction of the extrusion
np_in	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

a property map associating points to the vertices of input
Type: a class model of ReadablePropertyMap with boost::graph_traits<InputMesh>::vertex_descriptor as key type and Point_3 as value type
Default: boost::get(CGAL::vertex_point, input)
Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t should be available for the vertices of input.

Parameters

np_out an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

a property map associating points to the vertices of output
Type: a class model of ReadWritePropertyMap with boost::graph_traits<OutputMesh>::vertex_descriptor as key type and Point_3 as value type
Default: boost::get(CGAL::vertex_point, output)
Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t should be available for the vertices of output.

◆ fair()

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

bool CGAL::Polygon_mesh_processing::fair	(	TriangleMesh &	tmesh,
		const VertexRange &	vertices,
		const NamedParameters &	np = `parameters::default_values()`
	)

#include <CGAL/Polygon_mesh_processing/fair.h>

fairs a region on a triangle mesh.

The points of the selected vertices are relocated to yield an as-smooth-as-possible surface patch, based on solving a linear bi-Laplacian system with boundary constraints, described in [4]. The optional parameter fairing_continuity gives the ability to control the tangential continuity Cⁿ of the output mesh.

The region described by vertices might contain multiple disconnected components. Note that the mesh connectivity is not altered in any way, only vertex locations get updated.

Fairing might fail if fixed vertices, which are used as boundary conditions, do not suffice to solve constructed linear system.

Note that if the vertex range to which fairing is applied contains all the vertices of the triangle mesh, fairing does not fail, but the mesh gets shrunk to CGAL::ORIGIN.

Template Parameters

TriangleMesh	a model of `FaceGraph` and `MutableFaceGraph`
VertexRange	a range of vertex descriptors of `TriangleMesh`, model of `Range`. Its iterator type is `InputIterator`.
NamedParameters	a sequence of Named Parameters

Parameters

tmesh	the triangle mesh with patches to be faired
vertices	the vertices of the patches to be faired (the positions of only those vertices will be changed)
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 ReadablePropertyMap with boost::graph_traits<TriangleMesh>::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 should be available for the vertices of tmesh.

A value controlling the tangential continuity of the output surface patch. The possible values are 0, 1 and 2, referring to the C⁰, C¹ and C² continuity.
Type: unsigned int
Default: 1
Extra: The larger fairing_continuity gets, the more fixed vertices are required.

an instance of the sparse linear solver used for fairing
Type: a class model of SparseLinearAlgebraWithFactorTraits_d
Default: If Eigen 3.2 (or greater) is available and CGAL_EIGEN3_ENABLED is defined, then the following overload of Eigen_solver_traits is provided as default value:
CGAL::Eigen_solver_traits<Eigen::SparseLU<CGAL::Eigen_sparse_matrix<double>::EigenType, Eigen::COLAMDOrdering<int> > >

Returns: true if fairing is successful, otherwise no vertices are relocated.

Precondition: is_triangle_mesh(tmesh)

Warning: This function involves linear algebra, that is computed using non-exact, floating-point arithmetic.

◆ isotropic_remeshing()

template<typename PolygonMesh , typename FaceRange , typename SizingFunction , typename NamedParameters = parameters::Default_named_parameters, typename = typename std::enable_if_t<!std::is_convertible_v<SizingFunction, double>>>

void CGAL::Polygon_mesh_processing::isotropic_remeshing	(	const FaceRange &	faces,
		SizingFunction &	sizing,
		PolygonMesh &	pmesh,
		const NamedParameters &	np = `parameters::default_values()`
	)

#include <CGAL/Polygon_mesh_processing/remesh.h>

remeshes a triangulated region of a polygon mesh.

This operation sequentially performs edge splits, edge collapses, edge flips, tangential relaxation and projection to the initial surface to generate a smooth mesh with a prescribed edge length.

Template Parameters

PolygonMesh	model of `MutableFaceGraph`. The descriptor types `boost::graph_traits<PolygonMesh>::face_descriptor` and `boost::graph_traits<PolygonMesh>::halfedge_descriptor` must be models of `Hashable`.
FaceRange	range of `boost::graph_traits<PolygonMesh>::face_descriptor`, model of `Range`. Its iterator type is `ForwardIterator`.
SizingFunction	model of `PMPSizingField`
NamedParameters	a sequence of Named Parameters

Parameters

pmesh	a polygon mesh with triangulated surface patches to be remeshed
faces	the range of triangular faces defining one or several surface patches to be remeshed
sizing	field that determines a target length for individual edges. If a number convertible to a `double` is passed, `Uniform_sizing_field()` will be used, with the number as a target edge length. If `0` is passed then only the edge-flip, tangential relaxation, and projection steps will be done.
np	an optional sequence of Named Parameters among the ones listed below

Precondition: if constraints protection is activated, the constrained edges must not be longer than 4/3*target_edge_length.

Optional Named Parameters

a property map associating points to the vertices of `pmesh` 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, 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: 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 `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
the number of iterations for the sequence of atomic operations performed (listed in the above description) Type: unsigned int Default: `1`
a property map containing the constrained-or-not status of each edge of `pmesh` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMesh>::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. Extra: Sub-edges generated by splitting are set to be constrained. Extra: Patch boundary edges (i.e. incident to only one face in the range) are always considered as constrained edges.
a property map containing the constrained-or-not status of each vertex of `pmesh`. Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMesh>::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: A constrained vertex cannot be modified during remeshing.
If `true`, the edges set as constrained in `edge_is_constrained_map` (or by default the boundary edges) are neither split nor collapsed during remeshing. Type: Boolean Default: `false` Extra: Note that around constrained edges that have their length higher than twice `target_edge_length`, remeshing will fail to provide good quality results. It can even fail to terminate because of cascading vertex insertions.
If `true`, the edges set as constrained in `edge_is_constrained_map` (or by default the boundary edges) are collapsed during remeshing. Type: Boolean Default: `true` Extra: This value is ignored if `protect_constraints` is `true`.
a property map with the patch id's associated to the faces of `faces` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMesh>::face_descriptor` as key type and the desired property, model of `CopyConstructible` and `LessThanComparable` as value type. Default: a default property map where each face is associated with the ID of the connected component it belongs to. Connected components are computed with respect to the constrained edges listed in the property map `edge_is_constrained_map` Extra: The map is updated during the remeshing process while new faces are created.
whether edges that are too long with respect to the given sizing are split Type: Boolean Default: `true`
whether edges that are too short with respect to the given sizing are collapsed Type: Boolean Default: `true`
whether edge flips are performed to improve shape and valence Type: Boolean Default: `true`
the number of iterations of tangential relaxation that are performed at each iteration of the remeshing process Type: unsigned int Default: `1`
If `true`, the end vertices of the edges set as constrained in `edge_is_constrained_map` and boundary edges move along the constrained polylines they belong to. Type: Boolean Default: `false`
A function object used to determinate if a vertex move should be allowed or not during the relaxation step. Type: Functor that provides `bool operator()(vertex_descriptor v, Point_3 src, Point_3 tgt)` returning `true` if the vertex `v` can be moved from `src` to `tgt`; `Point_3` being the value type of the vertex point map Default: If not provided, all moves are allowed.
whether vertices should be reprojected on the input surface after creation or displacement Type: Boolean Default: `true`
A function object used to project input vertices (moved by the smoothing) and created vertices Type: Unary functor that provides `Point_3 operator()(vertex_descriptor)`, `Point_3` being the value type of the vertex point map. Default: If not provided, vertices are projected on the input surface mesh.

See also: split_long_edges()

Examples: Polygon_mesh_processing/hausdorff_distance_remeshing_example.cpp.

◆ random_perturbation() [1/2]

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

void CGAL::Polygon_mesh_processing::random_perturbation	(	TriangleMesh &	tmesh,
		const double &	perturbation_max_size,
		const NamedParameters &	np = `parameters::default_values()`
	)

#include <CGAL/Polygon_mesh_processing/random_perturbation.h>

randomly perturbs the locations of all non-border vertices of a triangulated surface mesh.

By default, the vertices are re-projected onto the input surface after perturbation. Note that no geometric checks are performed after the perturbation (self-intersections might be introduced).

Template Parameters

TriangleMesh	model of `VertexListGraph`.
NamedParameters	a sequence of Named Parameters

Parameters

tmesh	the triangulated surface mesh
perturbation_max_size	the maximal length of moves that can be applied to vertices of `tmesh`.
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<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.
a property map containing the constrained-or-not status of each vertex of `tmesh` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMesh>::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: A constrained vertex cannot be modified at all during perturbation
indicates whether vertices are reprojected on the input surface after their coordinates random perturbation Type: Boolean Default: `true`
a value to seed the random number generator, and make the perturbation deterministic Type: unsigned int Default: `unsigned int(-1)`

◆ random_perturbation() [2/2]

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

void CGAL::Polygon_mesh_processing::random_perturbation	(	VertexRange	vertices,
		TriangleMesh &	tmesh,
		const double &	perturbation_max_size,
		const NamedParameters &	np = `parameters::default_values()`
	)

#include <CGAL/Polygon_mesh_processing/random_perturbation.h>

randomly perturbs the locations of non-border vertices of a triangulated surface mesh.

By default, the vertices are re-projected onto the input surface after perturbation. Note that no geometric checks are performed after the perturbation (self-intersections might be introduced).

Template Parameters

VertexRange	model of `Range`, holding vertices of type `boost::graph_traits<TriangleMesh>::vertex_descriptor`. Its iterator type is `ForwardIterator`.
TriangleMesh	model of `VertexListGraph`.
NamedParameters	a sequence of Named Parameters

Parameters

vertices	the range of vertices to be perturbed
tmesh	the triangulated surface mesh
perturbation_max_size	the maximal length of moves that can be applied to vertices of `tmesh`.
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<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.
a property map containing the constrained-or-not status of each vertex of `tmesh` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMesh>::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: A constrained vertex cannot be modified at all during perturbation
indicates whether vertices are reprojected on the input surface after their coordinates random perturbation Type: Boolean Default: `true`
a value to seed the random number generator, and make the perturbation deterministic Type: unsigned int Default: `unsigned int(-1)`

◆ refine()

template<typename TriangleMesh , typename FaceRange , typename FaceOutputIterator , typename VertexOutputIterator , typename NamedParameters = parameters::Default_named_parameters>

std::pair< FaceOutputIterator, VertexOutputIterator > CGAL::Polygon_mesh_processing::refine	(	TriangleMesh &	tmesh,
		const FaceRange &	faces,
		FaceOutputIterator	faces_out,
		VertexOutputIterator	vertices_out,
		const NamedParameters &	np = `parameters::default_values()`
	)

#include <CGAL/Polygon_mesh_processing/refine.h>

refines a region of a triangle mesh.

Template Parameters

TriangleMesh	model of `MutableFaceGraph`
FaceRange	range of face descriptors, model of `Range`. Its iterator type is `InputIterator`.
FaceOutputIterator	model of `OutputIterator` holding `boost::graph_traits<TriangleMesh>::face_descriptor` for patch faces
VertexOutputIterator	model of `OutputIterator` holding `boost::graph_traits<TriangleMesh>::vertex_descriptor` for patch vertices
NamedParameters	a sequence of Named Parameters

Parameters

tmesh	triangle mesh with patches to be refined
faces	the range of faces defining the patches to refine
faces_out	output iterator into which descriptors of new faces are recorded
vertices_out	output iterator into which descriptors of new vertices are recorded
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<TriangleMesh>::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.

a factor to control density of the output mesh, where larger values lead to denser refinements
Type: double
Default: \( \sqrt{2}\)
Extra: The density of vertices of faces_out is this factor times higher than the vertices of faces.

Returns: pair of faces_out and vertices_out

Precondition: is_triangle_mesh(tmesh)

◆ remesh_almost_planar_patches()

template<typename TriangleMeshIn , typename PolygonMeshOut , typename FacePatchMap , typename EdgeIsConstrainedMap , typename VertexCornerMap , typename NamedParametersIn = parameters::Default_named_parameters, typename NamedParametersOut = parameters::Default_named_parameters>

bool CGAL::Polygon_mesh_processing::remesh_almost_planar_patches	(	const TriangleMeshIn &	tm_in,
		PolygonMeshOut &	pm_out,
		std::size_t	nb_patches,
		std::size_t	nb_corners,
		FacePatchMap	face_patch_map,
		VertexCornerMap	vertex_corner_map,
		EdgeIsConstrainedMap	ecm,
		const NamedParametersIn &	np_in = `parameters::default_values()`,
		const NamedParametersOut &	np_out = `parameters::default_values()`
	)

#include <CGAL/Polygon_mesh_processing/remesh_planar_patches.h>

generates a new triangle mesh pm_out with the minimal number of triangles from a partition of tm_in.

The terminology used here and the global idea is very similar to what is done by remesh_planar_patches() except that here the partition into patches and corner identification is provided by the user. It allows to have a remeshing of almost coplanar regions, detected for example using the region growing algorithm with the functions region_growing_of_planes_on_faces() and detect_corners_of_regions(). If a patch cannot be triangulated, it is left untouched in the output and all its vertices become corners so that the output is still a valid conformal triangle mesh.

Returns: true if all patches could be triangulated and false otherwise.

Template Parameters

TriangleMeshIn	a model of `HalfedgeListGraph` and `FaceListGraph`
PolygonMeshOut	a model of `MutableFaceGraph`
FacePatchMap	a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMeshIn>::face_descriptor` as key type and `std::size_t` as value type
EdgeIsConstrainedMap	a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMeshIn>::edge_descriptor` as key type and `bool` as value type
VertexCornerMap	a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMeshIn>::vertex_descriptor` as key type and `std::size_t` as value type
NamedParametersIn	a sequence of Named Parameters
NamedParametersOut	a sequence of Named Parameters

Parameters

tm_in	input triangle mesh
pm_out	output polygon mesh
nb_patches	the number of patches in the partition
nb_corners	the number of corners
face_patch_map	a property map that contains for each face the id of its patch in the range `[0, nb_patches]`
vertex_corner_map	a property map that contains for each vertex that is a corner an id in the range `[0, nb_corners - 1]`, and `std::size_t(-1)` otherwise.
ecm	a property map that contains `true` if an edge is on the border of a patch and `false` otherwise.
np_in	an optional sequence of Named Parameters among the ones listed below:

Optional Named Parameters

a property map providing for each patch the normal of the supporting plane of the patch (used to triangulate it) Type: a class model of `ReadPropertyMap` with the value type of `FacePatchMap` as key and `GeomTraits::Vector_3` as value type, `GeomTraits` being the type of the parameter `geom_traits` Default: If not provided, patch normals will be estimated using corners of the patches
a property map associating points to the vertices of `tm_in` Type: a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMeshIn>::vertex_descriptor` as key type and `GeomTraits::Point_3` as value type, `GeomTraits` being the type of the parameter `geom_traits` Default: `boost::get(CGAL::vertex_point, tm_in)` Extra: If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` must be available in `TriangleMeshIn`.
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.

Parameters

np_out an optional sequence of Named Parameters among the ones listed below:

Optional Named Parameters

if `true`, faces of `pm_out` will not be triangulated, but the one with more than one connected component of the boundary. Type: `bool` Default: false
a property map associating points to the vertices of `pm_out` Type: a class model of `WritablePropertyMap` with `boost::graph_traits<PolygonMeshOut>::vertex_descriptor` as key type and `GeomTraits::Point_3` as value type, `GeomTraits` being the type of the parameter `geom_traits` Default: `boost::get(CGAL::vertex_point, pm_out)` Extra: If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` must be available in `PolygonMeshOut`.
a property map filled by this function and that will contain for each face the id of its patch in the range `[0, number of patches - 1]` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMeshOut>::face_descriptor` as key type and `std::size_t` as value type Default: None
a property map filled by this function and that will contain for each vertex its corner an id in the range `[0, number of corners - 1]` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMeshOut>::vertex_descriptor` as key type and `std::size_t` as value type Default: None
a callable with `visitor(pm_out)` being called once `tm_in` is no longer needed and before `pm_out` starts being built. It should be used in the case when `tm_in` and `pm_out` are the same mesh, so that `pm_out` can be cleared before being filled. Type: `visitor(pm_out)` must be a valid expression. Default: None

◆ remesh_planar_patches()

template<typename TriangleMeshIn , typename PolygonMeshOut , typename NamedParametersIn = parameters::Default_named_parameters, typename NamedParametersOut = parameters::Default_named_parameters>

void CGAL::Polygon_mesh_processing::remesh_planar_patches	(	const TriangleMeshIn &	tm_in,
		PolygonMeshOut &	pm_out,
		const NamedParametersIn &	np_in = `parameters::default_values()`,
		const NamedParametersOut &	np_out = `parameters::default_values()`
	)

#include <CGAL/Polygon_mesh_processing/remesh_planar_patches.h>

generates a new triangle mesh pm_out with the minimal number of triangles while preserving the shape of tm_in.

In practice, this means that connected components of edge-connected faces belonging to the same plane are first extracted (each such connected component is called a patch). Then, the connected components of vertex-connected patch border edges belonging to the same line are extracted. Endpoints of such components and vertices incident to more than two patches (or two patches + one mesh boundary) are called corners. pm_out contains the 2D constrained Delaunay triangulation of each patch using only corner vertices on the boundary of the patch.

Warning: if tm_in contains a non-manifold vertex, pm_out will be empty. Those vertices must be duplicated with duplicate_non_manifold_vertices() to get an output.

Template Parameters

TriangleMeshIn	a model of `HalfedgeListGraph` and `FaceListGraph`
PolygonMeshOut	a model of `MutableFaceGraph`
NamedParametersIn	a sequence of Named Parameters
NamedParametersOut	a sequence of Named Parameters

Parameters

tm_in	input triangle mesh
pm_out	output polygon mesh
np_in	an optional sequence of Named Parameters among the ones listed below:

Optional Named Parameters

a property map associating points to the vertices of `tm_in` Type: a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMeshIn>::vertex_descriptor` as key type and `GeomTraits::Point_3` as value type, `GeomTraits` being the type of the parameter `geom_traits` Default: `boost::get(CGAL::vertex_point, tm_in)` Extra: If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` must be available in `TriangleMeshIn`.
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 where the user should put `true` for edges that must be considered as on the boundary of a patch. Additionally, the map is updated by this function and will contain `true` if, based on the angle criteria, an edge is on the boundary of a patch and `false` otherwise. Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMeshIn>::edge_descriptor` as key type and `bool` as value type Default: None
a property map filled by this function and that will contain for each face the id of its patch in the range `[0, number of patches - 1]` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMeshIn>::face_descriptor` as key type and `std::size_t` as value type Default: None
a property map filled by this function and that will contain for each vertex that is a corner an id in the range `[0, number of corners - 1]`, and `std::size_t(-1)` otherwise. Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMeshIn>::vertex_descriptor` as key type and `std::size_t` as value type Default: None
The maximum angle, given as a cosine, (i) between the normals of the supporting planes of adjacent faces such that they are considered coplanar, and (ii) for the smallest angle between the supporting line of a segment and an adjacent segment such that they are considered collinear. Type: `FT` type from the `geom_traits` parameter Default: 1, which means exact coplanarity and collinearity Extra: The value must be in the interval `[0,1]`

Parameters

np_out an optional sequence of Named Parameters among the ones listed below:

Optional Named Parameters

if `true`, faces of `pm_out` will not be triangulated, but the one with more than one connected component of the boundary. Type: `bool` Default: false
a property map associating points to the vertices of `pm_out` Type: a class model of `WritablePropertyMap` with `boost::graph_traits<PolygonMeshOut>::vertex_descriptor` as key type and `GeomTraits::Point_3` as value type, `GeomTraits` being the type of the parameter `geom_traits` Default: `boost::get(CGAL::vertex_point, pm_out)` Extra: If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` must be available in `PolygonMeshOut`.
a property map filled by this function and that will contain for each face the id of its patch in the range `[0, number of patches - 1]`, the patch id of two identical patches in the input and output meshes being equal. Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMeshOut>::face_descriptor` as key type and `std::size_t` as value type Default: None
a property map filled by this function and that will contain for each vertex its corner an id in the range `[0, number of corners - 1]` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMeshOut>::vertex_descriptor` as key type and `std::size_t` as value type Default: None
a callable with `visitor(pm_out)` being called once `tm_in` is no longer needed and before `pm_out` starts being built. It should be used in the case when `tm_in` and `pm_out` are the same mesh, so that `pm_out` can be cleared before being filled. Type: `visitor(pm_out)` must be a valid expression. Default: None

◆ smooth_shape()

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

void CGAL::Polygon_mesh_processing::smooth_shape	(	const FaceRange &	faces,
		TriangleMesh &	tmesh,
		const double	time,
		const NamedParameters &	np = `parameters::default_values()`
	)

#include <CGAL/Polygon_mesh_processing/smooth_shape.h>

smooths the overall shape of the mesh by using the mean curvature flow.

The effect depends on the curvature of each area and on a time step which represents the amount by which vertices are allowed to move. The result conformally maps the initial surface to a sphere.

Template Parameters

TriangleMesh	model of `MutableFaceGraph`.
FaceRange	range of `boost::graph_traits<TriangleMesh>::face_descriptor`, model of `Range`. Its iterator type is `ForwardIterator`.
NamedParameters	a sequence of Named Parameters

Parameters

tmesh	a polygon mesh with triangulated surface patches to be smoothed.
faces	the range of triangular faces defining one or several surface patches to be smoothed.
time	a time step that corresponds to the speed by which the surface is smoothed. A larger time step results in faster convergence but details may be distorted to a larger extent compared to more iterations with a smaller step. Typical values scale in the interval (1e-6, 1].
np	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

the number of iterations for the sequence of the smoothing iterations performed Type: unsigned int Default: `1`
a property map containing the constrained-or-not status of each vertex of `tmesh`. Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMesh>::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: A constrained vertex cannot be modified at all during smoothing.
Whether to apply rescaling after smoothing. This is useful because the mean curvature flow tends to shrink the surface. Type: Boolean Default: `true` Extra: Scaling can only be applied if the mesh is closed and if there is no more than a single constrained vertex. Extra: If a vertex is constrained, it is the fixed point of the scaling, otherwise the centroid is used.
a property map associating points to the vertices of `tmesh` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMesh>::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.
an instance of the sparse linear solver used for smoothing Type: a class model of `SparseLinearAlgebraWithFactorTraits_d` Default: if Eigen 3.2 (or greater) is available and `CGAL_EIGEN3_ENABLED` is defined, then the following overload of `Eigen_solver_traits` is provided as default value: `CGAL::Eigen_solver_traits<Eigen::BiCGSTAB<CGAL::Eigen_sparse_matrix<double>::EigenType, Eigen::IncompleteLUT<double> > >`

Warning: This function involves linear algebra, that is computed using non-exact, floating-point arithmetic.

See also: angle_and_area_smoothing()

◆ split_long_edges()

template<typename PolygonMesh , typename EdgeRange , typename SizingFunction , typename NamedParameters = parameters::Default_named_parameters, typename = typename std::enable_if_t<!std::is_convertible_v<SizingFunction, double>>>

void CGAL::Polygon_mesh_processing::split_long_edges	(	const EdgeRange &	edges,
		SizingFunction &	sizing,
		PolygonMesh &	pmesh,
		const NamedParameters &	np = `parameters::default_values()`
	)

#include <CGAL/Polygon_mesh_processing/remesh.h>

splits the edges listed in edges into sub-edges that are not longer than the given threshold max_length.

Note this function is useful to split constrained edges before calling isotropic_remeshing() with protection of constraints activated (to match the constrained edge length required by the remeshing algorithm to be guaranteed to terminate)

Template Parameters

PolygonMesh	model of `MutableFaceGraph` that has an internal property map for `CGAL::vertex_point_t`.
EdgeRange	range of `boost::graph_traits<PolygonMesh>::edge_descriptor`, model of `Range`. Its iterator type is `InputIterator`.
SizingFunction	model of `PMPSizingField`
NamedParameters	a sequence of Named Parameters

Parameters

pmesh	a polygon mesh
edges	the range of edges to be split if they are longer than given threshold
sizing	the sizing function that is used to split edges from 'edges' list. If a number convertible to a `double` is passed, `Uniform_sizing_field()` will be used, with the number as target edge length.
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 `ReadWritePropertyMap` 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`.
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
a property map with the patch id's associated to the faces of `faces` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMesh>::face_descriptor` as key type and the desired property, model of `CopyConstructible` and `LessThanComparable` as value type. Default: a default property map where each face is associated with the ID of the connected component it belongs to. Connected components are computed with respect to the constrained edges listed in the property map `edge_is_constrained_map` Extra: The map is updated during the remeshing process while new faces are created.
a property map containing the constrained-or-not status of each edge of `pmesh` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMesh>::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.

See also: isotropic_remeshing()

◆ surface_Delaunay_remeshing()

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

TriangleMeshOut CGAL::Polygon_mesh_processing::surface_Delaunay_remeshing	(	const TriangleMesh &	tmesh,
		const NamedParameters &	np = `parameters::default_values()`
	)

#include <CGAL/Polygon_mesh_processing/surface_Delaunay_remeshing.h>

remeshes a surface triangle mesh following the Delaunay refinement algorithm described in the 3D Mesh Generation package.

Template Parameters

TriangleMesh	model of `FaceListGraph`
TriangleMeshOut	model of `FaceListGraph`, model of `DefaultConstructible`, with an internal property map for `CGAL::vertex_point_t` with `geom_traits::Point_3` as value type.
NamedParameters	a sequence of Named Parameters

Parameters

tmesh	a triangle surface mesh
np	an optional sequence of Named Parameters among the ones listed below

Returns: the triangulated surface mesh following the requirements of the input meshing criteria

Optional Named Parameters

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 construction kernels are not supported by this function.
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)` Extra: If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` must be available in `TriangleMesh`.
the dihedral angle bound (in degrees) for detection of feature edges Type: A number type `FT`, either deduced from the `geom_traits` Named Parameters if provided, or from the geometric traits class deduced from the point property map of `TriangleMesh`. Default: `60` Extra: Border edges are protected, along with detected sharp edges. Extra: If the given value is `180`, only the border edges are protected.
a property map containing the constrained-or-not status of each edge of `tmesh` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMesh>::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
a set of polylines that will be resampled and appear as protected polyline constraints in the output mesh Type: a class model of `Range`, of which value type is model of `MeshPolyline_3` Default: an empty range of segments
If `true`, the feature edges of the input are re-sampled and present in the output mesh. If `edge_is_constrained_map` is provided, the corresponding "constrained" edges are protected. Else, if `polyline_constraints` is provided, the corresponding polylines are protected. Otherwise, `features_angle_bound` is used, and the edges that form a sharp dihedral angle with respect to that bound are protected. Type: Boolean Default: `false` Extra: Note that only one of these three input parameters is taken into account, in the priority order listed above.
a property map with the patch id's associated to the faces of `faces` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMesh>::face_descriptor` as key type and the desired property, model of `CopyConstructible` and `LessThanComparable`, as value type. Default: a default property map where each face is associated with the ID of the connected component it belongs to. Connected components are computed with respect to the constrained edges listed in the property map `edge_is_constrained_map`. Extra: The map is updated during the remeshing process while new faces are created.
A scalar field (resp. a constant) providing a space-varying (resp. a uniform) upper bound for the lengths of curve edges. This parameter has to be set to a positive value when 1-dimensional features protection is used (when `protect_constraints` is `true`). Type: A number type `FT` model of the concept `Field`, or a model of the concept `MeshDomainField_3` Default: `(std::numeric_limits<FT>::max)()`, with `FT` a number type, either deduced from the `geom_traits` Named Parameters if provided, or from the geometric traits class deduced from the point property map of `TriangleMesh`.
A scalar field (resp. a constant) describing a space-varying (resp. a uniform) upper bound for the radii of the surface Delaunay balls. Type: A number type `FT` model of the concept `Field`, or a model of the concept `MeshDomainField_3` Default: `0.`
A lower bound for the angles (in degrees) of the surface mesh facets. Type: A number type `FT` model of the concept `Field` Default: `0.`
A scalar field (resp. a constant) describing a space-varying (resp. a uniform) upper bound for the distance between the facet circumcenter and the center of its surface Delaunay ball. Type: A number type `FT` model of the concept `Field`, or a model of the concept `MeshDomainField_3` Default: `0.`
The set of topological constraints which have to be verified by each surface facet. The default value is `CGAL::FACET_VERTICES_ON_SURFACE`. See `CGAL::Mesh_facet_topology` manual page for a description of the possible values. Type: `CGAL::Mesh_facet_topology` Default: `CGAL::FACET_VERTICES_ON_SURFACE`

Precondition: tmesh must be free of self-intersections.

Note: Only one of the named parameters defining constrained edges is taken into account for meshing, in the following priority order : edge_is_constrained_map, polyline_constraints, and features_angle_bound. The selected edges are protected only if protect_constraints is set to true.

◆ tangential_relaxation()

template<typename VertexRange , class TriangleMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>

void CGAL::Polygon_mesh_processing::tangential_relaxation	(	const VertexRange &	vertices,
		TriangleMesh &	tm,
		const NamedParameters &	np = `parameters::default_values()`
	)

#include <CGAL/Polygon_mesh_processing/tangential_relaxation.h>

applies an iterative area-based tangential smoothing to the given range of vertices.

Each vertex v is relocated to its gravity-weighted centroid, and the relocation vector is projected back to the tangent plane to the surface at v, iteratively. The connectivity remains unchanged.

Template Parameters

TriangleMesh	model of `FaceGraph` and `VertexListGraph`. The descriptor types `boost::graph_traits<TriangleMesh>::face_descriptor` and `boost::graph_traits<TriangleMesh>::halfedge_descriptor` must be models of `Hashable`.
VertexRange	range of `boost::graph_traits<TriangleMesh>::vertex_descriptor`, model of `Range`. Its iterator type is `ForwardIterator`.
NamedParameters	a sequence of Named Parameters

Parameters

vertices	the range of vertices which will be relocated by relaxation
tm	the triangle mesh to which `vertices` belong
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 `ReadWritePropertyMap` with `boost::graph_traits<TriangleMesh>::vertex_descriptor` as key type and `Point_3` as value type Default: `boost::get(CGAL::vertex_point, tm)` 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_3` type, using `CGAL::Kernel_traits` Extra: The geometric traits class must be compatible with the vertex `Point_3` type. Extra: Exact constructions kernels are not supported by this function.
the number of smoothing iterations Type: unsigned int Default: `1`
a property map containing the constrained-or-not status of each edge of `tm`. The endpoints of a constrained edge cannot be moved by relaxation. Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMesh>::edge_descriptor` as key type and `bool` as value type. It must be default constructible. Default: a default property map where no edges are constrained Extra: Boundary edges are always considered as constrained edges.
a property map containing the constrained-or-not status of each vertex of `tm`. A constrained vertex cannot be modified during relaxation. Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMesh>::vertex_descriptor` as key type and `bool` as value type. It must be default constructible. Default: a default property map where no vertices are constrained
If `true`, the end vertices of the edges set as constrained in `edge_is_constrained_map` and boundary edges move along the constrained polylines they belong to. Type: Boolean Default: `false`
A function object used to determinate if a vertex move should be allowed or not Type: Unary functor that provides `bool operator()(vertex_descriptor v, Point_3 src, Point_3 tgt)` returning `true` if the vertex `v` can be moved from `src` to `tgt`; `Point_3` being the value type of the vertex point map Default: If not provided, all moves are allowed.
An object containing sizing field for individual vertices. Used to derive smoothing weights. Type: A model of `PMPSizingField`. Default: If not provided, smoothing weights are the same for all vertices.

◆ triangulate_face()

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

bool CGAL::Polygon_mesh_processing::triangulate_face	(	typename boost::graph_traits< PolygonMesh >::face_descriptor	f,
		PolygonMesh &	pmesh,
		const NamedParameters &	np = `parameters::default_values()`
	)

#include <CGAL/Polygon_mesh_processing/triangulate_faces.h>

triangulates a single face of a polygon mesh.

This function depends on the package 2D Triangulations.

Template Parameters

PolygonMesh	a model of `FaceListGraph` and `MutableFaceGraph`
NamedParameters	a sequence of Named Parameters

Parameters

f	face to be triangulated
pmesh	the polygon mesh to which the face to be triangulated belongs
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 ReadWritePropertyMap 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
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 visitor that enables to track how faces are triangulated into subfaces
Type: a class model of PMPTriangulateFaceVisitor and PMPHolefillingVisitor
Default: Triangulate_faces::Default_visitor<PolygonMesh>
Extra: Note that the visitor will be copied, so it must not have any data member that does not have a reference-like type.

This function calls CGAL::Polygon_mesh_processing::triangulate_hole_polyline(). Refer to its documentation for its named parameters.

Precondition: The face f is not degenerate.

Returns: true if the face has been triangulated.

See also: triangulate_faces()

◆ triangulate_faces() [1/2]

template<typename FaceRange , typename PolygonMesh , typename NamedParameters = parameters::Default_named_parameters>

bool CGAL::Polygon_mesh_processing::triangulate_faces	(	FaceRange	face_range,
		PolygonMesh &	pmesh,
		const NamedParameters &	np = `parameters::default_values()`
	)

#include <CGAL/Polygon_mesh_processing/triangulate_faces.h>

triangulates given faces of a polygon mesh.

This function depends on the package 2D Triangulations.

Template Parameters

FaceRange	range of `boost::graph_traits<PolygonMesh>::face_descriptor`, model of `Range`. Its iterator type is `InputIterator`.
PolygonMesh	a model of `FaceListGraph` and `MutableFaceGraph`
NamedParameters	a sequence of Named Parameters

Parameters

face_range	the range of faces to be triangulated
pmesh	the polygon mesh to be triangulated
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 ReadWritePropertyMap 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
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 visitor that enables to track how faces are triangulated into subfaces
Type: a class model of PMPTriangulateFaceVisitor and PMPHolefillingVisitor
Default: Triangulate_faces::Default_visitor<PolygonMesh>
Extra: Note that the visitor will be copied, so it must not have any data member that does not have a reference-like type.

This function calls CGAL::Polygon_mesh_processing::triangulate_hole_polyline() for each face. Refer to its documentation for its named parameters.

Precondition: No face within face_range is degenerate.

Returns: true if all the faces have been triangulated.

See also: triangulate_face(); triangulate_polygons()

Examples: Polygon_mesh_processing/triangulate_faces_split_visitor_example.cpp.

◆ triangulate_faces() [2/2]

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

bool CGAL::Polygon_mesh_processing::triangulate_faces	(	PolygonMesh &	pmesh,
		const NamedParameters &	np = `parameters::default_values()`
	)

#include <CGAL/Polygon_mesh_processing/triangulate_faces.h>

triangulates all faces of a polygon mesh.

This function depends on the package 2D Triangulations.

Template Parameters

PolygonMesh	a model of `FaceListGraph` and `MutableFaceGraph`
NamedParameters	a sequence of Named Parameters

Parameters

pmesh	the polygon mesh to be triangulated
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 ReadWritePropertyMap 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
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 visitor that enables to track how faces are triangulated into subfaces
Type: a class model of PMPTriangulateFaceVisitor and PMPHolefillingVisitor
Default: Triangulate_faces::Default_visitor<PolygonMesh>
Extra: Note that the visitor will be copied, so it must not have any data member that does not have a reference-like type.

This function calls CGAL::Polygon_mesh_processing::triangulate_hole_polyline() on all the faces of the polygon mesh. Refer to its documentation for its named parameters.

Precondition: No face of pmesh is degenerate.

Returns: true if all the faces have been triangulated.

See also: triangulate_face(); triangulate_polygons()

◆ triangulate_polygons()

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

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

#include <CGAL/Polygon_mesh_processing/triangulate_faces.h>

triangulates all polygons of a polygon soup.

This function depends on the package 2D Triangulations.

Template Parameters

PointRange	a model of `ConstRange`. The value type of its iterator is the point type.
PolygonRange	a model of the concepts `SequenceContainer` and `Swappable`, whose `value_type` is itself a model of the concept `SequenceContainer` whose `value_type` is `std::size_t`.
NamedParameters	a sequence of Named Parameters

Parameters

points	the point geometry of the soup to be triangulated
polygons	the polygons to be triangulated
np	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

a property map associating points to the elements of the 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>

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 visitor that enables to track how polygons are divided into triangles
Type: a class model of PMPTriangulateFaceVisitor and PMPHolefillingVisitor
Default: Triangulate_polygons::Default_visitor
Extra: Note that the visitor will be copied, so it must not have any data member that does not have a reference-like type.

This function calls CGAL::Polygon_mesh_processing::triangulate_hole_polyline() for each polygon. Refer to its documentation for its named parameters.

Precondition: No polygon within polygons is degenerate.

Returns: true if all the polygons have been triangulated.

See also: triangulate_faces()

Classes

Functions

Function Documentation

◆ angle_and_area_smoothing() [1/2]

◆ angle_and_area_smoothing() [2/2]

◆ extrude_mesh() [1/2]

◆ extrude_mesh() [2/2]

◆ fair()

◆ isotropic_remeshing()

◆ random_perturbation() [1/2]

◆ random_perturbation() [2/2]

◆ refine()

◆ remesh_almost_planar_patches()

◆ remesh_planar_patches()

◆ smooth_shape()

◆ split_long_edges()

◆ surface_Delaunay_remeshing()

◆ tangential_relaxation()

◆ triangulate_face()

◆ triangulate_faces() [1/2]

◆ triangulate_faces() [2/2]

◆ triangulate_polygons()