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

CGAL 4.8 - 3D Envelopes

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Envelope_3/envelope_triangles.cpp
// Constructing the lower and the upper envelope of a set of triangles.
#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>
#include <iostream>
#include <list>
typedef CGAL::Exact_rational Number_type;
typedef CGAL::Cartesian<Number_type> Kernel;
typedef CGAL::Env_triangle_traits_3<Kernel> Traits_3;
typedef Kernel::Point_3 Point_3;
typedef Traits_3::Surface_3 Triangle_3;
typedef CGAL::Env_surface_data_traits_3<Traits_3, char> Data_traits_3;
typedef Data_traits_3::Surface_3 Data_triangle_3;
typedef CGAL::Envelope_diagram_2<Data_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.
if (fit->is_unbounded())
{
std::cout << "[Unbounded face]";
}
else
{
// Print the vertices along the outer boundary of the face.
ccb = fit->outer_ccb();
std::cout << "[Face] ";
do
{
std::cout << '(' << ccb->target()->point() << ") ";
++ccb;
} 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 (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 (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 (sit = eit->surfaces_begin(); sit != eit->surfaces_end(); ++sit)
std::cout << ' ' << sit->data();
std::cout << std::endl;
}
return;
}
/* The main program: */
int main ()
{
// Construct the input triangles, makred A and B.
std::list<Data_triangle_3> triangles;
triangles.push_back (Data_triangle_3 (Triangle_3 (Point_3 (0, 0, 0),
Point_3 (0, 6, 0),
Point_3 (5, 3, 4)),
'A'));
triangles.push_back (Data_triangle_3 (Triangle_3 (Point_3 (6, 0, 0),
Point_3 (6, 6, 0),
Point_3 (1, 3, 4)),
'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);
}