顶点坐标从General_polygon_2

Vertex coordinates from General_polygon_2

本文关键字：polygon General 坐标顶点更新时间：2023-10-16

说明

、指针或示例，说明如何从General_Polygon_2中提取顶点坐标将不胜感激。

用例是偏移（带有圆的闵可夫斯基和）一个简单的多边形。施工精度并不重要。我似乎可以构造源多边形以提供给approximated_offset_2，但是一旦构造了偏移多边形，我就无法弄清楚如何从来自outer_boundary()方法的General_polygon_2中提取顶点。

简化的示例代码如下：

#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 holesn", 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;
}

类似以下内容的内容应该可以完成这项工作：

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";  
}

此处给出了所有成员函数的列表。

approximated_offset_2 返回一个Polygon_with_holes，outer_boundary()你可以得到General_polygon_2，但你不能只通过它的曲线迭代它的顶点，然后你可以得到曲线的目标和源，正如 Sloriot 提到的。目标点和源点不是Kernel::Point_2成员，因此您不能使用=运算符，但您可以获得target.x()和target.y()，它们是其坐标并且是类 CoordNT 的成员，这不是双精度/浮点数，而是 3 个数字(alpha, beta, gamma)，您可以从方程 x = a+b * sqrt（c） 计算出确切的值。

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;
for(cit = outer_boundary.curves_begin();
            cit !=outer_boundary.curves_end();++cit){
        source = Point2((cit->source().x().alpha())+
                (cit->source().x().beta()*sqrt(cit->source().x().gamma())),
                (cit->source().y().alpha())+
                (cit->source().y().beta()*sqrt(cit->source().y().gamma())));
        target = Point2((cit->target().x().alpha())+
                (cit->target().x().beta()*sqrt(cit->target().x().gamma())),
                (cit->target().y().alpha())+
                (cit->target().y().beta()*sqrt(cit->target().y().gamma())));