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

CGAL 4.8 - 2D Envelopes

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Envelope_2/convex_hull.cpp
// Compute the convex hull of set of points using the lower envelope and upper
// envelopes of their dual line.
#include <CGAL/Exact_rational.h>
#include <CGAL/Cartesian.h>
#include <CGAL/Arr_linear_traits_2.h>
#include <CGAL/Arr_curve_data_traits_2.h>
#include <CGAL/Envelope_diagram_1.h>
#include <CGAL/envelope_2.h>
#include <vector>
typedef CGAL::Exact_rational Number_type;
typedef CGAL::Cartesian<Number_type> Kernel;
typedef CGAL::Arr_linear_traits_2<Kernel> Linear_traits_2;
typedef Linear_traits_2::Point_2 Point_2;
typedef Linear_traits_2::Line_2 Line_2;
typedef CGAL::Arr_curve_data_traits_2<Linear_traits_2,
unsigned int> Traits_2;
typedef Traits_2::X_monotone_curve_2 Dual_line_2;
typedef CGAL::Envelope_diagram_1<Traits_2> Diagram_1;
int main (int argc, char* argv[])
{
// Read the points from the input file.
const char* filename = (argc > 1) ? argv[1] : "ch_points.dat";
std::ifstream in_file(filename);
if (!in_file.is_open()) {
std::cerr << "Failed to open " << filename << " ..." << std::endl;
return -1;
}
// Read the points from the file, and construct their dual lines.
std::list<Dual_line_2> dual_lines;
unsigned int n;
in_file >> n;
std::vector<Point_2> points;
points.resize(n);
for (unsigned int k = 0; k < n; ++k) {
int px, py;
in_file >> px >> py;
points[k] = Point_2 (px, py);
// The line dual to the point (p_x, p_y) is y = p_x*x - p_y,
// or: p_x*x - y - p_y = 0:
Line_2 line = Line_2 (Number_type(px), Number_type(-1), Number_type(-py));
// Generate the x-monotone curve based on the line and the point index.
dual_lines.push_back (Dual_line_2 (line, k));
}
in_file.close();
// Compute the lower envelope of dual lines, which corresponds to the upper
// part of the convex hull, and their upper envelope, which corresponds to
// the lower part of the convex hull.
Diagram_1 min_diag;
Diagram_1 max_diag;
lower_envelope_x_monotone_2(dual_lines.begin(), dual_lines.end(), min_diag);
upper_envelope_x_monotone_2(dual_lines.begin(), dual_lines.end(), max_diag);
// Output the points along the boundary convex hull in counterclockwise
// order. We start by traversing the minimization diagram from left to
// right, then the maximization diagram from right to left.
std::cout << "The convex hull of " << points.size() << " input points:";
Diagram_1::Edge_const_handle e = min_diag.leftmost();
while (e != min_diag.rightmost()) {
std::cout << " (" << points[e->curve().data()] << ')';
e = e->right()->right();
}
// Handle the degenerate case of a vertical convex hull edge:
if (e->curve().data() != max_diag.leftmost()->curve().data())
std::cout << " (" << points[e->curve().data()] << ')';
e = max_diag.leftmost();
while (e != max_diag.rightmost()) {
std::cout << " (" << points[e->curve().data()] << ')';
e = e->right()->right();
}
std::cout << std::endl;
return 0;
}