添加链接 注册    登录
link管理
链接快照平台
  • 输入网页链接，自动生成快照
  • 标签化管理网页链接
相关文章推荐
求醉的枕头  ·  CodeGuru Forums·  4 月前    · 
可爱的滑板  ·  Using ts-node with ...·  8 月前    · 
微醺的豌豆  ·  MySQL / MariaDB ...·  9 月前    · 
霸气的大蒜  ·  机器学习在材料服役性能预测中的应用-Appl ...·  9 月前    · 
善良的凉面  ·  PP-LCNet: ...·  1 年前    · 
link管理  ›  CGAL 6.0 - 2D Polygons: User Manual
kernel typedef cgal
https://doc.cgal.org/latest/Polygon/index.html
失落的咖啡豆
5 月前
Introduction

A polygon is a closed chain of edges. Several algorithms are available for polygons. For some of those algorithms, it is necessary that the polygon is simple. A polygon is simple if edges don't intersect, except consecutive edges, which intersect in their common vertex.

The following algorithms are available:

  • find the leftmost, rightmost, topmost and bottommost vertex.
  • compute the (signed) area.
  • check if a polygon is simple.
  • check if a polygon is convex.
  • find the orientation (clockwise or counterclockwise)
  • check if a point lies inside a polygon.

    • All those operations take two forward iterators as parameters in order to describe the polygon. These parameters have a point type as value type.

    The type Polygon_2 can be used to represent polygons. Polygons are dynamic. Vertices can be modified, inserted and erased. They provide the algorithms described above as member functions. Moreover, they provide ways of iterating over the vertices and edges.

    The Polygon_2 class is a wrapper around a container of points, but little more. Especially, computed values are not cached. That is, when the Polygon_2::is_simple() member function is called twice or more, the result is computed each time anew.

    Polygons with Holes and Multipolygons with Holes

    This package also provides classes to represent polygons with holes and multipolygons with holes.

    For polygons with holes, these are Polygon_with_holes_2 and General_polygon_with_holes_2 . They can store a polygon that represents the outer boundary and a sequence of polygons that represent the holes.

    For multipolygons with holes, there is Multipolygon_with_holes_2 . It stores a sequence of polygons with holes.

    These classes do not add any semantic requirements on the simplicity or orientation of their boundary polygons.

    Examples The Polygon Class

    The following example creates a polygon and illustrates the usage of some member functions.

    File Polygon/Polygon.cpp

    #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
    #include <CGAL/Polygon_2.h>
    #include <iostream>
    typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
    typedef K::Point_2 Point;
    typedef CGAL::Polygon_2<K> Polygon_2;
    using std::cout; using std::endl;
    int main()
    Point points[] = { Point(0,0), Point(5.1,0), Point(1,1), Point(0.5,6)};
    Polygon_2 pgn(points, points+4);
    // check if the polygon is simple.
    cout << "The polygon is " <<
    (pgn.is_simple() ? "" : "not " ) << "simple." << endl;
    // check if the polygon is convex
    cout << "The polygon is " <<
    (pgn.is_convex() ? "" : "not " ) << "convex." << endl;
    return 0;
    CGAL::Exact_predicates_inexact_constructions_kernel
    CGAL::Polygon_2
    The class Polygon_2 implements polygons.
    Definition: Polygon_2.h:65
    The Multipolygon with Holes Class

    The following example shows the creation of a multipolygon with holes and the traversal of the polygons in it.

    File Polygon/multipolygon.cpp

    #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
    #include <CGAL/Multipolygon_with_holes_2.h>
    using Kernel = CGAL::Exact_predicates_inexact_constructions_kernel ;
    using Point_2 = Kernel::Point_2 ;
    using Polygon_2 = CGAL::Polygon_2<Kernel> ;
    using Polygon_with_holes_2 = CGAL::Polygon_with_holes_2<Kernel> ;
    using Multipolygon_with_holes_2 = CGAL::Multipolygon_with_holes_2<Kernel> ;
    int main() {
    Point_2 p1_outer[] = { Point_2 (0,0), Point_2 (1,0), Point_2 (1,1), Point_2 (0,1)};
    Point_2 p1_inner[] = { Point_2 (0.2,0.2), Point_2 (0.8,0.2), Point_2 (0.8,0.8), Point_2 (0.2,0.8)};
    Polygon_with_holes_2 p1(Polygon_2(p1_outer, p1_outer+4));
    Polygon_2 h(p1_inner, p1_inner+4);
    p1.add_hole(h);
    Point_2 p2_outer[] = { Point_2 (0.4,0.4), Point_2 (0.6,0.4), Point_2 (0.6,0.6), Point_2 (0.4,0.6)};
    Polygon_with_holes_2 p2(Polygon_2(p2_outer, p2_outer+4));
    Multipolygon_with_holes_2 mp;
    mp.add_polygon_with_holes(p1);
    mp.add_polygon_with_holes(p2);
    for ( auto const & p: mp.polygons_with_holes()) {
    std::cout << p << std::endl;
    return 0;
    CGAL::Multipolygon_with_holes_2
    The class Multipolygon_with_holes_2 models the concept MultipolygonWithHoles_2.
    Definition: Multipolygon_with_holes_2.h:35
    CGAL::Polygon_with_holes_2
    The class Polygon_with_holes_2 models the concept GeneralPolygonWithHoles_2.
    Definition: Polygon_with_holes_2.h:43
    Kernel::Point_2

    Figure 15.1 A polygon and some points


    Algorithms Operating on Sequences of Points

    The following example creates a polygon and illustrates the usage of some global functions that operate on sequences of points.

    File Polygon/polygon_algorithms.cpp

    #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
    #include <CGAL/Polygon_2_algorithms.h>
    #include <iostream>
    typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
    typedef K::Point_2 Point;
    using std::cout; using std::endl;
    void check_inside(Point pt, Point *pgn_begin, Point *pgn_end, K traits)
    cout << "The point " << pt;
    switch ( CGAL::bounded_side_2 (pgn_begin, pgn_end,pt, traits)) {
    case CGAL::ON_BOUNDED_SIDE :
    cout << " is inside the polygon.\n" ;
    break ;
    case CGAL::ON_BOUNDARY :
    cout << " is on the polygon boundary.\n" ;
    break ;
    case CGAL::ON_UNBOUNDED_SIDE :
    cout << " is outside the polygon.\n" ;
    break ;
    int main()
    Point points[] = { Point(0,0), Point(5.1,0), Point(1,1), Point(0.5,6)};
    // check if the polygon is simple.
    cout << "The polygon is "
    << ( CGAL::is_simple_2 (points, points+4, K()) ? "" : "not " )
    << "simple." << endl;
    check_inside(Point(0.5, 0.5), points, points+4, K());
    check_inside(Point(1.5, 2.5), points, points+4, K());
    check_inside(Point(2.5, 0), points, points+4, K());
    return 0;
    CGAL::bounded_side_2
    Bounded_side bounded_side_2(ForwardIterator first, ForwardIterator last, const Point &point, const PolygonTraits &traits)
    Computes if a point lies inside a polygon.
    CGAL::is_simple_2
    bool is_simple_2(ForwardIterator first, ForwardIterator last, const PolygonTraits &traits)
    Checks if the polygon defined by the iterator range [first,last) is simple, that is,...
    CGAL::ON_BOUNDARY
    ON_BOUNDARY
    CGAL::ON_UNBOUNDED_SIDE
    ON_UNBOUNDED_SIDE
    CGAL::ON_BOUNDED_SIDE
    ON_BOUNDED_SIDE
    Polygons in 3D Space

    Sometimes it is useful to run a 2D algorithm on 3D data. Polygons may be contours of a 3D object, where the contours are organized in parallel slices, generated by segmentation of image data from a scanner.

    In order to avoid an explicit projection on the xy plane, one can use the traits class Projection_traits_xy_3 which is part of the 2D and 3D Linear Geometric Kernel.

    File Polygon/projected_polygon.cpp

    #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
    #include <CGAL/Projection_traits_yz_3.h>
    #include <CGAL/Polygon_2_algorithms.h>
    #include <iostream>
    typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
    typedef K::Point_3 Point_3 ;
    int main()
    Point_3 points[4] = { Point_3 (0,1,1), Point_3 (0,2,1), Point_3 (0,2,2), Point_3 (0,1,2) };
    bool b = CGAL::is_simple_2 (points,
    points+4,
    CGAL::Projection_traits_yz_3<K> ());
    if (!b){
    std::cerr << "Error polygon is not simple" << std::endl;
    return 1;
    return 0;
    CGAL::Projection_traits_yz_3
    Kernel::Point_3
    Iterating over Vertices and Edges

    The polygon class provides member functions such as Polygon_2::vertices_begin() and Polygon_2::vertices_end() to iterate over the vertices. It additionally provides a member function Polygon_2::vertices() that returns a range, mainly to be used with modern for loops. The same holds for edges and for the holes of the class Polygon_with_holes_2 .

    File Polygon/ranges.cpp

    #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
    #include <CGAL/Polygon_2.h>
    typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
    typedef CGAL::Polygon_2<K> Polygon_2;
    typedef K::Point_2 Point_2 ;
    typedef K::Segment_2 Segment_2 ;
    int main()
    // create a polygon and put some points in it
    Polygon_2 p;
    p.push_back( Point_2 (0,0));
    p.push_back( Point_2 (4,0));
    p.push_back( Point_2 (4,4));
    for ( const Point_2 & p : p.vertices()){
    std::cout << p << std::endl;
    // As the range is not light weight, we have to use a reference
    const Polygon_2::Vertices & range = p.vertices();
    for ( auto it = range.begin(); it!= range.end(); ++it){
    std::cout << *it << std::endl;
    for ( const Segment_2 & e : p.edges()){
    std::cout << e << std::endl;
    return EXIT_SUCCESS;
    CGAL::Polygon_2::Vertices
    Container Vertices
    a range type to iterate over the vertices
    Definition: Polygon_2.h:124
    Kernel::Segment_2
    Draw a Polygon

    A polygon can be visualized by calling the CGAL::draw<P>() function as shown in the following example. This function opens a new window showing the given polygon. A call to this function is blocking, that is the program continues as soon as the user closes the window. Versions for polygons with holes and multipolygons with holes also exist, cf. CGAL::draw<PH>() and CGAL::draw<MPH>() .

    File Polygon/draw_polygon.cpp

    #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
    #include <CGAL/Polygon_2.h>
    #include <CGAL/draw_polygon_2.h>
    typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
    typedef CGAL::Polygon_2<K> Polygon_2;
    typedef CGAL::Point_2<K> Point;
    int main()
    // create a polygon and put some points in it
    Polygon_2 p;
    p.push_back(Point(0,0));
    p.push_back(Point(4,0));
    p.push_back(Point(4,4));
    p.push_back(Point(2,2));
    p.push_back(Point(0,4));
    CGAL::draw (p);
    return EXIT_SUCCESS;
    CGAL::Point_2
    CGAL::draw
    void draw(const MPH &aph)
    opens a new window and draws aph, an instance of the CGAL::Multipolygon_with_holes_2 class.

    This function requires CGAL_Qt6 , and is only available if the macro CGAL_USE_BASIC_VIEWER is defined. Linking with the cmake target CGAL::CGAL_Basic_viewer will link with CGAL_Qt6 and add the definition CGAL_USE_BASIC_VIEWER .

    Figure 15.2 Result of the run of the draw_polygon program. A window shows the polygon and allows to navigate through the scene.


     
    推荐文章
    求醉的枕头  ·  CodeGuru Forums
    4 月前
    可爱的滑板  ·  Using ts-node with Global Types | Blake Williams
    8 月前
    微醺的豌豆  ·  MySQL / MariaDB Schema Retrieval for TINYINT being... - Qlik Community - 2339516
    9 月前
    霸气的大蒜  ·  机器学习在材料服役性能预测中的应用-Application of Machine Learning in Predicting Service Performance of Materials
    9 月前
    善良的凉面  ·  PP-LCNet: 一个轻量级的卷积神经网络 | AI技术聚合
    1 年前
    Link管理   ·   51好读   ·   Sov5搜索   ·   小百科
    link管理 - 链接快照平台