Pierre Alliez, David Cohen-Steiner, and 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.
Parameters
Optional parameters of the functions of this package are implemented as BGL named parameters. The page Named Parameters describes their usage.
Concepts
Main Functions
Classes
◆
#include <CGAL/Variational_shape_approximation.h>
Seeding method enumeration for Variational Shape Approximation algorithm.
Enumerator Random seeding.
Incremental seeding.
Hierarchical seeding.
◆
#include <CGAL/Surface_mesh_approximation/approximate_triangle_mesh.h>
Verbose level enumeration.
Enumerator Silent.
Main steps.
Verbose.
◆
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
Parameters
tm triangle surface mesh to be approximated np an 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
an instance of a geometric traits class
Type: a model of Kernel
Default: a CGAL Kernel deduced from the point type, using CGAL::Kernel_traits
Extra: Exact constructions kernels are not supported by this function.
vertex_point_map
a property map associating points to the vertices of tm
Type: a class model of ReadablePropertyMap 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.
verbose_level
the verbose level
Type: CGAL::Surface_mesh_approximation::Verbose_level
Default: CGAL::Surface_mesh_approximation::SILENT
seeding_method
the selection of seeding method
Type: CGAL::Surface_mesh_approximation::Seeding_method
Default: CGAL::Surface_mesh_approximation::HIERARCHICAL
max_number_of_proxies
the maximum number of proxies used to approximate the input mesh
Type: std::size_t
Default: num_faces(tm) / 3, used when min_error_drop is also not provided
min_error_drop
the minimum error drop of the approximation, expressed as the ratio between two iterations of proxy addition
Type: geom_traits::FT
Default: 0.1, used when max_number_of_proxies is also not provided
number_of_relaxations
the number of relaxation iterations interleaved within seeding
Type: std::size_t
Default: 5
number_of_iterations
the number of partitioning and fitting iterations after seeding
Type: std::size_t
Default: std::min(std::max(number_of_faces / max_number_of_proxies, 20), 60)
Meshing Named Parameters
subdivision_ratio
the chord subdivision ratio threshold to the chord length or average edge length
Type: geom_traits::FT
Default: 5.0
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
Type: Boolean
Default: false
with_dihedral_angle
If true, the subdivision_ratio is weighted by dihedral angle
Type: Boolean
Default: false
optimize_anchor_location
If true, optimize the anchor locations
Type: Boolean
Default: true
pca_plane
If true, use PCA plane fitting, otherwise use the default area averaged plane parameters
Type: Boolean
Default: false
Output Named Parameters
face_proxy_map
a property map to output the proxy index of each face of the input polygon mesh
Type: a model of WritablePropertyMap boost::graph_traits<TriangleMesh>::face_descriptor as key and std::size_t as value type
Default: no output operation is performed
Extra: A proxy is a set of connected faces which are placed under the same proxy patch (see Figure 76.3 )
Extra: The proxy-ids are contiguous in range [0, number_of_proxies - 1]
proxies
an OutputIterator
Type: a class model of OutputIterator CGAL::Surface_mesh_approximation::L21_metric_vector_proxy_no_area_weighting::Proxy value type
Default: no output operation is performed
anchors
an OutputIterator
Type: a class model of OutputIterator geom_traits::Point_3 value type
Default: no output operation is performed
triangles
an OutputIterator
Type: a class model of OutputIterator std::array<std::size_t, 3> value type
Default: no output operation is performed
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 .
1.8.13