CGAL 6.2 - 3D Envelopes

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Envelope_3/envelope_triangles.cpp
// Constructing the lower and the upper envelope of a set of triangles.
#include <iostream>
#include <list>
#include <CGAL/Exact_rational.h>
#include <CGAL/Cartesian.h>
#include <CGAL/Env_triangle_traits_3.h>
#include <CGAL/Env_surface_data_traits_3.h>
#include <CGAL/envelope_3.h>
using Number_type = CGAL::Exact_rational;
using Kernel = CGAL::Cartesian<Number_type>;
using Traits_3 = CGAL::Env_triangle_traits_3<Kernel>;
using Point_3 = Kernel::Point_3;
using Triangle_3 = Traits_3::Surface_3;
using Data_traits_3 = CGAL::Env_surface_data_traits_3<Traits_3, char>;
using Data_triangle_3 = Data_traits_3::Surface_3;
using Envelope_diagram_2 = CGAL::Envelope_diagram_2<Data_traits_3>;
/* Auxiliary function - print the features of the given envelope diagram. */
void print_diagram(const Envelope_diagram_2& diag) {
// Go over all arrangement faces.
for (auto fit = diag.faces_begin(); fit != diag.faces_end(); ++fit) {
// Print the face boundary.
if (fit->is_unbounded()) std::cout << "[Unbounded face]";
else {
// Print the vertices along the outer boundary of the face.
auto ccb = fit->outer_ccb();
std::cout << "[Face] ";
do std::cout << '(' << ccb->target()->point() << ") ";
while (++ccb != fit->outer_ccb());
}
// Print the labels of the triangles that induce the envelope on this face.
std::cout << "--> " << fit->number_of_surfaces() << " triangles:";
for (auto sit = fit->surfaces_begin(); sit != fit->surfaces_end(); ++sit)
std::cout << ' ' << sit->data();
std::cout << std::endl;
}
// Go over all arrangement edges.
Envelope_diagram_2::Edge_const_iterator eit;
for (auto eit = diag.edges_begin(); eit != diag.edges_end(); ++eit) {
// Print the labels of the triangles that induce the envelope on this edge.
std::cout << "[Edge] (" << eit->source()->point()
<< ") (" << eit->target()->point()
<< ") --> " << eit->number_of_surfaces()
<< " triangles:";
for (auto sit = eit->surfaces_begin(); sit != eit->surfaces_end(); ++sit)
std::cout << ' ' << sit->data();
std::cout << std::endl;
}
}
/* The main program: */
int main() {
// Construct the input triangles, makred A and B.
std::list<Data_triangle_3> triangles;
auto t1 = Triangle_3(Point_3 (0, 0, 0), Point_3 (0, 6, 0), Point_3 (5, 3, 4));
triangles.push_back(Data_triangle_3(t1, 'A'));
auto t2 = Triangle_3(Point_3 (6, 0, 0), Point_3 (6, 6, 0), Point_3 (1, 3, 4));
triangles.push_back(Data_triangle_3(t2, 'B'));
// Compute and print the minimization diagram.
Envelope_diagram_2 min_diag;
CGAL::lower_envelope_3(triangles.begin(), triangles.end(), min_diag);
std::cout << std::endl << "The minimization diagram:" << std::endl;
print_diagram(min_diag);
// Compute and print the maximization diagram.
Envelope_diagram_2 max_diag;
CGAL::upper_envelope_3 (triangles.begin(), triangles.end(), max_diag);
std::cout << std::endl << "The maximization diagram:" << std::endl;
print_diagram (max_diag);
return 0;
}
CGAL::Env_surface_data_traits_3
The class Env_surface_data_traits_3 is a model of the EnvelopeTraits_3 concept and serves as a decora...
Definition: Env_surface_data_traits_3.h:39
CGAL::Env_triangle_traits_3
The traits class template Env_triangle_traits_3 models the EnvelopeTraits_3 concept,...
Definition: Env_triangle_traits_3.h:41
CGAL::Envelope_diagram_2
The class-template Envelope_diagram_2 represents the minimization diagram that corresponds to the low...
Definition: envelope_3.h:26
Kernel::Point_3
Kernel::Triangle_3
CGAL::upper_envelope_3
void upper_envelope_3(InputIterator begin, InputIterator end, Envelope_diagram_2< Traits > &diag)
Computes the upper envelope of a set of surfaces in , as given by the range [begin,...
CGAL::lower_envelope_3
void lower_envelope_3(InputIterator begin, InputIterator end, Envelope_diagram_2< Traits > &diag)
Computes the lower envelope of a set of surfaces in , as given by the range [begin,...
Kernel
CGAL::Cartesian