CGAL 6.1.1 - 3D Envelopes

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Envelope_3/envelope_planes.cpp
// Constructing the lower and the upper envelope of a set of planes.
#include <iostream>
#include <list>
#include <CGAL/Exact_rational.h>
#include <CGAL/Cartesian.h>
#include <CGAL/Env_plane_traits_3.h>
#include <CGAL/envelope_3.h>
using Number_type = CGAL::Exact_rational;
using Kernel = CGAL::Cartesian<Number_type>;
using Plane_3 = Kernel::Plane_3;
using Traits_3 = CGAL::Env_plane_traits_3<Kernel>;
using Surface_3 = Traits_3::Surface_3;
using Envelope_diagram_2 = CGAL::Envelope_diagram_2<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.
// Print the vertices along the outer boundary of the face.
auto ccb = fit->outer_ccb();
std::cout << "[Face] ";
do if (!ccb->is_fictitious()) std::cout << '(' << ccb->curve() << ") ";
while (++ccb != fit->outer_ccb());
// Print the planes that induce the envelope on this face.
std::cout << "--> " << fit->number_of_surfaces() << " planes:";
for (auto sit = fit->surfaces_begin(); sit != fit->surfaces_end(); ++sit)
std::cout << ' ' << sit->plane();
std::cout << std::endl;
}
}
/* The main program: */
int main() {
// Construct the input planes.
std::list<Surface_3> planes;
planes.push_back(Surface_3(Plane_3(0, -1, 1, 0)));
planes.push_back(Surface_3(Plane_3(-1, 0, 1, 0)));
planes.push_back(Surface_3(Plane_3(0, 1 , 1, 0)));
planes.push_back(Surface_3(Plane_3(1, 0, 1, 0)));
// Compute and print the minimization diagram.
Envelope_diagram_2 min_diag;
CGAL::lower_envelope_3(planes.begin(), planes.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(planes.begin(), planes.end(), max_diag);
std::cout << std::endl << "The maximization diagram:" << std::endl;
print_diagram (max_diag);
return 0;
}
CGAL::Env_plane_traits_3
The traits class template Env_plane_traits_3 models the EnvelopeTraits_3 concept, and is used for the...
Definition: Env_plane_traits_3.h:38
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::Plane_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