\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 3D Envelopes

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Envelope_3/envelope_planes.cpp
// Constructing the lower and the upper envelope of a set of planes.
#include <CGAL/Exact_rational.h>
#include <CGAL/Cartesian.h>
#include <CGAL/Env_plane_traits_3.h>
#include <CGAL/envelope_3.h>
#include <iostream>
#include <list>
typedef CGAL::Exact_rational Number_type;
typedef CGAL::Cartesian<Number_type> Kernel;
typedef Kernel::Plane_3 Plane_3;
typedef CGAL::Env_plane_traits_3<Kernel> Traits_3;
typedef Traits_3::Surface_3 Surface_3;
typedef CGAL::Envelope_diagram_2<Traits_3> Envelope_diagram_2;
/* Auxiliary function - print the features of the given envelope diagram. */
void print_diagram (const Envelope_diagram_2& diag)
{
// Go over all arrangement faces.
Envelope_diagram_2::Face_const_iterator fit;
Envelope_diagram_2::Ccb_halfedge_const_circulator ccb;
Envelope_diagram_2::Surface_const_iterator sit;
for (fit = diag.faces_begin(); fit != diag.faces_end(); ++fit)
{
// Print the face boundary.
// Print the vertices along the outer boundary of the face.
ccb = fit->outer_ccb();
std::cout << "[Face] ";
do
{
if(!ccb->is_fictitious())
std::cout << '(' << ccb->curve() << ") ";
++ccb;
} while (ccb != fit->outer_ccb());
// Print the planes that induce the envelope on this face.
std::cout << "--> " << fit->number_of_surfaces()
<< " planes:";
for (sit = fit->surfaces_begin(); sit != fit->surfaces_end(); ++sit)
std::cout << ' ' << sit->plane();
std::cout << std::endl;
}
return;
}
/* 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);
}