Triangulated Surface Mesh Approximation Reference

Pierre Alliez, David Cohen-Steiner, Lingjie Zhu

This package implements the Variational Shape Approximation method to approximate an input surface triangle mesh by a simpler surface triangle mesh. The algorithm proceeds by iterative clustering of triangles, the clustering process being seeded randomly, incrementally or hierarchically. While the default function runs an automated version of the algorithm, interactive control is possible via a class interface. The API is flexible and can be extended to user-defined proxies and error metrics.

Introduced in: CGAL 4.14
BibTeX: cgal:az-tsma-19b
Depends on: Eigen
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 BGL named parameters. The page Named Parameters describes their usage and provides the list of parameters used in this package.

Concepts

• ErrorMetricProxy

Main Functions

• CGAL::Surface_mesh_approximation::approximate_triangle_mesh()

Classes

• CGAL::Surface_mesh_approximation::L21_metric_plane_proxy
• CGAL::Surface_mesh_approximation::L2_metric_plane_proxy
• CGAL::Variational_shape_approximation

Modules
	Named Parameters
	How to use BGL Optional Named Parameters
	Concepts

Classes
class	CGAL::Surface_mesh_approximation::L21_metric_plane_proxy< TriangleMesh, VertexPointMap, GeomTraits >
	Approximation L21 metric of vector proxy. More...
class	CGAL::Surface_mesh_approximation::L2_metric_plane_proxy< TriangleMesh, VertexPointMap, GeomTraits >
	Approximation L2 metric of plane proxy. More...
class	CGAL::Variational_shape_approximation< TriangleMesh, VertexPointMap, ErrorMetricProxy, GeomTraits, Concurrency_tag >
	Main class for Variational Shape Approximation algorithm. More...

Enumerations
enum	CGAL::Surface_mesh_approximation::Verbose_level { CGAL::Surface_mesh_approximation::SILENT, CGAL::Surface_mesh_approximation::MAIN_STEPS, CGAL::Surface_mesh_approximation::VERBOSE }
	Verbose level enumeration. More...
enum	CGAL::Surface_mesh_approximation::Seeding_method { CGAL::Surface_mesh_approximation::RANDOM, CGAL::Surface_mesh_approximation::INCREMENTAL, CGAL::Surface_mesh_approximation::HIERARCHICAL }
	Seeding method enumeration for Variational Shape Approximation algorithm. More...

Functions
template<typename TriangleMesh , typename NamedParameters >
bool	CGAL::Surface_mesh_approximation::approximate_triangle_mesh (const TriangleMesh &tm, const NamedParameters &np)
	approximates the input mesh with plane proxies. More...

Enumeration Type Documentation

Seeding_method

enum CGAL::Surface_mesh_approximation::Seeding_method

#include <CGAL/Variational_shape_approximation.h>

Seeding method enumeration for Variational Shape Approximation algorithm.

Enumerator
RANDOM	Random seeding.
INCREMENTAL	Incremental seeding.
HIERARCHICAL	Hierarchical seeding.

Verbose_level

enum CGAL::Surface_mesh_approximation::Verbose_level

#include <CGAL/Surface_mesh_approximation/approximate_triangle_mesh.h>

Verbose level enumeration.

Enumerator
SILENT	Silent.
MAIN_STEPS	Main steps.
VERBOSE	Verbose.

Function Documentation

approximate_triangle_mesh()

template<typename TriangleMesh , typename NamedParameters >

bool CGAL::Surface_mesh_approximation::approximate_triangle_mesh	(	const TriangleMesh &	tm,
		const NamedParameters &	np
	)

#include <CGAL/Surface_mesh_approximation/approximate_triangle_mesh.h>

approximates the input mesh with plane proxies.

This function uses the Variational Shape Approximation algorithm described in [1] to approximate a triangle surface mesh, with indexed triangles as output.

Template Parameters

TriangleMesh	model of FaceListGraph
NamedParameters	a sequence of Named Parameters

Parameters

tm	triangle surface mesh to be approximated
np	optional sequence of Named Parameters among the ones listed below

Returns

true if the indexed triangles represent a 2-manifold, oriented surface mesh, and false otherwise.

Approximation Named Parameters

geom_traits	a geometric traits class instance, model of Kernel. Exact constructions kernels are not supported by this function.
vertex_point_map	the property map with the points associated to the vertices of tm. Instance of a class model of ReadablePropertyMap.
verbose_level	set verbose level.
seeding_method	selection of seeding method.
max_number_of_proxies	maximum number of proxies to approximate the input mesh.
min_error_drop	minimum error drop of the approximation, expressed in ratio between two iterations of proxy addition.
number_of_relaxations	number of relaxation iterations interleaved within seeding.
number_of_iterations	number of partitioning and fitting iterations after seeding.

Meshing Named Parameters

subdivision_ratio	chord subdivision ratio threshold to the chord length or average edge length.
relative_to_chord	if true the subdivision_ratio is the ratio of the furthest vertex distance to the chord length, otherwise is the average edge length.
with_dihedral_angle	if set to true the subdivision_ratio is weighted by dihedral angle.
optimize_anchor_location	if set to true, optimize the anchor locations.
pca_plane	set true if use PCA plane fitting, otherwise use the default area averaged plane parameters.

Output Named Parameters

face_proxy_map	a WritablePropertyMap with boost::graph_traits<TriangleMesh>::face_descriptor as key and std::size_t as value type. A proxy is a set of connected faces which are placed under the same proxy patch (see Figure 71.3). The proxy-ids are contiguous in range [0, number_of_proxies - 1].
proxies	output iterator over proxies.
anchors	output iterator over anchor points.
triangles	output iterator over indexed triangles.

Examples:

Surface_mesh_approximation/vsa_approximation_2_example.cpp, Surface_mesh_approximation/vsa_approximation_example.cpp, Surface_mesh_approximation/vsa_segmentation_example.cpp, and Surface_mesh_approximation/vsa_simple_approximation_example.cpp.