Vertex coordinates from General_polygon_2

Question

Explanations, pointers, or examples that show how to extract vertex coordinates from a General_Polygon_2 would be greatly appreciated.

The use case is offsetting (Minkowski sum with a circle) a simple polygon. Construction accuracy is not critical. I can seem to construct the source polygon to supply to approximated_offset_2 , but I have not been able to figure out, once the offset polygon has been constructed, how to extract vertices from the General_polygon_2 that comes from the outer_boundary() method.

A reduced example code is below:

#include <vector>
#include <cmath>
#include <cstdio>

// CGAL includes
#include <CGAL/Cartesian.h>
#include <CGAL/Polygon_2.h>
#include <CGAL/approximated_offset_2.h>
#include <CGAL/offset_polygon_2.h>
#include <CGAL/Lazy_exact_nt.h>
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>

// typedefs for CGAL items
typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
typedef CGAL::Polygon_2<Kernel> Polygon_2;
typedef CGAL::Point_2<Kernel> Point_2;
typedef CGAL::Gps_circle_segment_traits_2<Kernel> Gps_traits_2;
typedef Gps_traits_2::Polygon_with_holes_2 Offset_polygon_with_holes_2;
typedef CGAL::Lazy_exact_nt<CGAL::Quotient<CGAL::MP_Float> > NT;

typedef struct {double x; double y;} vertex_2;

void init_regular_ngon_2(std::vector<vertex_2>& ngon_vertices, const double center_x, const double center_y, const double r)
{
  unsigned int i, num_subdiv;
  double theta;

  num_subdiv = ngon_vertices.size();

  for (i = 0; i < num_subdiv; i++)
  {
    theta = 2.0 * M_PI * (double)i / (double)num_subdiv;
    ngon_vertices[i].y = center_y + (r * sin(theta));
    ngon_vertices[i].x = center_x + (r * cos(theta));
  }
}

void ngon_2_to_CGAL_poly(const std::vector<vertex_2>& ngon_vertices, Polygon_2& dest_poly)
{
  unsigned int i;

  for (i = 0; i < ngon_vertices.size(); i++)
  {
    dest_poly.push_back(Point_2(ngon_vertices[i].x, ngon_vertices[i].y));
  }
}

int main(void)
{
  CGAL::Lazy_exact_nt<NT>::set_relative_precision_of_to_double(1E-8);

  Polygon_2 test_poly;
  Offset_polygon_with_holes_2 offset_poly;
  std::vector<vertex_2> ngon(8);

  init_regular_ngon_2(ngon, 0.0, 0.0, 5.0);
  ngon_2_to_CGAL_poly(ngon, test_poly);

  offset_poly = approximated_offset_2(test_poly, 0.85, 1E-5);
  printf("The offset polygon has %d verts and %d holes\n", offset_poly.outer_boundary().size(), offset_poly.number_of_holes());

  // How to obtain vertex coordinates comprising offset polygon boundary??  Goal is to to store these in a vector of vertex_2 for later manipulation.

  return 0;
}

Answer 1

Something like the following should do the job:

typedef Gps_traits_2::General_polygon_2 General_polygon_2;
const General_polygon_2& outer_boundary = offset_poly.outer_boundary();
General_polygon_2::Curve_const_iterator cit=outer_boundary.curves_begin(),
                                        cit_end=outer_boundary.curves_end();

for(;cit!=cit_end;++cit)
{
  bool is_linear = cit->is_linear();
  std::cout << cit->source() << " " << cit->target() << "\n";  
}

The list of all member functions are given here.