CGAL 带约束的Delaunay三角剖分

本文使用CGAL进行简单的2D Delaunay 三角剖分,添加内外边界及点作为约束剖分。

Code

#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Constrained_Delaunay_triangulation_2.h>
#include <CGAL/draw_triangulation_2.h>
#include <CGAL/mark_domain_in_triangulation.h>
#include <CGAL/Polygon_2.h>
#include <iostream>
#include <unordered_map>
#include <boost/property_map/property_map.hpp>

typedef CGAL::Exact_predicates_inexact_constructions_kernel       K;
typedef CGAL::Triangulation_vertex_base_2<K>                      Vb;
typedef CGAL::Constrained_triangulation_face_base_2<K>            Fb;
typedef CGAL::Triangulation_data_structure_2<Vb, Fb>              TDS;
typedef CGAL::Exact_predicates_tag                                Itag;
typedef CGAL::Constrained_Delaunay_triangulation_2<K, TDS, Itag>  CDT;
typedef CDT::Face_handle                                          Face_handle;
typedef CDT::Point                                                Point;
typedef CGAL::Polygon_2<K>                                        Polygon_2;

int main()
{
    //construct two non-intersecting nested polygons
    Polygon_2 polygon1;
    polygon1.push_back(Point(0, 0));
    polygon1.push_back(Point(2, 0));
    polygon1.push_back(Point(2, 2));
    polygon1.push_back(Point(1, 1.75));
    polygon1.push_back(Point(0, 2));
    Polygon_2 polygon2;
    polygon2.push_back(Point(0.5, 0.5));
    polygon2.push_back(Point(1.5, 0.5));
    polygon2.push_back(Point(1.5, 1.5));
    polygon2.push_back(Point(0.5, 1.5));
    //Insert the polygons into a constrained triangulation
    CDT cdt;
    cdt.insert_constraint(polygon1.vertices_begin(), polygon1.vertices_end(), true);
    cdt.insert_constraint(polygon2.vertices_begin(), polygon2.vertices_end(), true);
    cdt.insert_constraint(Point(0.25, 0.25), Point(0.25, 1.75));
    std::unordered_map<Face_handle, bool> in_domain_map;
    boost::associative_property_map< std::unordered_map<Face_handle, bool> >
        in_domain(in_domain_map);
    //Mark facets that are inside the domain bounded by the polygon
    CGAL::mark_domain_in_triangulation(cdt, in_domain);
    unsigned int count = 0;
    for (Face_handle f : cdt.finite_face_handles())
    {
        if (get(in_domain, f)) ++count;
    }
    std::cout << "There are " << count << " faces in the domain." << std::endl;
    assert(count > 0);
    assert(count < cdt.number_of_faces());
    CGAL::draw(cdt, in_domain);
    return 0;
}

Build

项目结构：

CMakeLists.txt:

cmake_minimum_required(VERSION 3.1...3.23)
project(triangulation)
find_package(CGAL REQUIRED OPTIONAL_COMPONENTS Qt5)
create_single_source_cgal_program("triangulation.cpp")
if(CGAL_Qt5_FOUND)
  #link it with the required CGAL libraries
  target_link_libraries(triangulation PUBLIC CGAL::CGAL_Basic_viewer)
endif()

CMake构建及运行:

cmake -B build -S . -DCMAKE_TOOLCHAIN_FILE=D:\vcpkg\scripts\buildsystems\vcpkg.cmake
cmake --build build --config Debug
.\build\Debug\triangulation.exe

Result

黄色部分为约束剖分的结果面片