I have a vector of 2D points (N elements) in the plane. I want to make the convex hull of these points. After that, I want to retrieve the vector index of each vertex in the convex hull, how can I do this?
I know that, there is such possibility for triangulation by making use of vector<pair<Point_2, unsigned> >, but when I use paired point in making convex hull, it produces a bunch of errors. This is the related piece of code that I use:
#include <iostream> #include <CGAL/Exact_predicates_inexact_constructions_kernel.h> #include <CGAL/convex_hull_2.h> #include <CGAL/convex_hull_traits_2.h> using namespace std; typedef CGAL::Exact_predicates_inexact_constructions_kernel K; typedef K::Point_2 Point_2; typedef pair<Point_2, unsigned> Paired; typedef CGAL::convex_hull_traits_2<Paired> ch_traits; typedef vector<Paired> Vector; int main() { Vector points; Vector result; for (int i = 0; i < 5; i++) points.push_back(make_pair(Point_2(i, i), i)); CGAL::convex_hull_2( points.begin(), points.end(), back_inserter(result), const Traits &ch_traits ); return 0; }
You need to provide a traits class model of ConvexHullTraits, the pair type being your point type. In practice it is rather simple, you simply need a struct containing all functors, with the operators simply forwarding to the CGAL traits class functor using pair::first.
Here is a simple example:
#include <iostream> #include <CGAL/Exact_predicates_inexact_constructions_kernel.h> #include <CGAL/convex_hull_2.h> #include <CGAL/convex_hull_traits_2.h> #include <boost/foreach.hpp> typedef CGAL::Exact_predicates_inexact_constructions_kernel K; typedef K::Point_2 Point_2; typedef std::pair<Point_2, unsigned> Point_with_info; template <class F> struct Forward_functor : public F { template <class Point_2> bool operator() (const Point_2& p, const Point_2& q) const { return static_cast<const F*>(this)->operator()(p.first, q.first); } template <class Point_2> bool operator() (const Point_2& p, const Point_2& q, const Point_2& r) const { return static_cast<const F*>(this)->operator()(p.first, q.first, r.first); } template <class Point_2> bool operator() (const Point_2& p, const Point_2& q, const Point_2& r, const Point_2& s) const { return static_cast<const F*>(this)->operator()(p.first, q.first, r.first, s.first); } }; struct CH_traits_for_point_with_info { typedef Point_with_info Point_2; typedef CGAL::Convex_hull_traits_2<K> Base; typedef Forward_functor<Base::Less_xy_2> Less_xy_2; typedef Forward_functor<Base::Less_yx_2> Less_yx_2; typedef Forward_functor<Base::Less_signed_distance_to_line_2> Less_signed_distance_to_line_2; typedef Forward_functor<Base::Less_rotate_ccw_2> Less_rotate_ccw_2; typedef Forward_functor<Base::Left_turn_2> Left_turn_2; typedef Forward_functor<Base::Equal_2> Equal_2; struct Orientation_2 { CGAL::Orientation operator()(const Point_2& p, const Point_2& q, const Point_2& r) const { return Base::Orientation_2()(p.first, q.first, r.first); } }; Equal_2 equal_2_object () const { return Equal_2(); } Less_xy_2 less_xy_2_object () const { return Less_xy_2(); } Less_yx_2 less_yx_2_object () const { return Less_yx_2(); } Less_signed_distance_to_line_2 less_signed_distance_to_line_2_object () const { return Less_signed_distance_to_line_2(); } Less_rotate_ccw_2 less_rotate_ccw_2_object () const { return Less_rotate_ccw_2(); } Left_turn_2 left_turn_2_object () const { return Left_turn_2(); } Orientation_2 orientation_2_object () const { return Orientation_2(); } }; int main() { std::vector<Point_with_info> input_points; std::vector<Point_with_info> result; input_points.push_back( Point_with_info(Point_2(0,0), 0) ); input_points.push_back( Point_with_info(Point_2(1,0), 1) ); input_points.push_back( Point_with_info(Point_2(0,1), 2) ); input_points.push_back( Point_with_info(Point_2(0.25,0.25), 3) ); CGAL::convex_hull_2(input_points.begin(), input_points.end(), back_inserter(result), CH_traits_for_point_with_info() ); BOOST_FOREACH(const Point_with_info& p, result) { std::cout << p.first << " - " << p.second << "\n"; } return 0; }
Here is a more complicated example where the points are not copied and the algorithm is working with point indices:
#include <iostream> #include <CGAL/Exact_predicates_inexact_constructions_kernel.h> #include <CGAL/convex_hull_2.h> #include <CGAL/convex_hull_traits_2.h> #include <boost/foreach.hpp> typedef CGAL::Exact_predicates_inexact_constructions_kernel K; typedef K::Point_2 Point_2; template <class F> struct Forward_functor : public F { const std::vector<Point_2>& points; Forward_functor(const std::vector<Point_2>& points) : points(points) {} template <class Id> bool operator() (const Id& p, const Id& q) const { return static_cast<const F*>(this)->operator()(points[p], points[q]); } template <class Id> bool operator() (const Id& p, const Id& q, const Id& r) const { return static_cast<const F*>(this)->operator()(points[p], points[q], points[r]); } template <class Id> bool operator() (const Id& p, const Id& q, const Id& r, const Id& s) const { return static_cast<const F*>(this)->operator()(points[p], points[q], points[r], points[s]); } }; struct CH_traits_for_point_with_info { const std::vector<K::Point_2>& points; CH_traits_for_point_with_info(const std::vector<K::Point_2>& points) : points(points) {} typedef unsigned Point_2; typedef CGAL::Convex_hull_traits_2<K> Base; typedef Forward_functor<Base::Less_xy_2> Less_xy_2; typedef Forward_functor<Base::Less_yx_2> Less_yx_2; typedef Forward_functor<Base::Less_signed_distance_to_line_2> Less_signed_distance_to_line_2; typedef Forward_functor<Base::Less_rotate_ccw_2> Less_rotate_ccw_2; typedef Forward_functor<Base::Left_turn_2> Left_turn_2; typedef Forward_functor<Base::Equal_2> Equal_2; struct Orientation_2 { const std::vector<K::Point_2>& points; Orientation_2(const std::vector<K::Point_2>& points) : points(points) {} CGAL::Orientation operator()(Point_2 p, Point_2 q, Point_2 r) const { return Base::Orientation_2()(points[p], points[q], points[r]); } }; Equal_2 equal_2_object () const { return Equal_2(points); } Less_xy_2 less_xy_2_object () const { return Less_xy_2(points); } Less_yx_2 less_yx_2_object () const { return Less_yx_2(points); } Less_signed_distance_to_line_2 less_signed_distance_to_line_2_object () const { return Less_signed_distance_to_line_2(points); } Less_rotate_ccw_2 less_rotate_ccw_2_object () const { return Less_rotate_ccw_2(points); } Left_turn_2 left_turn_2_object () const { return Left_turn_2(points); } Orientation_2 orientation_2_object () const { return Orientation_2(points); } }; int main() { std::vector<Point_2> input_points; std::vector<unsigned> ids; std::vector<unsigned> result; input_points.push_back( Point_2(0,0) ); input_points.push_back( Point_2(0,1) ); input_points.push_back( Point_2(1,0) ); input_points.push_back( Point_2(0.25,0.25) ); ids.push_back(0); ids.push_back(1); ids.push_back(2); ids.push_back(3); CGAL::convex_hull_2(ids.begin(), ids.end(), back_inserter(result), CH_traits_for_point_with_info(input_points) ); BOOST_FOREACH(unsigned i, result) { std::cout << input_points[i] << " - " << i << "\n"; } return 0; }
