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

CGAL 4.8 - 2D Envelopes

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Envelope_2/envelope_circles.cpp
// Constructing the envelopes of a set of circles using the circle-segment
// traits.
#include <CGAL/Exact_rational.h>
#include <CGAL/Cartesian.h>
#include <CGAL/Arr_circle_segment_traits_2.h>
#include <CGAL/Arrangement_2.h>
#include <CGAL/Envelope_diagram_1.h>
#include <CGAL/envelope_2.h>
typedef CGAL::Exact_rational Number_type;
typedef CGAL::Cartesian<Number_type> Kernel;
typedef Kernel::Point_2 Kernel_point_2;
typedef Kernel::Circle_2 Circle_2;
typedef CGAL::Arr_circle_segment_traits_2<Kernel> Traits_2;
typedef Traits_2::Curve_2 Curve_2;
typedef CGAL::Envelope_diagram_1<Traits_2> Diagram_1;
void print_diagram (const Diagram_1& diag)
{
Diagram_1::Edge_const_handle e = diag.leftmost();
Diagram_1::Vertex_const_handle v;
while (e != diag.rightmost())
{
std::cout << "Edge: ";
if (! e->is_empty())
{
Circle_2 circ = e->curve().supporting_circle();
std::cout << " (x - " << CGAL::to_double(circ.center().x()) << ")^2 +"
<< " (y - " << CGAL::to_double(circ.center().y()) << ")^2 = "
<< CGAL::to_double(circ.squared_radius()) << std::endl;
}
else
std::cout << " [empty]" << std::endl;
v = e->right();
std::cout << "Vertex (" << CGAL::to_double(v->point().x()) << ' '
<< CGAL::to_double(v->point().y()) << ')' << std::endl;
e = v->right();
}
CGAL_assertion (e->is_empty());
std::cout << "Edge: [empty]" << std::endl;
return;
}
int main ()
{
// Create four input circles.
Curve_2 circles[4];
circles[0] = Circle_2 (Kernel_point_2 (1, 3), CGAL::square(2));
circles[1] = Circle_2 (Kernel_point_2 (4, 5), CGAL::square(4));
circles[2] = Circle_2 (Kernel_point_2 (5, 1), CGAL::square(1));
circles[3] = Circle_2 (Kernel_point_2 (6, 7), CGAL::square(2));
// Compute the minimization diagram that represents their lower envelope.
Diagram_1 min_diag;
lower_envelope_2 (&(circles[0]), &(circles[4]), min_diag);
print_diagram (min_diag);
// Compute the maximization diagram that represents the upper envelope.
Diagram_1 max_diag;
upper_envelope_2 (&(circles[0]), &(circles[4]), max_diag);
print_diagram (max_diag);
return (0);
}