CGAL 4.11 - Point Set Processing

Collection of algorithms of point set processing (smoothing, simplification, etc.).

## Classes

class  CGAL::Point_set_with_structure< Traits >
A 3D point set with structure information based on a set of detected planes. More...

## Functions

template<class FT , class VCMTraits >
bool CGAL::vcm_is_on_feature_edge (cpp11::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<class ForwardIterator , class PointPMap , class Kernel >
void CGAL::compute_vcm (ForwardIterator first, ForwardIterator beyond, PointPMap point_pmap, std::vector< cpp11::array< typename Kernel::FT, 6 > > &ccov, double offset_radius, double convolution_radius, const Kernel &kernel)
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 ForwardIterator , typename PointPMap , typename NormalPMap , typename VCMTraits >
void CGAL::vcm_estimate_normals (ForwardIterator first, ForwardIterator beyond, PointPMap point_pmap, NormalPMap normal_pmap, double offset_radius, double convolution_radius, VCMTraits)
Estimates normal directions of the points in the range [first, beyond) using the Voronoi Covariance Measure with a radius for the convolution. More...

template<typename ForwardIterator , typename PointPMap , typename NormalPMap , typename VCMTraits >
void CGAL::vcm_estimate_normals (ForwardIterator first, ForwardIterator beyond, PointPMap point_pmap, NormalPMap normal_pmap, double offset_radius, unsigned int k, VCMTraits)
Estimates normal directions of the points in the range [first, beyond) using the Voronoi Covariance Measure with a number of neighbors for the convolution. More...

template<typename Traits , typename OutputIterator >
OutputIterator CGAL::structure_point_set (typename Traits::Input_range::iterator first, typename Traits::Input_range::iterator beyond, typename Traits::Point_map point_map, typename Traits::Normal_map normal_map, OutputIterator output, Shape_detection_3::Efficient_RANSAC< Traits > &shape_detection, double epsilon, double attraction_factor=3.)
This is an implementation of the Point Set Structuring algorithm. More...

template<typename ForwardIterator , typename PointPMap , typename NormalPMap , typename Kernel >
ForwardIterator CGAL::mst_orient_normals (ForwardIterator first, ForwardIterator beyond, PointPMap point_pmap, NormalPMap normal_pmap, unsigned int k, const Kernel &kernel)
Orients the normals of the [first, beyond) range of points using the propagation of a seed orientation through a minimum spanning tree of the Riemannian graph [Hoppe92]. More...

template<typename Concurrency_tag , typename OutputIterator , typename RandomAccessIterator , typename PointPMap , typename Kernel >
OutputIterator CGAL::wlop_simplify_and_regularize_point_set (RandomAccessIterator first, RandomAccessIterator beyond, OutputIterator output, PointPMap point_pmap, double select_percentage, double radius, unsigned int iter_number, bool require_uniform_sampling, const Kernel &)
This is an implementation of the Weighted Locally Optimal Projection (WLOP) simplification algorithm. More...

template<typename Concurrency_tag , typename ForwardIterator , typename PointPMap , typename NormalPMap , typename Kernel >
double CGAL::bilateral_smooth_point_set (ForwardIterator first, ForwardIterator beyond, PointPMap point_pmap, NormalPMap normal_pmap, unsigned int k, typename Kernel::FT sharpness_angle, const Kernel &)
This function smooths an input point set by iteratively projecting each point onto the implicit surface patch fitted over its k nearest neighbors. More...

template<typename Concurrency_tag , typename OutputIterator , typename ForwardIterator , typename PointPMap , typename NormalPMap , typename Kernel >
OutputIterator CGAL::edge_aware_upsample_point_set (ForwardIterator first, ForwardIterator beyond, OutputIterator output, PointPMap point_pmap, NormalPMap normal_pmap, const typename Kernel::FT sharpness_angle, typename Kernel::FT edge_sensitivity, typename Kernel::FT neighbor_radius, const std::size_t number_of_output_points, const Kernel &)
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 ForwardIterator , typename PointPMap , typename DiagonalizeTraits , typename Kernel >
ForwardIterator CGAL::hierarchy_simplify_point_set (ForwardIterator begin, ForwardIterator end, PointPMap point_pmap, const unsigned int size, const double var_max, const DiagonalizeTraits &, const Kernel &)
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 ForwardIterator , typename PointPMap , typename Kernel >
ForwardIterator CGAL::random_simplify_point_set (ForwardIterator first, ForwardIterator beyond, PointPMap, double removed_percentage, const Kernel &)
Randomly deletes a user-specified fraction of the input points. More...

template<typename Concurrency_tag , typename InputIterator , typename PointPMap , typename Kernel , typename SvdTraits >
void CGAL::jet_smooth_point_set (InputIterator first, InputIterator beyond, PointPMap point_pmap, unsigned int k, const Kernel &, unsigned int degree_fitting=2, unsigned int degree_monge=2)
Smoothes the [first, beyond) range of points using jet fitting on the k nearest neighbors and reprojection onto the jet. More...

template<typename Concurrency_tag , typename InputIterator , typename PointPMap , typename Kernel >
Kernel::FT CGAL::compute_average_spacing (InputIterator first, InputIterator beyond, PointPMap point_pmap, unsigned int k, const Kernel &)
Computes average spacing from k nearest neighbors. More...

template<typename Concurrency_tag , typename ForwardIterator , typename PointPMap , typename NormalPMap , typename Kernel , typename SvdTraits >
void CGAL::jet_estimate_normals (ForwardIterator first, ForwardIterator beyond, PointPMap point_pmap, NormalPMap normal_pmap, unsigned int k, const Kernel &, unsigned int degree_fitting=2)
Estimates normal directions of the [first, beyond) range of points using jet fitting on the k nearest neighbors. More...

template<typename SamplesInputIterator , typename SamplesPointPMap , typename QueriesInputIterator , typename QueriesPointPMap , typename OutputIterator , typename Kernel >
OutputIterator CGAL::estimate_local_k_neighbor_scales (SamplesInputIterator first, SamplesInputIterator beyond, SamplesPointPMap samples_pmap, QueriesInputIterator first_query, QueriesInputIterator beyond_query, QueriesPointPMap queries_pmap, OutputIterator output, const Kernel &)
Estimates the local scale in a K nearest neighbors sense on a set of user-defined query points. More...

template<typename InputIterator , typename PointPMap , typename Kernel >
std::size_t CGAL::estimate_global_k_neighbor_scale (InputIterator first, InputIterator beyond, PointPMap point_pmap, const Kernel &kernel)
Estimates the global scale in a K nearest neighbors sense. More...

template<typename SamplesInputIterator , typename SamplesPointPMap , typename QueriesInputIterator , typename QueriesPointPMap , typename OutputIterator , typename Kernel >
OutputIterator CGAL::estimate_local_range_scales (SamplesInputIterator first, SamplesInputIterator beyond, SamplesPointPMap samples_pmap, QueriesInputIterator first_query, QueriesInputIterator beyond_query, QueriesPointPMap queries_pmap, OutputIterator output, const Kernel &)
Estimates the local scale in a range sense on a set of user-defined query points. More...

template<typename InputIterator , typename PointPMap , typename Kernel >
Kernel::FT CGAL::estimate_global_range_scale (InputIterator first, InputIterator beyond, PointPMap point_pmap, const Kernel &kernel)
Estimates the global scale in a range sense. More...

template<typename Concurrency_tag , typename ForwardIterator , typename PointPMap , typename NormalPMap , typename Kernel >
void CGAL::pca_estimate_normals (ForwardIterator first, ForwardIterator beyond, PointPMap point_pmap, NormalPMap normal_pmap, unsigned int k, const Kernel &)
Estimates normal directions of the [first, beyond) range of points by linear least squares fitting of a plane over the k nearest neighbors. More...

template<typename InputIterator , typename PointPMap , typename Kernel >
InputIterator CGAL::remove_outliers (InputIterator first, InputIterator beyond, PointPMap point_pmap, unsigned int k, double threshold_percent, double threshold_distance, const Kernel &)
Removes outliers: More...

template<typename ForwardIterator , typename PointPMap , typename Kernel >
ForwardIterator CGAL::grid_simplify_point_set (ForwardIterator first, ForwardIterator beyond, PointPMap point_pmap, double epsilon, const Kernel &)
Merges points which belong to the same cell of a grid of cell size = epsilon. More...

## Function Documentation

template<typename Concurrency_tag , typename ForwardIterator , typename PointPMap , typename NormalPMap , typename Kernel >
 double CGAL::bilateral_smooth_point_set ( ForwardIterator first, ForwardIterator beyond, PointPMap point_pmap, NormalPMap normal_pmap, unsigned int k, typename Kernel::FT sharpness_angle, const Kernel & )

This function smooths an input point set by iteratively projecting each point onto the implicit surface patch fitted over its k 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.

Precondition
Normals must be unit vectors
k >= 2
Template Parameters
 Concurrency_tag enables sequential versus parallel algorithm. Possible values are Sequential_tag and Parallel_tag. ForwardIterator iterator over input points. PointPMap is a model of ReadWritePropertyMap with the value type of ForwardIterator as key and Kernel::Point_3 as value type. It can be omitted if the value type of ForwardIterator is convertible to Kernel::Point_3. NormalPMap is a model of ReadWritePropertyMap with the value type of ForwardIterator as key and Kernel::Vector_3 as value type. Kernel Geometric traits class. It can be omitted and deduced automatically from the value type of PointPMap using Kernel_traits.
Returns
Average point movement error. It's a convergence criterium for the algorithm. This value can help the user to decide how many iterations are sufficient.
Parameters
 first forward iterator on the first input point. beyond past-the-end iterator. point_pmap point property map. normal_pmap normal property map. k size of the neighborhood for the implicit surface patch fitting. The larger the value is, the smoother the result will be. sharpness_angle controls the sharpness of the result. The larger the value is, the smoother the result will be. The range of possible value is [0, 90].

#include <CGAL/bilateral_smooth_point_set.h>

template<typename Concurrency_tag , typename InputIterator , typename PointPMap , typename Kernel >
 Kernel::FT CGAL::compute_average_spacing ( InputIterator first, InputIterator beyond, PointPMap point_pmap, unsigned int k, const Kernel & )

Computes average spacing from k nearest neighbors.

Precondition
k >= 2.
Template Parameters
 Concurrency_tag enables sequential versus parallel algorithm. Possible values are Sequential_tag and Parallel_tag. InputIterator iterator over input points. PointPMap is a model of ReadablePropertyMap with value type Point_3. It can be omitted if the value type of InputIterator is convertible to Point_3. Kernel Geometric traits class. It can be omitted and deduced automatically from the value type of PointPMap.
Returns
average spacing (scalar).
Parameters
 first iterator over the first input point. beyond past-the-end iterator over the input points. point_pmap property map: value_type of InputIterator -> Point_3 k number of neighbors.

#include <CGAL/compute_average_spacing.h>

template<class ForwardIterator , class PointPMap , class Kernel >
 void CGAL::compute_vcm ( ForwardIterator first, ForwardIterator beyond, PointPMap point_pmap, std::vector< cpp11::array< typename Kernel::FT, 6 > > & ccov, double offset_radius, double convolution_radius, const Kernel & kernel )

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 noise-free 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:

$$\begin{bmatrix} a[0] & a[1] & a[2] \\ a[1] & a[3] & a[4] \\ a[2] & a[4] & a[5] \\ \end{bmatrix}$$
Template Parameters
 ForwardIterator iterator over input points. PointPMap is a model of ReadablePropertyMap with a value_type = Kernel::Point_3. CovariancePMap is a model of ReadWritePropertyMap with a value_type = cpp11::array. Kernel Geometric traits class.
CGAL::vcm_is_on_feature_edge()
CGAL::vcm_estimate_normals()
Todo:
replace ccov by a property map.

#include <CGAL/vcm_estimate_normals.h>

Examples:
Point_set_processing_3/edges_example.cpp.
template<typename Concurrency_tag , typename OutputIterator , typename ForwardIterator , typename PointPMap , typename NormalPMap , typename Kernel >
 OutputIterator CGAL::edge_aware_upsample_point_set ( ForwardIterator first, ForwardIterator beyond, OutputIterator output, PointPMap point_pmap, NormalPMap normal_pmap, const typename Kernel::FT sharpness_angle, typename Kernel::FT edge_sensitivity, typename Kernel::FT neighbor_radius, const std::size_t number_of_output_points, const Kernel & )

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 point-based rendering, hole filling, and sparse surface reconstruction. Normals of points are required as input. For more details, please refer to [5].

Template Parameters
 Concurrency_tag enables sequential versus parallel versions of compute_average_spacing() (called internally). Possible values are Sequential_tag and Parallel_tag. OutputIterator Type of the output iterator. The type of the objects put in it is std::pair. Note that the user may use a function_output_iterator to match specific needs. ForwardIterator iterator over input points. PointPMap is a model of ReadablePropertyMap with the value type of ForwardIterator as key and Kernel::Point_3 as value type. It can be omitted if the value type of ForwardIterator is convertible to Kernel::Point_3. NormalPMap is a model of ReadablePropertyMap with the value type of ForwardIterator as key and Kernel::Vector_3 as value type. Kernel Geometric traits class. It can be omitted and deduced automatically from the value type of PointPMap using Kernel_traits.
Parameters
 first forward iterator on the first input point. beyond past-the-end iterator. output output iterator where output points and normals are put. point_pmap point property map. normal_pmap vector property map. sharpness_angle controls the preservation of sharp features. The larger the value is, the smoother the result will be. The range of possible values is [0, 90]. See section Parameter: sharpness_angle for an example. edge_sensitivity larger values of edge-sensitivity give higher priority to inserting points along sharp features. The range of possible values is [0, 1]. See section Parameter: edge_sensitivity for an example. neighbor_radius indicates the radius of the largest hole that should be filled. The default value is set to 3 times the average spacing of the point set. If the value given by user is smaller than the average spacing, the function will use the default value instead. number_of_output_points number of output points to generate.

#include <CGAL/edge_aware_upsample_point_set.h>

template<typename InputIterator , typename PointPMap , typename Kernel >
 std::size_t CGAL::estimate_global_k_neighbor_scale ( InputIterator first, InputIterator beyond, PointPMap point_pmap, const Kernel & kernel )

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).

Template Parameters
 InputIterator iterator over input points. PointPMap is a model of ReadablePropertyMap with value type Point_3 or Point_2. It can be omitted if the value type of InputIterator is convertible to Point_3 or to Point_2. Kernel Geometric traits class. It can be omitted and deduced automatically from the value type of PointPMap.
Note
This function accepts both 2D and 3D points.
Returns
The estimated scale in the K nearest neighbors sense.
Parameters
 first iterator over the first input point. beyond past-the-end iterator over the input points. point_pmap property map: value_type of InputIterator -> Point_3 or Point_2 kernel geometric traits.

#include <CGAL/estimate_scale.h>

Examples:
Point_set_processing_3/scale_estimation_example.cpp.
template<typename InputIterator , typename PointPMap , typename Kernel >
 Kernel::FT CGAL::estimate_global_range_scale ( InputIterator first, InputIterator beyond, PointPMap point_pmap, const Kernel & kernel )

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).

Template Parameters
 InputIterator iterator over input points. PointPMap is a model of ReadablePropertyMap with value type Point_3 or Point_2. It can be omitted if the value type of InputIterator is convertible to Point_3 or to Point_2. Kernel Geometric traits class. It can be omitted and deduced automatically from the value type of PointPMap.
Note
This function accepts both 2D and 3D points.
Returns
The estimated scale in the range sense.
Parameters
 first iterator over the first input point. beyond past-the-end iterator over the input points. point_pmap property map: value_type of InputIterator -> Point_3 or Point_3 kernel geometric traits.

#include <CGAL/estimate_scale.h>

Examples:
Point_set_processing_3/scale_estimation_example.cpp.
template<typename SamplesInputIterator , typename SamplesPointPMap , typename QueriesInputIterator , typename QueriesPointPMap , typename OutputIterator , typename Kernel >
 OutputIterator CGAL::estimate_local_k_neighbor_scales ( SamplesInputIterator first, SamplesInputIterator beyond, SamplesPointPMap samples_pmap, QueriesInputIterator first_query, QueriesInputIterator beyond_query, QueriesPointPMap queries_pmap, OutputIterator output, const Kernel & )

Estimates the local scale in a K nearest neighbors sense on a set of user-defined 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).

Template Parameters
 SamplesInputIterator iterator over input sample points. SamplesPointPMap is a model of ReadablePropertyMap with value type Point_3 or Point_2. It can be omitted if the value type of SamplesInputIterator is convertible to Point_3 or to Point_2. QueriesInputIterator iterator over points where scale should be computed. QueriesInputIterator is a model of ReadablePropertyMap with value type Point_3 or Point_2. It can be omitted if the value type of QueriesInputIterator is convertible to Point_3 or to Point_2. OutputIterator is used to store the computed scales. It accepts values of type std::size_t. Kernel Geometric traits class. It can be omitted and deduced automatically from the value type of SamplesPointPMap.
Note
This function accepts both 2D and 3D points, but sample points and query must have the same dimension.
Parameters
 first iterator over the first input sample. beyond past-the-end iterator over the input samples. samples_pmap property map: value_type of InputIterator -> Point_3 or Point_2 first_query iterator over the first point where scale must be estimated beyond_query past-the-end iterator over the points where scale must be estimated queries_pmap property map: value_type of InputIterator -> Point_3 or Point_2 output output iterator to store the computed scales

#include <CGAL/estimate_scale.h>

Examples:
Point_set_processing_3/scale_estimation_2d_example.cpp.
template<typename SamplesInputIterator , typename SamplesPointPMap , typename QueriesInputIterator , typename QueriesPointPMap , typename OutputIterator , typename Kernel >
 OutputIterator CGAL::estimate_local_range_scales ( SamplesInputIterator first, SamplesInputIterator beyond, SamplesPointPMap samples_pmap, QueriesInputIterator first_query, QueriesInputIterator beyond_query, QueriesPointPMap queries_pmap, OutputIterator output, const Kernel & )

Estimates the local scale in a range sense on a set of user-defined 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).

Template Parameters
 SamplesInputIterator iterator over input sample points. SamplesPointPMap is a model of ReadablePropertyMap with value type Point_3 or Point_2. It can be omitted if the value type of SamplesInputIterator is convertible to Point_3 or to Point_2. QueriesInputIterator iterator over points where scale should be computed. QueriesInputIterator is a model of ReadablePropertyMap with value type Point_3 or Point_2. It can be omitted if the value type of QueriesInputIterator is convertible to Point_3 or to Point_2. OutputIterator is used to store the computed scales. It accepts values of type Kernel::FT. Kernel Geometric traits class. It can be omitted and deduced automatically from the value type of SamplesPointPMap.
Note
This function accepts both 2D and 3D points, but sample points and query must have the same dimension.
Parameters
 first iterator over the first input sample. beyond past-the-end iterator over the input samples. samples_pmap property map: value_type of InputIterator -> Point_3 or Point_2 first_query iterator over the first point where scale must be estimated beyond_query past-the-end iterator over the points where scale must be estimated queries_pmap property map: value_type of InputIterator -> Point_3 or Point_2 output output iterator to store the computed scales

#include <CGAL/estimate_scale.h>

template<typename ForwardIterator , typename PointPMap , typename Kernel >
 ForwardIterator CGAL::grid_simplify_point_set ( ForwardIterator first, ForwardIterator beyond, PointPMap point_pmap, double epsilon, const Kernel & )

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 erase-remove idiom). For this reason it should not be called on sorted containers.

Precondition
epsilon > 0
Template Parameters
 ForwardIterator iterator over input points. PointPMap is a model of ReadablePropertyMap with value type Point_3. It can be omitted if the value type of ForwardIterator is convertible to Point_3. Kernel Geometric traits class. It can be omitted and deduced automatically from the value type of PointPMap.
Returns
iterator over the first point to remove.
Parameters
 first iterator over the first input point. beyond past-the-end iterator over the input points. point_pmap property map: value_type of ForwardIterator -> Point_3 epsilon tolerance value when merging 3D points.

#include <CGAL/grid_simplify_point_set.h>

Examples:
Point_set_processing_3/grid_simplification_example.cpp, Point_set_processing_3/grid_simplify_indices.cpp, and Point_set_processing_3/scale_estimation_example.cpp.
template<typename ForwardIterator , typename PointPMap , typename DiagonalizeTraits , typename Kernel >
 ForwardIterator CGAL::hierarchy_simplify_point_set ( ForwardIterator begin, ForwardIterator end, PointPMap point_pmap, const unsigned int size, const double var_max, const DiagonalizeTraits & , const Kernel & )

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 erase-remove idiom). For this reason it should not be called on sorted containers.

Precondition
0 < var_max < 1/3
size > 0
Template Parameters
 ForwardIterator iterator over input points. PointPMap is a model of ReadablePropertyMap with value type Point_3. It can be omitted if the value type of ForwardIterator is convertible to Point_3. DiagonalizeTraits 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 Internal_diagonalize_traits is used. Kernel Geometric traits class. It can be omitted and deduced automatically from the value type of PointPMap.
Returns
iterator over the first point to remove.

#include <CGAL/hierarchy_simplify_point_set.h>

Examples:
Point_set_processing_3/hierarchy_simplification_example.cpp.
template<typename Concurrency_tag , typename ForwardIterator , typename PointPMap , typename NormalPMap , typename Kernel , typename SvdTraits >
 void CGAL::jet_estimate_normals ( ForwardIterator first, ForwardIterator beyond, PointPMap point_pmap, NormalPMap normal_pmap, unsigned int k, const Kernel & , unsigned int degree_fitting = 2 )

Estimates normal directions of the [first, beyond) range of points using jet fitting on the k nearest neighbors.

The output normals are randomly oriented.

Precondition
k >= 2
Template Parameters
 Concurrency_tag enables sequential versus parallel algorithm. Possible values are Sequential_tag and Parallel_tag. ForwardIterator iterator model of the concept of the same name over input points and able to store output normals. PointPMap is a model of ReadablePropertyMap with value type Point_3. It can be omitted if the value type of ForwardIterator is convertible to Point_3. NormalPMap is a model of WritablePropertyMap with value type Vector_3. Kernel Geometric traits class. It can be omitted and deduced automatically from the value type of PointPMap. SvdTraits template parameter for the class Monge_via_jet_fitting that can be ommited under conditions described in the documentation of Monge_via_jet_fitting.
Parameters
 first iterator over the first input point. beyond past-the-end iterator over the input points. point_pmap property map: value_type of ForwardIterator -> Point_3. normal_pmap property map: value_type of ForwardIterator -> Vector_3. k number of neighbors. degree_fitting fitting degree

#include <CGAL/jet_estimate_normals.h>

template<typename Concurrency_tag , typename InputIterator , typename PointPMap , typename Kernel , typename SvdTraits >
 void CGAL::jet_smooth_point_set ( InputIterator first, InputIterator beyond, PointPMap point_pmap, unsigned int k, const Kernel & , unsigned int degree_fitting = 2, unsigned int degree_monge = 2 )

Smoothes the [first, beyond) range of points using jet fitting on the k 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.

Precondition
k >= 2
Template Parameters
 Concurrency_tag enables sequential versus parallel algorithm. Possible values are Sequential_tag and Parallel_tag. InputIterator iterator over input points. PointPMap is a model of ReadWritePropertyMap with value type Point_3. It can be omitted if the value type of InputIterator is convertible to Point_3. Kernel Geometric traits class. It can be omitted and deduced automatically from the value type of PointPMap. SvdTraits template parameter for the class Monge_via_jet_fitting that can be ommited under conditions described in the documentation of Monge_via_jet_fitting.
Parameters
 first iterator over the first input point. beyond past-the-end iterator over the input points. point_pmap property map: value_type of InputIterator -> Point_3. k number of neighbors. degree_fitting fitting degree degree_monge Monge degree

#include <CGAL/jet_smooth_point_set.h>

template<typename ForwardIterator , typename PointPMap , typename NormalPMap , typename Kernel >
 ForwardIterator CGAL::mst_orient_normals ( ForwardIterator first, ForwardIterator beyond, PointPMap point_pmap, NormalPMap normal_pmap, unsigned int k, const Kernel & kernel )

Orients the normals of the [first, beyond) range of points using the propagation of a seed orientation through a minimum spanning tree of the Riemannian graph [Hoppe92].

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 erase-remove idiom). For this reason it should not be called on sorted containers.

Warning
This function may fail when Boost version 1.54 is used, because of the following bug: https://svn.boost.org/trac/boost/ticket/9012
Precondition
Normals must be unit vectors
k >= 2
Template Parameters
 ForwardIterator iterator over input points. PointPMap is a model of ReadablePropertyMap with value type Point_3. It can be omitted if the value type of ForwardIterator is convertible to Point_3. NormalPMap is a model of ReadWritePropertyMap with value type Vector_3 . Kernel Geometric traits class. It can be omitted and deduced automatically from the value type of PointPMap.
Returns
iterator over the first point with an unoriented normal.
Parameters
 first iterator over the first input point. beyond past-the-end iterator over the input points. point_pmap property map: value_type of ForwardIterator -> Point_3. normal_pmap property map: value_type of ForwardIterator -> Vector_3. k number of neighbors kernel geometric traits.

#include <CGAL/mst_orient_normals.h>

Examples:
Point_set_processing_3/normals_example.cpp.
template<typename Concurrency_tag , typename ForwardIterator , typename PointPMap , typename NormalPMap , typename Kernel >
 void CGAL::pca_estimate_normals ( ForwardIterator first, ForwardIterator beyond, PointPMap point_pmap, NormalPMap normal_pmap, unsigned int k, const Kernel & )

Estimates normal directions of the [first, beyond) range of points by linear least squares fitting of a plane over the k nearest neighbors.

The output normals are randomly oriented.

Precondition
k >= 2
Template Parameters
 Concurrency_tag enables sequential versus parallel algorithm. Possible values are Sequential_tag and Parallel_tag. ForwardIterator iterator over input points. PointPMap is a model of ReadablePropertyMap with value type Point_3. It can be omitted if the value type of ForwardIterator is convertible to Point_3. NormalPMap is a model of WritablePropertyMap with value type Vector_3. Kernel Geometric traits class. It can be omitted and deduced automatically from the value type of PointPMap.
Parameters
 first iterator over the first input point. beyond past-the-end iterator over the input points. point_pmap property map: value_type of ForwardIterator -> Point_3. normal_pmap property map: value_type of ForwardIterator -> Vector_3. k number of neighbors.

#include <CGAL/pca_estimate_normals.h>

template<typename ForwardIterator , typename PointPMap , typename Kernel >
 ForwardIterator CGAL::random_simplify_point_set ( ForwardIterator first, ForwardIterator beyond, PointPMap , double removed_percentage, const Kernel & )

Randomly deletes a user-specified 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 erase-remove idiom). For this reason it should not be called on sorted containers.

Template Parameters
 ForwardIterator iterator over input points. PointPMap is a model of ReadablePropertyMap with value type Point_3. It can be omitted if the value type of ForwardIterator is convertible to Point_3. Kernel Geometric traits class. It can be omitted and deduced automatically from the value type of PointPMap.
Returns
iterator over the first point to remove.
Parameters
 first iterator over the first input point. beyond past-the-end iterator over the input points. removed_percentage percentage of points to remove.

#include <CGAL/random_simplify_point_set.h>

template<typename InputIterator , typename PointPMap , typename Kernel >
 InputIterator CGAL::remove_outliers ( InputIterator first, InputIterator beyond, PointPMap point_pmap, unsigned int k, double threshold_percent, double threshold_distance, const Kernel & )

Removes outliers:

• computes average squared distance to the K nearest neighbors,
• and sorts the points in increasing order of average distance.

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 erase-remove idiom). For this reason it should not be called on sorted containers.

Precondition
k >= 2
Template Parameters
 InputIterator iterator over input points. PointPMap is a model of ReadablePropertyMap with value type Point_3. It can be omitted ifthe value type of InputIterator is convertible to Point_3. Kernel Geometric traits class. It can be omitted and deduced automatically from the value type of PointPMap.
Returns
iterator over the first point to remove.
Note
There are two thresholds that can be used: threshold_percent and threshold_distance. This function returns the smallest number of outliers such that at least one of these threshold is fullfilled. 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.
Parameters
 first iterator over the first input point. beyond past-the-end iterator over the input points. point_pmap property map: value_type of InputIterator -> Point_3 k number of neighbors. 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)

#include <CGAL/remove_outliers.h>

Examples:
Point_set_processing_3/remove_outliers_example.cpp.
template<typename Traits , typename OutputIterator >
 OutputIterator CGAL::structure_point_set ( typename Traits::Input_range::iterator first, typename Traits::Input_range::iterator beyond, typename Traits::Point_map point_map, typename Traits::Normal_map normal_map, OutputIterator output, Shape_detection_3::Efficient_RANSAC< Traits > & shape_detection, double epsilon, double attraction_factor = 3. )

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].

Template Parameters
 Traits a model of EfficientRANSACTraits that must provide in addition a function Intersect_3 intersection_3_object() const and a functor Intersect_3 with: boost::optional< boost::variant< Traits::Plane_3, Traits::Line_3 > > operator()(typename Traits::Plane_3, typename Traits::Plane_3) boost::optional< boost::variant< Traits::Line_3, Traits::Point_3 > > operator()(typename Traits::Line_3, typename Traits::Plane_3) OutputIterator Type of the output iterator. The type of the objects put in it is std::pair. Note that the user may use a function_output_iterator to match specific needs.
Note
If no plane is found in the shape detection object, the algorithm does nothing and the output points are the unaltered input points.
Both property maps can be omitted if the default constructors of these property maps can be safely used.
Parameters
 first iterator over the first input point. beyond past-the-end iterator over the input points. point_map property map: value_type of InputIterator -> Point_3. normal_map property map: value_type of InputIterator -> Vector_3. output output iterator where output points are written shape_detection shape detection object epsilon size parameter attraction_factor attraction factor

#include <CGAL/structure_point_set.h>

Examples:
Point_set_processing_3/structuring_example.cpp.
template<typename ForwardIterator , typename PointPMap , typename NormalPMap , typename VCMTraits >
 void CGAL::vcm_estimate_normals ( ForwardIterator first, ForwardIterator beyond, PointPMap point_pmap, NormalPMap normal_pmap, double offset_radius, double convolution_radius, VCMTraits )

Estimates normal directions of the points in the range [first, beyond) 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.

Template Parameters
 ForwardIterator iterator over input points. PointPMap is a model of ReadablePropertyMap with a value_type = Kernel::Point_3. NormalPMap is a model of WritablePropertyMap with a value_type = Kernel::Vector_3. 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.
Parameters
 first iterator over the first input point. beyond past-the-end iterator over the input points. point_pmap property map: value_type of ForwardIterator -> Point_3. normal_pmap property map: value_type of ForwardIterator -> Vector_3. offset_radius offset radius. convolution_radius convolution radius.

#include <CGAL/vcm_estimate_normals.h>

template<typename ForwardIterator , typename PointPMap , typename NormalPMap , typename VCMTraits >
 void CGAL::vcm_estimate_normals ( ForwardIterator first, ForwardIterator beyond, PointPMap point_pmap, NormalPMap normal_pmap, double offset_radius, unsigned int k, VCMTraits )

Estimates normal directions of the points in the range [first, beyond) 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.

Template Parameters
 ForwardIterator iterator over input points. PointPMap is a model of ReadablePropertyMap with a value_type = Kernel::Point_3. NormalPMap is a model of WritablePropertyMap with a value_type = Kernel::Vector_3. 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.
Parameters
 first iterator over the first input point. beyond past-the-end iterator over the input points. point_pmap property map: value_type of ForwardIterator -> Point_3. normal_pmap property map: value_type of ForwardIterator -> Vector_3. offset_radius offset radius. k number of neighbor points used for the convolution.

#include <CGAL/vcm_estimate_normals.h>

template<class FT , class VCMTraits >
 bool CGAL::vcm_is_on_feature_edge ( cpp11::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.

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].

Template Parameters
 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.
CGAL::compute_vcm()

#include <CGAL/vcm_estimate_edges.h>

Examples:
Point_set_processing_3/edges_example.cpp.
template<typename Concurrency_tag , typename OutputIterator , typename RandomAccessIterator , typename PointPMap , typename Kernel >
 OutputIterator CGAL::wlop_simplify_and_regularize_point_set ( RandomAccessIterator first, RandomAccessIterator beyond, OutputIterator output, PointPMap point_pmap, double select_percentage, double radius, unsigned int iter_number, bool require_uniform_sampling, const Kernel & )

This is an implementation of the Weighted Locally Optimal Projection (WLOP) simplification algorithm.

The WLOP simplification algorithm can produce a set of denoised, outlier-free 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.

Template Parameters
 Concurrency_tag enables sequential versus parallel algorithm. Possible values are Sequential_tag and Parallel_tag. OutputIterator Type of the output iterator. It must accept objects of type Kernel::Point_3. RandomAccessIterator Iterator over input points. PointPMap is a model of ReadablePropertyMap with the value type of ForwardIterator as key type and Kernel::Point_3 as value type. It can be omitted if the value type of RandomAccessIterator is convertible to Kernel::Point_3. Kernel Geometric traits class. It can be omitted and deduced automatically from the value type of PointPMap using Kernel_traits.
Parameters
 first random-access iterator to the first input point. beyond past-the-end iterator. output output iterator where output points are put. point_pmap point property map. select_percentage percentage of points to retain. The default value is set to 5 (%). 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. The default value is set to 8 times the average spacing of the point set. iter_number 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 non-uniform. The default value is false.

#include <CGAL/wlop_simplify_and_regularize_point_set.h>`

Examples:
Point_set_processing_3/wlop_simplify_and_regularize_point_set_example.cpp.