\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D Arrangements

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Arrangement_on_surface_2/edge_manipulation.cpp
// Using the edge-manipulation functions.
#include <CGAL/basic.h>
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/Arr_segment_traits_2.h>
#include <CGAL/Arrangement_2.h>
#include "arr_print.h"
typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
typedef CGAL::Arr_segment_traits_2<Kernel> Traits_2;
typedef Traits_2::Point_2 Point_2;
typedef Traits_2::X_monotone_curve_2 Segment_2;
typedef CGAL::Arrangement_2<Traits_2> Arrangement_2;
typedef Arrangement_2::Vertex_handle Vertex_handle;
typedef Arrangement_2::Halfedge_handle Halfedge_handle;
int main()
{
// Step(a) - construct a triangular face.
Arrangement_2 arr;
Segment_2 s1(Point_2(667, 1000), Point_2(4000, 5000));
Segment_2 s2(Point_2(4000, 0), Point_2(4000, 5000));
Segment_2 s3(Point_2(667, 1000), Point_2(4000, 0));
Halfedge_handle e1 = arr.insert_in_face_interior(s1, arr.unbounded_face());
Vertex_handle v1 = e1->source();
Vertex_handle v2 = e1->target();
Halfedge_handle e2 = arr.insert_from_right_vertex(s2, v2);
Vertex_handle v3 = e2->target();
arr.insert_at_vertices(s3, v3, v1);
// Step (b) - create additional two faces inside the triangle.
Point_2 p1(4000, 3666), p2(4000, 1000);
Segment_2 s4(Point_2(4000, 5000), p1);
Segment_2 s5(p1, p2);
Segment_2 s6(Point_2(4000, 0), p2);
Halfedge_handle e4 = arr.split_edge(e2, s4, Segment_2(Point_2(4000, 0), p1));
Vertex_handle w1 = e4->target();
Halfedge_handle e5 = arr.split_edge(e4->next(), s5, s6);
Vertex_handle w2 = e5->target();
Halfedge_handle e6 = e5->next();
Segment_2 s7(p1, Point_2(3000, 2666));
Segment_2 s8(p2, Point_2(3000, 1333));
Segment_2 s9(Point_2(3000, 2666), Point_2(2000, 1666));
Segment_2 s10(Point_2(3000, 1333), Point_2(2000, 1666));
Segment_2 s11(Point_2(3000, 1333), Point_2(3000, 2666));
Halfedge_handle e7 = arr.insert_from_right_vertex(s7, w1);
Vertex_handle v4 = e7->target();
Halfedge_handle e8 = arr.insert_from_right_vertex(s8, w2);
Vertex_handle v5 = e8->target();
Vertex_handle v6 =
arr.insert_in_face_interior(Point_2(2000, 1666), e8->face());
arr.insert_at_vertices(s9, v4, v6);
arr.insert_at_vertices(s10, v5, v6);
arr.insert_at_vertices(s11, v4, v5);
// Step(c) - remove and merge faces to form a single hole in the traingle.
arr.remove_edge(e7);
arr.remove_edge(e8);
e5 = arr.merge_edge(e5, e6, Segment_2(e5->source()->point(),
e6->target()->point()));
e2 = arr.merge_edge(e4, e5, s2);
print_arrangement(arr);
return 0;
}