CGAL 6.2 - Manual

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Classification/gis_tutorial_example.cpp
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Projection_traits_xy_3.h>
#include <CGAL/Delaunay_triangulation_2.h>
#include <CGAL/Triangulation_vertex_base_with_info_2.h>
#include <CGAL/Triangulation_face_base_with_info_2.h>
#include <CGAL/boost/graph/graph_traits_Delaunay_triangulation_2.h>
#include <CGAL/boost/graph/border.h>
#include <CGAL/boost/graph/copy_face_graph.h>
#include <CGAL/Point_set_3.h>
#include <CGAL/Point_set_3/IO.h>
#include <CGAL/compute_average_spacing.h>
#include <CGAL/Surface_mesh.h>
#include <CGAL/Polygon_mesh_processing/locate.h>
#include <CGAL/Polygon_mesh_processing/triangulate_hole.h>
#include <CGAL/Polygon_mesh_processing/remesh.h>
#include <boost/graph/adjacency_list.hpp>
#include <CGAL/boost/graph/split_graph_into_polylines.h>
#include <CGAL/IO/WKT.h>
#include <CGAL/Constrained_Delaunay_triangulation_2.h>
#include <CGAL/Constrained_triangulation_plus_2.h>
#include <CGAL/Polyline_simplification_2/simplify.h>
#include <CGAL/Polyline_simplification_2/Squared_distance_cost.h>
#include <CGAL/Classification.h>
#include <CGAL/Random.h>
#include <fstream>
#include <queue>
#include "include/Color_ramp.h"
using Kernel = CGAL::Exact_predicates_inexact_constructions_kernel;
using Projection_traits = CGAL::Projection_traits_xy_3<Kernel>;
using Point_2 = Kernel::Point_2;
using Point_3 = Kernel::Point_3;
using Segment_3 = Kernel::Segment_3;
// Triangulated Irregular Network
using TIN = CGAL::Delaunay_triangulation_2<Projection_traits>;
// Triangulated Irregular Network (with info)
using Point_set = CGAL::Point_set_3<Point_3>;
using Vbi = CGAL::Triangulation_vertex_base_with_info_2 <Point_set::Index, Projection_traits>;
using Fbi = CGAL::Triangulation_face_base_with_info_2<int, Projection_traits>;
using TDS = CGAL::Triangulation_data_structure_2<Vbi, Fbi>;
using TIN_with_info = CGAL::Delaunay_triangulation_2<Projection_traits, TDS>;
namespace Classification = CGAL::Classification;
#ifdef CGAL_LINKED_WITH_TBB
using Concurrency_tag = CGAL::Parallel_tag;
#else
using Concurrency_tag = CGAL::Sequential_tag;
#endif
bool face_has_isovalue (TIN::Face_handle fh, double isovalue)
{
bool above = false, below = false;
for (int i = 0; i < 3; ++ i)
{
// Face has isovalue if one of its vertices is above and another
// one below
if (fh->vertex(i)->point().z() > isovalue)
above = true;
if (fh->vertex(i)->point().z() < isovalue)
below = true;
}
return (above && below);
}
Segment_3 isocontour_in_face (TIN::Face_handle fh, double isovalue)
{
Point_3 source;
Point_3 target;
bool source_found = false;
for (int i = 0; i < 3; ++ i)
{
Point_3 p0 = fh->vertex((i+1) % 3)->point();
Point_3 p1 = fh->vertex((i+2) % 3)->point();
// Check if the isovalue crosses segment (p0,p1)
if ((p0.z() - isovalue) * (p1.z() - isovalue) > 0)
continue;
double zbottom = p0.z();
double ztop = p1.z();
if (zbottom > ztop)
{
std::swap (zbottom, ztop);
std::swap (p0, p1);
}
// Compute position of segment vertex
double ratio = (isovalue - zbottom) / (ztop - zbottom);
Point_3 p = CGAL::barycenter (p0, (1 - ratio), p1,ratio);
if (source_found)
target = p;
else
{
source = p;
source_found = true;
}
}
return Segment_3 (source, target);
}
template <typename Graph>
class Polylines_visitor
{
private:
std::vector<std::vector<Point_3> >& polylines;
Graph& graph;
public:
Polylines_visitor (Graph& graph, std::vector<std::vector<Point_3> >& polylines)
: polylines (polylines), graph(graph) { }
void start_new_polyline()
{
polylines.push_back (std::vector<Point_3>());
}
void add_node (typename Graph::vertex_descriptor vd)
{
polylines.back().push_back (graph[vd]);
}
void end_polyline()
{
// filter small polylines
if (polylines.back().size() < 50)
polylines.pop_back();
}
};
namespace PS = CGAL::Polyline_simplification_2;
using CDT_vertex_base = PS::Vertex_base_2<Projection_traits>;
using CDT_face_base = CGAL::Constrained_triangulation_face_base_2<Projection_traits>;
using CDT_TDS = CGAL::Triangulation_data_structure_2<CDT_vertex_base, CDT_face_base>;
using CDT = CGAL::Constrained_Delaunay_triangulation_2<Projection_traits, CDT_TDS>;
using CTP = CGAL::Constrained_triangulation_plus_2<CDT>;
int main (int argc, char** argv)
{
const std::string fname = argc != 2 ? CGAL::data_file_path("points_3/b9_training.ply") : argv[1];
if (argc != 2)
{
std::cerr << "Usage: " << argv[0] << " points.ply" << std::endl;
std::cerr << "Running with default value " << fname << "\n";
}
// Read points
std::ifstream ifile (fname, std::ios_base::binary);
CGAL::Point_set_3<Point_3> points;
ifile >> points;
std::cerr << points.size() << " point(s) read" << std::endl;
// Create DSM
TIN dsm (points.points().begin(), points.points().end());
using Mesh = CGAL::Surface_mesh<Point_3>;
Mesh dsm_mesh;
CGAL::copy_face_graph (dsm, dsm_mesh);
std::ofstream dsm_ofile ("dsm.ply", std::ios_base::binary);
CGAL::IO::set_binary_mode (dsm_ofile);
CGAL::IO::write_PLY (dsm_ofile, dsm_mesh);
dsm_ofile.close();
auto idx_to_point_with_info
= [&](const Point_set::Index& idx) -> std::pair<Point_3, Point_set::Index>
{
return std::make_pair (points.point(idx), idx);
};
TIN_with_info tin_with_info
(boost::make_transform_iterator (points.begin(), idx_to_point_with_info),
boost::make_transform_iterator (points.end(), idx_to_point_with_info));
double spacing = CGAL::compute_average_spacing<Concurrency_tag>(points, 6);
spacing *= 2;
auto face_height
= [&](const TIN_with_info::Face_handle fh) -> double
{
double out = 0.;
for (int i = 0; i < 3; ++ i)
out = (std::max) (out, CGAL::abs(fh->vertex(i)->point().z() - fh->vertex((i+1)%3)->point().z()));
return out;
};
// Initialize faces info
for (TIN_with_info::Face_handle fh : tin_with_info.all_face_handles())
if (tin_with_info.is_infinite(fh) || face_height(fh) > spacing) // Filtered faces are given info() = -2
fh->info() = -2;
else // Pending faces are given info() = -1;
fh->info() = -1;
// Flooding algorithm
std::vector<int> component_size;
for (TIN_with_info::Face_handle fh : tin_with_info.finite_face_handles())
{
if (fh->info() != -1)
continue;
std::queue<TIN_with_info::Face_handle> todo;
todo.push(fh);
int size = 0;
while (!todo.empty())
{
TIN_with_info::Face_handle current = todo.front();
todo.pop();
if (current->info() != -1)
continue;
current->info() = int(component_size.size());
++ size;
for (int i = 0; i < 3; ++ i)
todo.push (current->neighbor(i));
}
component_size.push_back (size);
}
std::cerr << component_size.size() << " connected component(s) found" << std::endl;
Mesh tin_colored_mesh;
Mesh::Property_map<Mesh::Face_index, CGAL::IO::Color>
color_map = tin_colored_mesh.add_property_map<Mesh::Face_index, CGAL::IO::Color>("f:color").first;
CGAL::copy_face_graph (tin_with_info, tin_colored_mesh,
CGAL::parameters::face_to_face_output_iterator
(boost::make_function_output_iterator
([&](const std::pair<TIN_with_info::Face_handle, Mesh::Face_index>& ff)
{
// Color unassigned faces gray
if (ff.first->info() < 0)
color_map[ff.second] = CGAL::IO::Color(128, 128, 128);
else
{
// Random color seeded by the component ID
CGAL::Random r (ff.first->info());
color_map[ff.second] = CGAL::IO::Color (r.get_int(64, 192),
r.get_int(64, 192),
r.get_int(64, 192));
}
})));
std::ofstream tin_colored_ofile ("colored_tin.ply", std::ios_base::binary);
CGAL::IO::set_binary_mode (tin_colored_ofile);
CGAL::IO::write_PLY (tin_colored_ofile, tin_colored_mesh);
tin_colored_ofile.close();
int min_size = int(points.size() / 2);
std::vector<TIN_with_info::Vertex_handle> to_remove;
for (TIN_with_info::Vertex_handle vh : tin_with_info.finite_vertex_handles())
{
TIN_with_info::Face_circulator circ = tin_with_info.incident_faces (vh),
start = circ;
// Remove a vertex if it's only adjacent to components smaller than threshold
bool keep = false;
do
{
if (circ->info() >= 0 && component_size[std::size_t(circ->info())] > min_size)
{
keep = true;
break;
}
}
while (++ circ != start);
if (!keep)
to_remove.push_back (vh);
}
std::cerr << to_remove.size() << " vertices(s) will be removed after filtering" << std::endl;
for (TIN_with_info::Vertex_handle vh : to_remove)
tin_with_info.remove (vh);
// Copy and keep track of overly large faces
Mesh dtm_mesh;
std::vector<Mesh::Face_index> face_selection;
Mesh::Property_map<Mesh::Face_index, bool> face_selection_map
= dtm_mesh.add_property_map<Mesh::Face_index, bool>("is_selected", false).first;
double limit = CGAL::square (5 * spacing);
CGAL::copy_face_graph (tin_with_info, dtm_mesh,
CGAL::parameters::face_to_face_output_iterator
(boost::make_function_output_iterator
([&](const std::pair<TIN_with_info::Face_handle, Mesh::Face_index>& ff)
{
double longest_edge = 0.;
bool border = false;
for (int i = 0; i < 3; ++ i)
{
longest_edge = (std::max)(longest_edge, CGAL::squared_distance
(ff.first->vertex((i+1)%3)->point(),
ff.first->vertex((i+2)%3)->point()));
TIN_with_info::Face_circulator circ
= tin_with_info.incident_faces (ff.first->vertex(i)),
start = circ;
do
{
if (tin_with_info.is_infinite (circ))
{
border = true;
break;
}
}
while (++ circ != start);
if (border)
break;
}
// Select if face is too big AND it's not
// on the border (to have closed holes)
if (!border && longest_edge > limit)
{
face_selection_map[ff.second] = true;
face_selection.push_back (ff.second);
}
})));
// Save original DTM
std::ofstream dtm_ofile ("dtm.ply", std::ios_base::binary);
CGAL::IO::set_binary_mode (dtm_ofile);
CGAL::IO::write_PLY (dtm_ofile, dtm_mesh);
dtm_ofile.close();
std::cerr << face_selection.size() << " face(s) are selected for removal" << std::endl;
// Expand face selection to keep a well formed 2-manifold mesh after removal
CGAL::expand_face_selection_for_removal (face_selection, dtm_mesh, face_selection_map);
face_selection.clear();
for (Mesh::Face_index fi : faces(dtm_mesh))
if (face_selection_map[fi])
face_selection.push_back(fi);
std::cerr << face_selection.size() << " face(s) are selected for removal after expansion" << std::endl;
for (Mesh::Face_index fi : face_selection)
CGAL::Euler::remove_face (halfedge(fi, dtm_mesh), dtm_mesh);
dtm_mesh.collect_garbage();
if (!dtm_mesh.is_valid())
std::cerr << "Invalid mesh!" << std::endl;
// Save filtered DTM
std::ofstream dtm_holes_ofile ("dtm_with_holes.ply", std::ios_base::binary);
CGAL::IO::set_binary_mode (dtm_holes_ofile);
CGAL::IO::write_PLY (dtm_holes_ofile, dtm_mesh);
dtm_holes_ofile.close();
// Get all holes
std::vector<Mesh::Halfedge_index> holes;
CGAL::extract_boundary_cycles (dtm_mesh, std::back_inserter (holes));
std::cerr << holes.size() << " hole(s) identified" << std::endl;
// Identify outer hull (hole with maximum size)
double max_size = 0.;
Mesh::Halfedge_index outer_hull;
for (Mesh::Halfedge_index hi : holes)
{
CGAL::Bbox_3 hole_bbox;
for (Mesh::Halfedge_index haf : CGAL::halfedges_around_face(hi, dtm_mesh))
{
const Point_3& p = dtm_mesh.point(target(haf, dtm_mesh));
hole_bbox += p.bbox();
}
double size = CGAL::squared_distance (Point_2(hole_bbox.xmin(), hole_bbox.ymin()),
Point_2(hole_bbox.xmax(), hole_bbox.ymax()));
if (size > max_size)
{
max_size = size;
outer_hull = hi;
}
}
// Fill all holes except the biggest (which is the outer hull of the mesh)
for (Mesh::Halfedge_index hi : holes)
if (hi != outer_hull)
CGAL::Polygon_mesh_processing::triangulate_refine_and_fair_hole
(dtm_mesh, hi, CGAL::parameters::fairing_continuity(0));
// Save DTM with holes filled
std::ofstream dtm_filled_ofile ("dtm_filled.ply", std::ios_base::binary);
CGAL::IO::set_binary_mode (dtm_filled_ofile);
CGAL::IO::write_PLY (dtm_filled_ofile, dtm_mesh);
dtm_filled_ofile.close();
CGAL::Polygon_mesh_processing::isotropic_remeshing (faces(dtm_mesh), spacing, dtm_mesh);
std::ofstream dtm_remeshed_ofile ("dtm_remeshed.ply", std::ios_base::binary);
CGAL::IO::set_binary_mode (dtm_remeshed_ofile);
CGAL::IO::write_PLY (dtm_remeshed_ofile, dtm_mesh);
dtm_remeshed_ofile.close();
TIN dtm_clean (dtm_mesh.points().begin(), dtm_mesh.points().end());
CGAL::Bbox_3 bbox = CGAL::bbox_3 (points.points().begin(), points.points().end());
// Generate raster image 1920-pixels large
std::size_t width = 1920;
std::size_t height = std::size_t((bbox.ymax() - bbox.ymin()) * 1920 / (bbox.xmax() - bbox.xmin()));
std::cerr << "Rastering with resolution " << width << "x" << height << std::endl;
// Use PPM format (Portable PixMap) for simplicity
std::ofstream raster_ofile ("raster.ppm", std::ios_base::binary);
// PPM header
raster_ofile << "P6" << std::endl // magic number
<< width << " " << height << std::endl // dimensions of the image
<< 255 << std::endl; // maximum color value
// Use rainbow color ramp output
Color_ramp color_ramp;
// Keeping track of location from one point to its neighbor allows
// for fast locate in DT
TIN::Face_handle location;
// Query each pixel of the image
for (std::size_t y = 0; y < height; ++ y)
for (std::size_t x = 0; x < width; ++ x)
{
Point_3 query (bbox.xmin() + x * (bbox.xmax() - bbox.xmin()) / double(width),
bbox.ymin() + (height-y) * (bbox.ymax() - bbox.ymin()) / double(height),
0); // not relevant for location in 2D
location = dtm_clean.locate (query, location);
// Points outside the convex hull will be colored black
std::array<unsigned char, 3> colors { 0, 0, 0 };
if (!dtm_clean.is_infinite(location))
{
std::array<double, 3> barycentric_coordinates
= CGAL::Polygon_mesh_processing::barycentric_coordinates
(Point_2 (location->vertex(0)->point().x(), location->vertex(0)->point().y()),
Point_2 (location->vertex(1)->point().x(), location->vertex(1)->point().y()),
Point_2 (location->vertex(2)->point().x(), location->vertex(2)->point().y()),
Point_2 (query.x(), query.y()),
Kernel());
double height_at_query
= (barycentric_coordinates[0] * location->vertex(0)->point().z()
+ barycentric_coordinates[1] * location->vertex(1)->point().z()
+ barycentric_coordinates[2] * location->vertex(2)->point().z());
// Color ramp generates a color depending on a value from 0 to 1
double height_ratio = (height_at_query - bbox.zmin()) / (bbox.zmax() - bbox.zmin());
colors = color_ramp.get(height_ratio);
}
raster_ofile.write (reinterpret_cast<char*>(&colors), 3);
}
raster_ofile.close();
// Smooth heights with 5 successive Gaussian filters
double gaussian_variance = 4 * spacing * spacing;
for (TIN::Vertex_handle vh : dtm_clean.finite_vertex_handles())
{
double z = vh->point().z();
double total_weight = 1;
TIN::Vertex_circulator circ = dtm_clean.incident_vertices (vh),
start = circ;
do
{
if (!dtm_clean.is_infinite(circ))
{
double sq_dist = CGAL::squared_distance (vh->point(), circ->point());
double weight = std::exp(- sq_dist / gaussian_variance);
z += weight * circ->point().z();
total_weight += weight;
}
}
while (++ circ != start);
z /= total_weight;
vh->point() = Point_3 (vh->point().x(), vh->point().y(), z);
}
std::array<double, 50> isovalues; // Contour 50 isovalues
for (std::size_t i = 0; i < isovalues.size(); ++ i)
isovalues[i] = bbox.zmin() + ((i+1) * (bbox.zmax() - bbox.zmin()) / (isovalues.size() - 2));
// First find on each face if they are crossed by some isovalues and
// extract segments in a graph
using Segment_graph = boost::adjacency_list<boost::listS, boost::vecS, boost::undirectedS, Point_3>;
Segment_graph graph;
using Map_p2v = std::map<Point_3, Segment_graph::vertex_descriptor>;
Map_p2v map_p2v;
for (TIN::Face_handle vh : dtm_clean.finite_face_handles())
for (double iv : isovalues)
if (face_has_isovalue (vh, iv))
{
Segment_3 segment = isocontour_in_face (vh, iv);
for (const Point_3& p : { segment.source(), segment.target() })
{
// Only insert end points of segments once to get a well connected graph
Map_p2v::iterator iter;
bool inserted;
std::tie (iter, inserted) = map_p2v.insert (std::make_pair (p, Segment_graph::vertex_descriptor()));
if (inserted)
{
iter->second = boost::add_vertex (graph);
graph[iter->second] = p;
}
}
boost::add_edge (map_p2v[segment.source()], map_p2v[segment.target()], graph);
}
// Split segments into polylines
std::vector<std::vector<Point_3> > polylines;
Polylines_visitor<Segment_graph> visitor (graph, polylines);
CGAL::split_graph_into_polylines (graph, visitor);
std::cerr << polylines.size() << " polylines computed, with "
<< map_p2v.size() << " vertices in total" << std::endl;
// Output to WKT file
std::ofstream contour_ofile ("contour.wkt");
contour_ofile.precision(18);
CGAL::IO::write_multi_linestring_WKT (contour_ofile, polylines);
contour_ofile.close();
// Construct constrained Delaunay triangulation with polylines as constraints
CTP ctp;
for (const std::vector<Point_3>& poly : polylines)
ctp.insert_constraint (poly.begin(), poly.end());
// Simplification algorithm with limit on distance
PS::simplify (ctp, PS::Squared_distance_cost(), PS::Stop_above_cost_threshold (16 * spacing * spacing));
polylines.clear();
for (CTP::Constraint_id cid : ctp.constraints())
{
polylines.push_back (std::vector<Point_3>());
polylines.back().reserve (ctp.vertices_in_constraint (cid).size());
for (CTP::Vertex_handle vh : ctp.vertices_in_constraint(cid))
polylines.back().push_back (vh->point());
}
std::size_t nb_vertices
= std::accumulate (polylines.begin(), polylines.end(), std::size_t(0),
[](std::size_t size, const std::vector<Point_3>& poly) -> std::size_t
{ return size + poly.size(); });
std::cerr << nb_vertices
<< " vertices remaining after simplification ("
<< 100. * (nb_vertices / double(map_p2v.size())) << "%)" << std::endl;
// Output to WKT file
std::ofstream simplified_ofile ("simplified.wkt");
simplified_ofile.precision(18);
CGAL::IO::write_multi_linestring_WKT (simplified_ofile, polylines);
simplified_ofile.close();
// Get training from input
std::optional<Point_set::Property_map<int>> training_map = points.property_map<int>("training");
if (training_map.has_value())
{
std::cerr << "Classifying ground/vegetation/building" << std::endl;
// Create labels
Classification::Label_set labels ({ "ground", "vegetation", "building" });
// Generate features
Classification::Feature_set features;
Classification::Point_set_feature_generator<Kernel, Point_set, Point_set::Point_map>
generator (points, points.point_map(), 5); // 5 scales
#ifdef CGAL_LINKED_WITH_TBB
// If TBB is used, features can be computed in parallel
features.begin_parallel_additions();
generator.generate_point_based_features (features);
features.end_parallel_additions();
#else
generator.generate_point_based_features (features);
#endif
// Train a random forest classifier
Classification::ETHZ::Random_forest_classifier classifier (labels, features);
classifier.train (points.range(training_map.value()));
// Classify with graphcut regularization
Point_set::Property_map<int> label_map = points.add_property_map<int>("labels").first;
Classification::classify_with_graphcut<Concurrency_tag>
(points, points.point_map(), labels, classifier,
generator.neighborhood().k_neighbor_query(12), // regularize on 12-neighbors graph
0.5f, // graphcut weight
12, // Subdivide to speed-up process
label_map);
// Evaluate
std::cerr << "Mean IoU on training data = "
<< Classification::Evaluation(labels,
points.range(training_map.value()),
points.range(label_map)).mean_intersection_over_union() << std::endl;
// Save the classified point set
std::ofstream classified_ofile ("classification_gis_tutorial.ply");
CGAL::IO::set_binary_mode (classified_ofile);
classified_ofile << points;
classified_ofile.close();
}
return EXIT_SUCCESS;
}
CGAL::Bbox_3
CGAL::Bbox_3::ymin
double ymin() const
CGAL::Bbox_3::xmax
double xmax() const
CGAL::Bbox_3::zmin
double zmin() const
CGAL::Bbox_3::zmax
double zmax() const
CGAL::Bbox_3::ymax
double ymax() const
CGAL::Bbox_3::xmin
double xmin() const
CGAL::Constrained_Delaunay_triangulation_2
CGAL::Constrained_triangulation_face_base_2
CGAL::Constrained_triangulation_plus_2
CGAL::Delaunay_triangulation_2
CGAL::Exact_predicates_inexact_constructions_kernel
CGAL::IO::Color
CGAL::Point_set_3
CGAL::Point_set_3::begin
iterator begin()
CGAL::Point_set_3::point
Point & point(const Index &index)
CGAL::Point_set_3::add_property_map
std::pair< Property_map< T >, bool > add_property_map(const std::string &name, const T t=T())
CGAL::Point_set_3::end
iterator end()
CGAL::Point_set_3::points
Point_range points() const
CGAL::Point_set_3::point_map
Point_map point_map()
CGAL::Point_set_3::range
Property_range< T > range(const Property_map< T > &pmap) const
CGAL::Point_set_3::property_map
std::optional< Property_map< T > > property_map(const std::string &name) const
CGAL::Projection_traits_xy_3
CGAL::Surface_mesh
CGAL::Triangulation_data_structure_2
CGAL::Triangulation_face_base_with_info_2
Kernel::Point_2
Kernel::Point_3
Kernel::Segment_3
CGAL::Polygon_mesh_processing::triangulate_refine_and_fair_hole
auto triangulate_refine_and_fair_hole(PolygonMesh &pmesh, typename boost::graph_traits< PolygonMesh >::halfedge_descriptor border_halfedge, const NamedParameters &np=parameters::default_values())
CGAL::Polygon_mesh_processing::isotropic_remeshing
void isotropic_remeshing(const FaceRange &faces, SizingFunction &sizing, PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
CGAL::Polygon_mesh_processing::barycentric_coordinates
Barycentric_coordinates< typename GeomTraits::FT > barycentric_coordinates(const Point &p, const Point &q, const Point &r, const Point &query, const GeomTraits &gt)
CGAL::Polygon_mesh_processing::bbox
CGAL::Bbox_3 bbox(const PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
CGAL::square
NT square(const NT &x)
CGAL::abs
NT abs(const NT &x)
CGAL::Euler::remove_face
void remove_face(typename boost::graph_traits< Graph >::halfedge_descriptor h, Graph &g)
CGAL::copy_face_graph
void copy_face_graph(const SourceMesh &sm, TargetMesh &tm, const NamedParameters1 &np1=parameters::default_values(), const NamedParameters2 &np2=parameters::default_values())
CGAL::extract_boundary_cycles
OutputIterator extract_boundary_cycles(const Graph &g, OutputIterator out)
CGAL::halfedges_around_face
Iterator_range< Halfedge_around_face_iterator< Graph > > halfedges_around_face(typename boost::graph_traits< Graph >::halfedge_descriptor h, const Graph &g)
CGAL::split_graph_into_polylines
void split_graph_into_polylines(const Graph &graph, Visitor &polyline_visitor, IsTerminal is_terminal)
CGAL::expand_face_selection_for_removal
void expand_face_selection_for_removal(const FaceRange &faces_to_be_deleted, TriangleMesh &tm, IsSelectedMap is_selected)
CGAL::parameters::features
unspecified_type features()
CGAL::IO::write_multi_linestring_WKT
std::ostream & write_multi_linestring_WKT(std::ostream &out, const MultiLineString &mls)
CGAL::IO::set_binary_mode
Mode set_binary_mode(std::ios &s)
CGAL::IO::write_PLY
bool write_PLY(std::ostream &os, const Surface_mesh< P > &sm, const std::string &comments, const NamedParameters &np=parameters::default_values())
CGAL::barycenter
CGAL::Point_2< Kernel > barycenter(const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2)
CGAL::squared_distance
Kernel::FT squared_distance(Type1< Kernel > obj1, Type2< Kernel > obj2)
CGAL::Classification
CGAL::Polyline_simplification_2
Kernel
CGAL::Parallel_tag
CGAL::Sequential_tag