/*! Print the given envelope diagram. */
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 (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;
}