mirror of https://github.com/CGAL/cgal
64 lines
2.1 KiB
C++
64 lines
2.1 KiB
C++
//! \file examples/Envelope_3/ex_envelope_planes.cpp
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// Constructing the lower and the upper envelope of a set of planes.
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#include <iostream>
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#include <list>
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#include <CGAL/Exact_rational.h>
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#include <CGAL/Cartesian.h>
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#include <CGAL/Env_plane_traits_3.h>
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#include <CGAL/envelope_3.h>
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using Number_type = CGAL::Exact_rational;
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using Kernel = CGAL::Cartesian<Number_type>;
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using Plane_3 = Kernel::Plane_3;
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using Traits_3 = CGAL::Env_plane_traits_3<Kernel>;
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using Surface_3 = Traits_3::Surface_3;
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using Envelope_diagram_2 = CGAL::Envelope_diagram_2<Traits_3>;
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/* Auxiliary function - print the features of the given envelope diagram. */
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void print_diagram(const Envelope_diagram_2& diag) {
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// Go over all arrangement faces.
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for (auto fit = diag.faces_begin(); fit != diag.faces_end(); ++fit) {
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// Print the face boundary.
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// Print the vertices along the outer boundary of the face.
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auto ccb = fit->outer_ccb();
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std::cout << "[Face] ";
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do if (!ccb->is_fictitious()) std::cout << '(' << ccb->curve() << ") ";
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while (++ccb != fit->outer_ccb());
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// Print the planes that induce the envelope on this face.
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std::cout << "--> " << fit->number_of_surfaces() << " planes:";
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for (auto sit = fit->surfaces_begin(); sit != fit->surfaces_end(); ++sit)
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std::cout << ' ' << sit->plane();
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std::cout << std::endl;
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}
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}
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/* The main program: */
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int main() {
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// Construct the input planes.
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std::list<Surface_3> planes;
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planes.push_back(Surface_3(Plane_3(0, -1, 1, 0)));
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planes.push_back(Surface_3(Plane_3(-1, 0, 1, 0)));
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planes.push_back(Surface_3(Plane_3(0, 1 , 1, 0)));
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planes.push_back(Surface_3(Plane_3(1, 0, 1, 0)));
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// Compute and print the minimization diagram.
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Envelope_diagram_2 min_diag;
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CGAL::lower_envelope_3(planes.begin(), planes.end(), min_diag);
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std::cout << std::endl << "The minimization diagram:" << std::endl;
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print_diagram(min_diag);
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// Compute and print the maximization diagram.
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Envelope_diagram_2 max_diag;
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CGAL::upper_envelope_3(planes.begin(), planes.end(), max_diag);
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std::cout << std::endl << "The maximization diagram:" << std::endl;
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print_diagram (max_diag);
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return 0;
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}
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