CGAL 5.6.3 - Triangulated Surface Mesh Approximation

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Triangulated Surface Mesh Approximation Reference

##

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.
Introduced in: CGAL 4.14
BibTeX: cgal:az-tsma-25b
Depends on: Eigen
License: GPL
Windows Demo: Polyhedron demo

## 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.

## 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
| 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.

## 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 | 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

  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. |
  a property map associating points to the vertices of `tm` 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, tm)` Extra: If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` must be available in `TriangleMesh`. |
  the verbose level Type: `CGAL::Surface_mesh_approximation::Verbose_level` Default: `CGAL::Surface_mesh_approximation::SILENT` |
  the selection of seeding method Type: `CGAL::Surface_mesh_approximation::Seeding_method` Default: `CGAL::Surface_mesh_approximation::HIERARCHICAL` |
  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 |
  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 |
  the number of relaxation iterations interleaved within seeding Type: `std::size_t` Default: `5` |
  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

  the chord subdivision ratio threshold to the chord length or average edge length Type: `geom_traits::FT` Default: `5.0` |
  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` |
  If `true`, the `subdivision_ratio` is weighted by dihedral angle Type: `Boolean` Default: `false` |
  If `true`, optimize the anchor locations Type: `Boolean` Default: `true` |
  If `true`, use PCA plane fitting, otherwise use the default area averaged plane parameters Type: `Boolean` Default: `false` |

Output Named Parameters

  a property map to output the proxy index of each face of the input polygon mesh Type: a model of `WritablePropertyMap` with `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]` |
  an `OutputIterator` to put proxies in Type: a class model of `OutputIterator` with `CGAL::Surface_mesh_approximation::L21_metric_vector_proxy_no_area_weighting::Proxy` value type Default: no output operation is performed |
  an `OutputIterator` to put anchor points in Type: a class model of `OutputIterator` with `geom_traits::Point_3` value type Default: no output operation is performed |
  an `OutputIterator` to put indexed triangles in Type: a class model of `OutputIterator` with `std::array<std::size_t, 3>` value type Default: no output operation is performed |