CGAL 5.0.1  Point Set Processing

Collection of algorithms of point set processing (smoothing, simplification, etc.).
Classes  
class  CGAL::Point_set_with_structure< Kernel > 
A 3D point set with structure information based on a set of detected planes. More...  
Functions  
template<typename ConcurrencyTag , typename PointRange , typename NamedParameters >  
double  CGAL::bilateral_smooth_point_set (PointRange &points, unsigned int k, const NamedParameters &np) 
This function smooths an input point set by iteratively projecting each point onto the implicit surface patch fitted over its nearest neighbors. More...  
template<typename ConcurrencyTag , typename PointRange , typename CGAL_BGL_NP_TEMPLATE_PARAMETERS >  
FT  CGAL::compute_average_spacing (const PointRange &points, unsigned int k, const CGAL_BGL_NP_CLASS &np) 
Computes average spacing from k nearest neighbors. More...  
template<typename ConcurrencyTag , typename PointRange , typename OutputIterator , typename NamedParameters >  
OutputIterator  CGAL::edge_aware_upsample_point_set (const PointRange &points, OutputIterator output, const NamedParameters &np) 
This method progressively upsamples the point set while approaching the edge singularities (detected by normal variation), which generates a denser point set from an input point set. More...  
template<typename PointRange , typename QueryPointRange , typename OutputIterator , typename NamedParameters >  
OutputIterator  CGAL::estimate_local_k_neighbor_scales (const PointRange &points, const QueryPointRange &queries, OutputIterator output, const NamedParameters &np) 
Estimates the local scale in a K nearest neighbors sense on a set of userdefined query points. More...  
template<typename PointRange , typename NamedParameters >  
std::size_t  CGAL::estimate_global_k_neighbor_scale (const PointRange &points, const NamedParameters &np) 
Estimates the global scale in a K nearest neighbors sense. More...  
template<typename PointRange , typename QueryPointRange , typename OutputIterator , typename NamedParameters >  
OutputIterator  CGAL::estimate_local_range_scales (const PointRange &points, const QueryPointRange &queries, OutputIterator output, const NamedParameters &np) 
Estimates the local scale in a range sense on a set of userdefined query points. More...  
template<typename PointRange , typename NamedParameters >  
FT  CGAL::estimate_global_range_scale (const PointRange &points, const NamedParameters &np) 
Estimates the global scale in a range sense. More...  
template<typename PointRange , typename NamedParameters >  
PointRange::iterator  CGAL::grid_simplify_point_set (PointRange &points, double epsilon, const NamedParameters &np) 
Merges points which belong to the same cell of a grid of cell size = epsilon . More...  
template<typename PointRange , typename NamedParameters >  
PointRange::iterator  CGAL::hierarchy_simplify_point_set (PointRange &points, const NamedParameters &np) 
Recursively split the point set in smaller clusters until the clusters have less than size elements or until their variation factor is below var_max . More...  
template<typename ConcurrencyTag , typename PointRange , typename NamedParameters >  
void  CGAL::jet_estimate_normals (PointRange &points, unsigned int k, const NamedParameters &np) 
Estimates normal directions of the range of points using jet fitting on the nearest neighbors. More...  
template<typename ConcurrencyTag , typename PointRange , typename NamedParameters >  
void  CGAL::jet_smooth_point_set (PointRange &points, unsigned int k, const NamedParameters &np) 
Smoothes the range of points using jet fitting on the nearest neighbors and reprojection onto the jet. More...  
template<typename PointRange , typename NamedParameters >  
PointRange::iterator  CGAL::mst_orient_normals (PointRange &points, unsigned int k, const NamedParameters &np) 
Orients the normals of the range of points using the propagation of a seed orientation through a minimum spanning tree of the Riemannian graph. More...  
template<typename ConcurrencyTag , typename PointRange , typename NamedParameters >  
void  CGAL::pca_estimate_normals (PointRange &points, unsigned int k, const NamedParameters &np) 
Estimates normal directions of the range of points by linear least squares fitting of a plane over the nearest neighbors. More...  
template<typename PointRange >  
PointRange::iterator  CGAL::random_simplify_point_set (PointRange &points, double removed_percentage) 
Randomly deletes a userspecified fraction of the input points. More...  
template<typename PointRange , typename NamedParameters >  
PointRange::iterator  CGAL::remove_outliers (PointRange &points, unsigned int k, const NamedParameters &np) 
Removes outliers: More...  
template<typename PointRange , typename PlaneRange , typename OutputIterator , typename NamedParameters >  
OutputIterator  CGAL::structure_point_set (const PointRange &points, const PlaneRange &planes, OutputIterator output, double epsilon, const NamedParameters &np) 
This is an implementation of the Point Set Structuring algorithm. More...  
template<class FT , class VCMTraits >  
bool  CGAL::vcm_is_on_feature_edge (std::array< FT, 6 > &cov, double threshold, VCMTraits) 
determines if a point is on a sharp feature edge from a point set for which the Voronoi covariance Measures have been computed. More...  
template<typename PointRange , typename NamedParameters >  
void  CGAL::compute_vcm (const PointRange &points, std::vector< std::array< double, 6 > > &ccov, double offset_radius, double convolution_radius, const NamedParameters &np) 
computes the Voronoi Covariance Measure (VCM) of a point cloud, a construction that can be used for normal estimation and sharp feature detection. More...  
template<typename PointRange , typename NamedParameters >  
void  CGAL::vcm_estimate_normals (PointRange &points, double offset_radius, double convolution_radius, const NamedParameters &np) 
Estimates normal directions of the range of points using the Voronoi Covariance Measure with a radius for the convolution. More...  
template<typename PointRange , typename NamedParameters >  
void  CGAL::vcm_estimate_normals (PointRange &points, double offset_radius, unsigned int k, const NamedParameters &np) 
Estimates normal directions of the range of points using the Voronoi Covariance Measure with a number of neighbors for the convolution. More...  
template<typename ConcurrencyTag , typename PointRange , typename OutputIterator , typename NamedParameters >  
OutputIterator  CGAL::wlop_simplify_and_regularize_point_set (PointRange &points, OutputIterator output, const NamedParameters &np) 
This is an implementation of the Weighted Locally Optimal Projection (WLOP) simplification algorithm. More...  
double CGAL::bilateral_smooth_point_set  (  PointRange &  points, 
unsigned int  k,  
const NamedParameters &  np  
) 
#include <CGAL/bilateral_smooth_point_set.h>
This function smooths an input point set by iteratively projecting each point onto the implicit surface patch fitted over its nearest neighbors.
Bilateral projection preserves sharp features according to the normal (gradient) information. Both point positions and normals will be modified. For more details, please see section 4 in [5].
A parallel version of this function is provided and requires the executable to be linked against the Intel TBB library. To control the number of threads used, the user may use the tbb::task_scheduler_init class. See the TBB documentation for more details.
ConcurrencyTag  enables sequential versus parallel algorithm. Possible values are Sequential_tag And Parallel_tag . 
PointRange  is a model of Range . The value type of its iterator is the key type of the named parameter point_map . 
points  input point range. 
k  size of the neighborhood for the implicit surface patch fitting. The larger the value is, the smoother the result will be. 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadWritePropertyMap with value type geom_traits::Point_3 . If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> is used. 
normal_map  a model of ReadWritePropertyMap with value type geom_traits::Vector_3 . 
neighbor_radius  spherical neighborhood radius. If provided, the neighborhood of a query point is computed with a fixed spherical radius instead of a fixed number of neighbors. In that case, the parameter k is used as a limit on the number of points returned by each spherical query (to avoid overly large number of points in high density areas). If no limit is wanted, use k=0 . 
sharpness_angle  controls the sharpness of the result. 
callback  an instance of std::function<bool(double)> . It is called regularly when the algorithm is running: the current advancement (between 0. and 1.) is passed as parameter. If it returns true , then the algorithm continues its execution normally; if it returns false , the algorithm is stopped, all points are left unchanged and the function return NaN . 
geom_traits  an instance of a geometric traits class, model of Kernel 
FT CGAL::compute_average_spacing  (  const PointRange &  points, 
unsigned int  k,  
const CGAL_BGL_NP_CLASS &  np  
) 
#include <CGAL/compute_average_spacing.h>
Computes average spacing from k nearest neighbors.
k >= 2.
ConcurrencyTag  enables sequential versus parallel algorithm. Possible values are Sequential_tag and Parallel_tag . 
PointRange  is a model of ConstRange . The value type of its iterator is the key type of the named parameter point_map . 
points  input point range. 
k  number of neighbors. 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadablePropertyMap with value type geom_traits::Point_3 . If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> is used. 
callback  an instance of std::function<bool(double)> . It is called regularly when the algorithm is running: the current advancement (between 0. and 1.) is passed as parameter. If it returns true , then the algorithm continues its execution normally; if it returns false , the algorithm is stopped and the average spacing value estimated on the processed subset is returned. 
geom_traits  an instance of a geometric traits class, model of Kernel 
FT
is a number type. It is either deduced from the geom_traits
Named Parameters if provided, or the geometric traits class deduced from the point property map of points
. void CGAL::compute_vcm  (  const PointRange &  points, 
std::vector< std::array< double, 6 > > &  ccov,  
double  offset_radius,  
double  convolution_radius,  
const NamedParameters &  np  
) 
#include <CGAL/vcm_estimate_normals.h>
computes the Voronoi Covariance Measure (VCM) of a point cloud, a construction that can be used for normal estimation and sharp feature detection.
The VCM associates to each point the covariance matrix of its Voronoi cell intersected with the ball of radius offset_radius
. In addition, if the second radius convolution_radius
is positive, the covariance matrices are smoothed via a convolution process. More specifically, each covariance matrix is replaced by the average of the matrices of the points located at a distance at most convolution_radius
. The choice for parameter offset_radius
should refer to the geometry of the underlying surface while the choice for parameter convolution_radius
should refer to the noise level in the point cloud. For example, if the point cloud is a uniform and noisefree sampling of a smooth surface, offset_radius
should be set to the minimum local feature size of the surface, while convolution_radius
can be set to zero.
The Voronoi covariance matrix of each vertex is stored in an array a
of length 6 and is as follow:
PointRange  is a model of Range . The value type of its iterator is the key type of the named parameter point_map . 
points  input point range. 
ccov  output range of covariance matrices. 
offset_radius  offset_radius. 
convolution_radius  convolution_radius. 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadablePropertyMap with value type geom_traits::Point_3 . If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> is used. 
geom_traits  an instance of a geometric traits class, model of Kernel 
OutputIterator CGAL::edge_aware_upsample_point_set  (  const PointRange &  points, 
OutputIterator  output,  
const NamedParameters &  np  
) 
#include <CGAL/edge_aware_upsample_point_set.h>
This method progressively upsamples the point set while approaching the edge singularities (detected by normal variation), which generates a denser point set from an input point set.
This has applications in pointbased rendering, hole filling, and sparse surface reconstruction. Normals of points are required as input. For more details, please refer to [5].
ConcurrencyTag  enables sequential versus parallel versions of compute_average_spacing() (called internally). Possible values are Sequential_tag and Parallel_tag . 
PointRange  is a model of ConstRange . The value type of its iterator is the key type of the named parameter point_map . 
OutputIterator  Type of the output iterator. The type of the objects put in it is std::pair<geom_traits::Point_3, geom_traits::Vector_3> . Note that the user may use a function_output_iterator to match specific needs. 
points  input point range. 
output  iterator where output points and normals are put. 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadablePropertyMap with value type geom_traits::Point_3 . If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> is used. 
normal_map  a model of ReadablePropertyMap with value type geom_traits::Vector_3 . 
sharpness_angle  controls the sharpness of the result. 
edge_sensitivity  controls the priority of points inserted along sharp features. See section Parameter: edge_sensitivity for an example. 
neighbor_radius  spherical neighborhood radius. 
number_of_output_points  is the number of output points to generate. 
geom_traits  an instance of a geometric traits class, model of Kernel 
std::size_t CGAL::estimate_global_k_neighbor_scale  (  const PointRange &  points, 
const NamedParameters &  np  
) 
#include <CGAL/estimate_scale.h>
Estimates the global scale in a K nearest neighbors sense.
The computed scale corresponds to the smallest scale such that the K subsets of points have the appearance of a surface in 3D or the appearance of a curve in 2D (see Automatic Scale Estimation).
PointRange  is a model of ConstRange . The value type of its iterator is the key type of the named parameter point_map . 
points  input point range. 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadablePropertyMap with value type geom_traits::Point_3 (or geom_traits::Point_2 ). If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> (or CGAL::Identity_property_map<geom_traits::Point_2> ) is used. 
geom_traits  an instance of a geometric traits class, model of Kernel 
FT CGAL::estimate_global_range_scale  (  const PointRange &  points, 
const NamedParameters &  np  
) 
#include <CGAL/estimate_scale.h>
Estimates the global scale in a range sense.
The computed scale corresponds to the smallest scale such that the subsets of points inside the sphere range have the appearance of a surface in 3D or the appearance of a curve in 2D (see Automatic Scale Estimation).
PointRange  is a model of ConstRange . The value type of its iterator is the key type of the named parameter point_map . 
points  input point range. 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadablePropertyMap with value type geom_traits::Point_3 (or geom_traits::Point_2 ). If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> (or CGAL::Identity_property_map<geom_traits::Point_2> ) is used. 
geom_traits  an instance of a geometric traits class, model of Kernel 
FT
is a number type. It is either deduced from the geom_traits
Named Parameters if provided, or the geometric traits class deduced from the point property map of points
. OutputIterator CGAL::estimate_local_k_neighbor_scales  (  const PointRange &  points, 
const QueryPointRange &  queries,  
OutputIterator  output,  
const NamedParameters &  np  
) 
#include <CGAL/estimate_scale.h>
Estimates the local scale in a K nearest neighbors sense on a set of userdefined query points.
The computed scales correspond to the smallest scales such that the K subsets of points have the appearance of a surface in 3D or the appearance of a curve in 2D (see Automatic Scale Estimation).
PointRange  is a model of ConstRange . The value type of its iterator is the key type of the named parameter point_map . 
QueryPointRange  is a model of ConstRange . The value type of its iterator is the key type of the named parameter query_point_map . 
OutputIterator  is used to store the computed scales. It accepts values of type std::size_t . 
points  input point range. 
queries  range of locations where scale must be estimated 
output  iterator to store the computed scales 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadablePropertyMap with value type geom_traits::Point_3 (or geom_traits::Point_2 ). If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> (or CGAL::Identity_property_map<geom_traits::Point_2> ) is used. 
query_point_map  a model of ReadablePropertyMap with value type geom_traits::Point_3 (or geom_traits::Point_2 ). If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> (or CGAL::Identity_property_map<geom_traits::Point_2> ) is used. 
geom_traits  an instance of a geometric traits class, model of Kernel 
OutputIterator CGAL::estimate_local_range_scales  (  const PointRange &  points, 
const QueryPointRange &  queries,  
OutputIterator  output,  
const NamedParameters &  np  
) 
#include <CGAL/estimate_scale.h>
Estimates the local scale in a range sense on a set of userdefined query points.
The computed scales correspond to the smallest scales such that the subsets of points included in the sphere range have the appearance of a surface in 3D or the appearance of a curve in 2D (see Automatic Scale Estimation).
PointRange  is a model of ConstRange . The value type of its iterator is the key type of the named parameter point_map . 
QueryPointRange  is a model of ConstRange . The value type of its iterator is the key type of the named parameter query_point_map . 
OutputIterator  is used to store the computed scales. It accepts values of type geom_traits::FT . 
points  input point range. 
queries  range of locations where scale must be estimated 
output  iterator to store the computed scales 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadablePropertyMap with value type geom_traits::Point_3 (or geom_traits::Point_2 ). If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> (or CGAL::Identity_property_map<geom_traits::Point_2> ) is used. 
query_point_map  a model of ReadablePropertyMap with value type geom_traits::Point_3 (or geom_traits::Point_2 ). If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> (or CGAL::Identity_property_map<geom_traits::Point_2> ) is used. 
geom_traits  an instance of a geometric traits class, model of Kernel 
PointRange::iterator CGAL::grid_simplify_point_set  (  PointRange &  points, 
double  epsilon,  
const NamedParameters &  np  
) 
#include <CGAL/grid_simplify_point_set.h>
Merges points which belong to the same cell of a grid of cell size = epsilon
.
This method modifies the order of input points so as to pack all remaining points first, and returns an iterator over the first point to remove (see eraseremove idiom). For this reason it should not be called on sorted containers.
epsilon > 0
PointRange  is a model of Range . The value type of its iterator is the key type of the named parameter point_map . 
points  input point range. 
epsilon  tolerance value when merging 3D points. 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadWritePropertyMap with value type geom_traits::Point_3 . If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> is used. 
callback  an instance of std::function<bool(double)> . It is called regularly when the algorithm is running: the current advancement (between 0. and 1.) is passed as parameter. If it returns true , then the algorithm continues its execution normally; if it returns false , the algorithm is stopped and simplification stops with no guarantee on the output. 
geom_traits  an instance of a geometric traits class, model of Kernel 
PointRange::iterator CGAL::hierarchy_simplify_point_set  (  PointRange &  points, 
const NamedParameters &  np  
) 
#include <CGAL/hierarchy_simplify_point_set.h>
Recursively split the point set in smaller clusters until the clusters have less than size
elements or until their variation factor is below var_max
.
This method modifies the order of input points so as to pack all remaining points first, and returns an iterator over the first point to remove (see eraseremove idiom). For this reason it should not be called on sorted containers.
0 < maximum_variation < 1/3
size > 0
PointRange  is a model of Range . The value type of its iterator is the key type of the named parameter point_map . 
points  input point range. 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadWritePropertyMap with value type geom_traits::Point_3 . If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> is used. 
size  maximum cluster size. 
maximum_variation  maximum cluster variation value. 
diagonalize_traits  a model of DiagonalizeTraits . It can be omitted: if Eigen 3 (or greater) is available and CGAL_EIGEN3_ENABLED is defined then an overload using Eigen_diagonalize_traits is provided. Otherwise, the internal implementation CGAL::Diagonalize_traits is used. 
callback  an instance of std::function<bool(double)> . It is called regularly when the algorithm is running: the current advancement (between 0. and 1.) is passed as parameter. If it returns true , then the algorithm continues its execution normally; if it returns false , the algorithm is stopped and simplification stops with no guarantee on the output. 
geom_traits  an instance of a geometric traits class, model of Kernel 
void CGAL::jet_estimate_normals  (  PointRange &  points, 
unsigned int  k,  
const NamedParameters &  np  
) 
#include <CGAL/jet_estimate_normals.h>
Estimates normal directions of the range of points
using jet fitting on the nearest neighbors.
The output normals are randomly oriented.
k >= 2
ConcurrencyTag  enables sequential versus parallel algorithm. Possible values are Sequential_tag and Parallel_tag . 
PointRange  is a model of Range . The value type of its iterator is the key type of the named parameter point_map . 
points  input point range. 
k  number of neighbors 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadablePropertyMap with value type geom_traits::Point_3 . If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> is used. 
normal_map  a model of ReadWritePropertyMap with value type geom_traits::Vector_3 . 
neighbor_radius  spherical neighborhood radius. If provided, the neighborhood of a query point is computed with a fixed spherical radius instead of a fixed number of neighbors. In that case, the parameter k is used as a limit on the number of points returned by each spherical query (to avoid overly large number of points in high density areas). If no limit is wanted, use k=0 . 
degree_fitting  degree of jet fitting. 
svd_traits  template parameter for the class Monge_via_jet_fitting . If Eigen 3.2 (or greater) is available and CGAL_EIGEN3_ENABLED is defined, then CGAL::Eigen_svd is used. 
callback  an instance of std::function<bool(double)> . It is called regularly when the algorithm is running: the current advancement (between 0. and 1.) is passed as parameter. If it returns true , then the algorithm continues its execution normally; if it returns false , the algorithm is stopped and the remaining normals are left unchanged. 
geom_traits  an instance of a geometric traits class, model of Kernel 
void CGAL::jet_smooth_point_set  (  PointRange &  points, 
unsigned int  k,  
const NamedParameters &  np  
) 
#include <CGAL/jet_smooth_point_set.h>
Smoothes the range of points
using jet fitting on the nearest neighbors and reprojection onto the jet.
As this method relocates the points, it should not be called on containers sorted w.r.t. point locations.
k >= 2
ConcurrencyTag  enables sequential versus parallel algorithm. Possible values are Sequential_tag and Parallel_tag . 
PointRange  is a model of Range . The value type of its iterator is the key type of the named parameter point_map . 
points  input point range. 
k  number of neighbors 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadablePropertyMap with value type geom_traits::Point_3 . If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> is used. 
neighbor_radius  spherical neighborhood radius. If provided, the neighborhood of a query point is computed with a fixed spherical radius instead of a fixed number of neighbors. In that case, the parameter k is used as a limit on the number of points returned by each spherical query (to avoid overly large number of points in high density areas). If no limit is wanted, use k=0 . 
degree_fitting  degree of jet fitting. 
degree_monge  Monge degree. 
svd_traits  template parameter for the class Monge_via_jet_fitting . If Eigen 3.2 (or greater) is available and CGAL_EIGEN3_ENABLED is defined, then CGAL::Eigen_svd is used. 
callback  an instance of std::function<bool(double)> . It is called regularly when the algorithm is running: the current advancement (between 0. and 1.) is passed as parameter. If it returns true , then the algorithm continues its execution normally; if it returns false , the algorithm is stopped and the remaining points are left unchanged. 
geom_traits  an instance of a geometric traits class, model of Kernel 
PointRange::iterator CGAL::mst_orient_normals  (  PointRange &  points, 
unsigned int  k,  
const NamedParameters &  np  
) 
#include <CGAL/mst_orient_normals.h>
Orients the normals of the range of points
using the propagation of a seed orientation through a minimum spanning tree of the Riemannian graph.
This method modifies the order of input points so as to pack all sucessfully oriented points first, and returns an iterator over the first point with an unoriented normal (see eraseremove idiom). For this reason it should not be called on sorted containers. It is based on [3].
k >= 2
PointRange  is a model of Range . The value type of its iterator is the key type of the named parameter point_map . 
points  input point range. 
k  number of neighbors. 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadablePropertyMap with value type geom_traits::Point_3 . If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> is used. 
normal_map  a model of ReadWritePropertyMap with value type geom_traits::Vector_3 . 
neighbor_radius  spherical neighborhood radius. If provided, the neighborhood of a query point is computed with a fixed spherical radius instead of a fixed number of neighbors. In that case, the parameter k is used as a limit on the number of points returned by each spherical query (to avoid overly large number of points in high density areas). If no limit is wanted, use k=0 . 
point_is_constrained_map  a model of ReadablePropertyMap with value type bool . Points with a true value will be used as seed points: their normal will be considered as already oriented, it won't be altered and it will be propagated to its neighbors. If this parameter is omitted, the highest point (highest Z coordinate) will be used as the unique seed with an upward oriented normal 
geom_traits  an instance of a geometric traits class, model of Kernel 
void CGAL::pca_estimate_normals  (  PointRange &  points, 
unsigned int  k,  
const NamedParameters &  np  
) 
#include <CGAL/pca_estimate_normals.h>
Estimates normal directions of the range of points
by linear least squares fitting of a plane over the nearest neighbors.
The output normals are randomly oriented.
k >= 2
ConcurrencyTag  enables sequential versus parallel algorithm. Possible values are Sequential_tag and Parallel_tag . 
PointRange  is a model of Range . The value type of its iterator is the key type of the named parameter point_map . 
points  input point range. 
k  number of neighbors 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadablePropertyMap with value type geom_traits::Point_3 . If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> is used. 
normal_map  a model of WritablePropertyMap with value type geom_traits::Vector_3 . 
neighbor_radius  spherical neighborhood radius. If provided, the neighborhood of a query point is computed with a fixed spherical radius instead of a fixed number of neighbors. In that case, the parameter k is used as a limit on the number of points returned by each spherical query (to avoid overly large number of points in high density areas). If no limit is wanted, use k=0 . 
callback  an instance of std::function<bool(double)> . It is called regularly when the algorithm is running: the current advancement (between 0. and 1.) is passed as parameter. If it returns true , then the algorithm continues its execution normally; if it returns false , the algorithm is stopped and the remaining normals are left unchanged. 
geom_traits  an instance of a geometric traits class, model of Kernel 
PointRange::iterator CGAL::random_simplify_point_set  (  PointRange &  points, 
double  removed_percentage  
) 
#include <CGAL/random_simplify_point_set.h>
Randomly deletes a userspecified fraction of the input points.
This method modifies the order of input points so as to pack all remaining points first, and returns an iterator over the first point to remove (see eraseremove idiom). For this reason it should not be called on sorted containers.
PointRange  is a model of Range . 
points  input point range. 
removed_percentage  percentage of points to remove. 
PointRange::iterator CGAL::remove_outliers  (  PointRange &  points, 
unsigned int  k,  
const NamedParameters &  np  
) 
#include <CGAL/remove_outliers.h>
Removes outliers:
This method modifies the order of input points so as to pack all remaining points first, and returns an iterator over the first point to remove (see eraseremove idiom). For this reason it should not be called on sorted containers.
k >= 2
PointRange  is a model of Range . The value type of its iterator is the key type of the named parameter point_map . 
points  input point range. 
k  number of neighbors 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadablePropertyMap with value type geom_traits::Point_3 . If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> is used. 
neighbor_radius  spherical neighborhood radius. If provided, the neighborhood of a query point is computed with a fixed spherical radius instead of a fixed number of neighbors. In that case, the parameter k is used as a limit on the number of points returned by each spherical query (to avoid overly large number of points in high density areas). If no limit is wanted, use k=0 . 
threshold_percent  maximum percentage of points to remove. 
threshold_distance  minimum distance for a point to be considered as outlier (distance here is the square root of the average squared distance to K nearest neighbors). 
callback  an instance of std::function<bool(double)> . It is called regularly when the algorithm is running: the current advancement (between 0. and 1.) is passed as parameter. If it returns true , then the algorithm continues its execution normally; if it returns false , the algorithm is stopped, all points are left unchanged and the function return points.end() . 
geom_traits  an instance of a geometric traits class, model of Kernel 
threshold_percent
and threshold_distance
. This function returns the smallest number of outliers such that at least one of these threshold is fulfilled. This means that if threshold_percent=100
, only threshold_distance
is taken into account; if threshold_distance=0
only threshold_percent
is taken into account. OutputIterator CGAL::structure_point_set  (  const PointRange &  points, 
const PlaneRange &  planes,  
OutputIterator  output,  
double  epsilon,  
const NamedParameters &  np  
) 
#include <CGAL/structure_point_set.h>
This is an implementation of the Point Set Structuring algorithm.
This algorithm takes advantage of a set of detected planes: it detects adjacency relationships between planes and resamples the detected planes, edges and corners to produce a structured point set.
The size parameter epsilon
is used both for detecting adjacencies and for setting the sampling density of the structured point set.
For more details, please refer to [6].
PointRange  is a model of ConstRange . The value type of its iterator is the key type of the named parameter point_map . 
PlaneRange  is a model of ConstRange . The value type of its iterator is the key type of the named parameter plane_map . 
OutputIterator  Type of the output iterator. The type of the objects put in it is std::pair<Kernel::Point_3, Kernel::Vector_3> . Note that the user may use a function_output_iterator to match specific needs. 
points  input point range. 
planes  input plane range. 
output  output iterator where output points are written 
epsilon  size parameter. 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadablePropertyMap with value type geom_traits::Point_3 . If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> is used. 
normal_map  a model of ReadablePropertyMap with value type geom_traits::Vector_3 . 
plane_index_map  a model of ReadablePropertyMap with value type int . Associates the index of a point in the input range to the index of plane (1 if point does is not assigned to a plane). 
plane_map  a model of ReadablePropertyMap with value type geom_traits::Plane_3 . If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Plane_3> is used. 
attraction_factor  multiple of epsilon used to connect simplices. 
geom_traits  an instance of a geometric traits class, model of Kernel 
void CGAL::vcm_estimate_normals  (  PointRange &  points, 
double  offset_radius,  
double  convolution_radius,  
const NamedParameters &  np  
) 
#include <CGAL/vcm_estimate_normals.h>
Estimates normal directions of the range of points
using the Voronoi Covariance Measure with a radius for the convolution.
The output normals are randomly oriented.
See compute_vcm()
for a detailed description of the parameters offset_radius
and convolution_radius
and of the Voronoi Covariance Measure.
PointRange  is a model of Range . The value type of its iterator is the key type of the named parameter point_map . 
points  input point range. 
offset_radius  offset_radius. 
convolution_radius  convolution_radius. 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadablePropertyMap with value type geom_traits::Point_3 . If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> is used. 
normal_map  a model of WritablePropertyMap with value type geom_traits::Vector_3 . 
diagonalize_traits  a model of DiagonalizeTraits . It can be omitted: if Eigen 3 (or greater) is available and CGAL_EIGEN3_ENABLED is defined then an overload using Eigen_diagonalize_traits is provided. Otherwise, the internal implementation CGAL::Diagonalize_traits is used. 
geom_traits  an instance of a geometric traits class, model of Kernel 
void CGAL::vcm_estimate_normals  (  PointRange &  points, 
double  offset_radius,  
unsigned int  k,  
const NamedParameters &  np  
) 
#include <CGAL/vcm_estimate_normals.h>
Estimates normal directions of the range of points
using the Voronoi Covariance Measure with a number of neighbors for the convolution.
The output normals are randomly oriented.
See compute_vcm()
for a detailed description of the parameter offset_radius
and of the Voronoi Covariance Measure.
PointRange  is a model of Range . The value type of its iterator is the key type of the named parameter point_map . 
points  input point range. 
offset_radius  offset_radius. 
k  number of neighbor points used for convolution. 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadablePropertyMap with value type geom_traits::Point_3 . If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> is used. 
normal_map  a model of WritablePropertyMap with value type geom_traits::Vector_3 . 
diagonalize_traits  a model of DiagonalizeTraits . It can be omitted: if Eigen 3 (or greater) is available and CGAL_EIGEN3_ENABLED is defined then an overload using Eigen_diagonalize_traits is provided. Otherwise, the internal implementation CGAL::Diagonalize_traits is used. 
geom_traits  an instance of a geometric traits class, model of Kernel 
bool CGAL::vcm_is_on_feature_edge  (  std::array< FT, 6 > &  cov, 
double  threshold,  
VCMTraits  
) 
#include <CGAL/vcm_estimate_edges.h>
determines if a point is on a sharp feature edge from a point set for which the Voronoi covariance Measures have been computed.
The sharpness of the edge, specified by parameter threshold
, is used to filtered points according to the external angle around a sharp feature.
A point is considered to be on a sharp feature if the external angle alpha
at the edge is such that alpha >= 2 / sqrt(3) * sqrt(threshold)
. In particular this means that if the input contains sharp features with different external angles, the one with the smallest external angle should be considered, which however would result in selecting more points on sharper regions. More details are provided in [7].
VCMTraits  is a model of DiagonalizeTraits . It can be omitted: if Eigen 3 (or greater) is available and CGAL_EIGEN3_ENABLED is defined then an overload using Eigen_diagonalize_traits is provided. Otherwise, the internal implementation Diagonalize_traits is used. 
OutputIterator CGAL::wlop_simplify_and_regularize_point_set  (  PointRange &  points, 
OutputIterator  output,  
const NamedParameters &  np  
) 
#include <CGAL/wlop_simplify_and_regularize_point_set.h>
This is an implementation of the Weighted Locally Optimal Projection (WLOP) simplification algorithm.
The WLOP simplification algorithm can produce a set of denoised, outlierfree and evenly distributed particles over the original dense point cloud. The core of the algorithm is a Weighted Locally Optimal Projection operator with a density uniformization term. For more details, please refer to [4].
A parallel version of WLOP is provided and requires the executable to be linked against the Intel TBB library. To control the number of threads used, the user may use the tbb::task_scheduler_init class. See the TBB documentation for more details.
ConcurrencyTag  enables sequential versus parallel algorithm. Possible values are Sequential_tag and Parallel_tag . 
PointRange  is a model of Range . The value type of its iterator is the key type of the named parameter point_map . 
OutputIterator  Type of the output iterator. It must accept objects of type geom_traits::Point_3 . 
points  input point range. 
output  iterator where output points are put. 
np  optional sequence of Named Parameters among the ones listed below. 
point_map  a model of ReadWritePropertyMap with value type geom_traits::Point_3 . If this parameter is omitted, CGAL::Identity_property_map<geom_traits::Point_3> is used. 
normal_map  a model of ReadWritePropertyMap with value type geom_traits::Vector_3 . 
select_percentage  percentage of points to retain. The default value is set to 5 (%). 
neighbor_radius  spherical neighborhood radius. This is a key parameter that needs to be finely tuned. The result will be irregular if too small, but a larger value will impact the runtime. In practice, choosing a radius such that the neighborhood of each sample point includes at least two rings of neighboring sample points gives satisfactory result. If this parameter is not provided, it is automatically set to 8 times the average spacing of the point set. 
number_of_iterations  number of iterations to solve the optimsation problem. The default value is 35. More iterations give a more regular result but increase the runtime. 
require_uniform_sampling  an optional preprocessing, which will give better result if the distribution of the input points is highly nonuniform. The default value is false . 
callback  an instance of std::function<bool(double)> . It is called regularly when the algorithm is running: the current advancement (between 0. and 1.) is passed as parameter. If it returns true , then the algorithm continues its execution normally; if it returns false , the algorithm is stopped, no output points are generated. 
geom_traits  an instance of a geometric traits class, model of Kernel 