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

CGAL 4.8 - 2D Envelopes

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Envelope_2/envelope_segments.cpp
// Constructing the lower envelope of a set of segments.
#include <CGAL/Exact_rational.h>
#include <CGAL/Cartesian.h>
#include <CGAL/Arr_segment_traits_2.h>
#include <CGAL/Arr_curve_data_traits_2.h>
#include <CGAL/Envelope_diagram_1.h>
#include <CGAL/envelope_2.h>
#include <list>
#include <iostream>
typedef CGAL::Exact_rational Number_type;
typedef CGAL::Cartesian<Number_type> Kernel;
typedef CGAL::Arr_segment_traits_2<Kernel> Segment_traits_2;
typedef Segment_traits_2::X_monotone_curve_2 Segment_2;
typedef CGAL::Arr_curve_data_traits_2<Segment_traits_2,
char> Traits_2;
typedef Traits_2::Point_2 Point_2;
typedef Traits_2::X_monotone_curve_2 Labeled_segment_2;
typedef CGAL::Envelope_diagram_1<Traits_2> Diagram_1;
int main ()
{
// Consrtuct the input segments and label them 'A' ... 'H'.
std::list<Labeled_segment_2> segments;
segments.push_back (Labeled_segment_2 (Segment_2 (Point_2 (0, 1),
Point_2 (2, 3)), 'A'));
segments.push_back (Labeled_segment_2 (Segment_2 (Point_2 (1, 2),
Point_2 (4, 5)), 'B'));
segments.push_back (Labeled_segment_2 (Segment_2 (Point_2 (1, 5),
Point_2 (7, 2)), 'C'));
segments.push_back (Labeled_segment_2 (Segment_2 (Point_2 (4, 2),
Point_2 (6, 4)), 'D'));
segments.push_back (Labeled_segment_2 (Segment_2 (Point_2 (8, 3),
Point_2 (8, 6)), 'E'));
segments.push_back (Labeled_segment_2 (Segment_2 (Point_2 (9, 2),
Point_2 (12, 4)), 'F'));
segments.push_back (Labeled_segment_2 (Segment_2 (Point_2 (10, 2),
Point_2 (12, 1)), 'G'));
segments.push_back (Labeled_segment_2 (Segment_2 (Point_2 (11, 0),
Point_2 (11, 5)), 'H'));
// Compute the minimization diagram that represents their lower envelope.
Diagram_1 min_diag;
lower_envelope_x_monotone_2 (segments.begin(), segments.end(),
min_diag);
// Print the minimization diagram.
Diagram_1::Edge_const_handle e = min_diag.leftmost();
Diagram_1::Vertex_const_handle v;
Diagram_1::Curve_const_iterator cit;
while (e != min_diag.rightmost())
{
std::cout << "Edge:";
if (! e->is_empty())
{
for (cit = e->curves_begin(); cit != e->curves_end(); ++cit)
std::cout << ' ' << cit->data();
}
else
std::cout << " [empty]";
std::cout << std::endl;
v = e->right();
std::cout << "Vertex (" << v->point() << "):";
for (cit = v->curves_begin(); cit != v->curves_end(); ++cit)
std::cout << ' ' << cit->data();
std::cout << std::endl;
e = v->right();
}
CGAL_assertion (e->is_empty());
std::cout << "Edge: [empty]" << std::endl;
return (0);
}