c++ - 几何、交集

Question

我有一个问题。我想将四边形与四边形相交。

int main(){
  typedef boost::geometry::model::point_xy<double> TBoostPoint;
  typedef boost::geometry::model::polygon<TBoostPoint> TBoostPoly;
  TBoostPoint point;
  TBoostPoly firstPoly, secondPoly;
  boost::geometry::read_wkt("POLYGON(
                (1.504477611940313, 3.761194029850755), 
                (1.504477611940305, 3.573134328358203),
                (1.316417910447765, 3.573134328358206),
                (1.316417910447769, 3.761194029850752))", firstPoly);
  boost::geometry::read_wkt("POLYGON(
                (1.504477611940313, 3.761194029850755), 
                (1.504477611940305, 3.573134328358203),
                (1.316417910447765, 3.573134328358206),
                (1.316417910447751, 3.761194029850769))", secondPoly);
 std::vector<TBoostPoly> outPoly;
 boost::geometry::intersection(firstPoly,secondPoly,outPoly);
}

outPoly - 是空的，但事实并非如此。

Answer 1

有两个主要问题。

输出未定义，因为输入无效。

1. 输入的 WKT 指定了许多无效的内环(由单个点组成)，而不是您预期的 5 个点的单个外环(不包括关闭点)。修复它:

   bg::read_wkt("POLYGON(( 1.504477611940313 3.761194029850755, 1.504477611940305 3.573134328358203, 1.316417910447765 3.573134328358206, 1.316417910447769 3.761194029850752))", first);
   bg::read_wkt("POLYGON(( 1.504477611940313 3.761194029850755, 1.504477611940305 3.573134328358203, 1.316417910447765 3.573134328358206, 1.316417910447751 3.761194029850769))", second); 
   

2. Boost Geometry 自始至终都假定您永远不会在记录的先决条件下犯错。如果您阅读多边形概念页面和 intersection 的先决条件，您将看到完整列表¹。

   如果不这样做，您将不会遇到友好的错误，只会出现无声的失败、损坏或错误的答案。是的。这很糟糕。

   更糟糕的是，在 Boost 1_57 (IIRC) 之前，BGeo 甚至没有 is_valid 工具来测试大量需求。好消息是，如果您升级到此版本或以后，您的生活会简单得多。

在这种情况下，您会了解到多边形未正确闭合:

Live On Coliru

#include <boost/geometry.hpp>
#include <boost/geometry/geometries/point_xy.hpp>
#include <boost/geometry/geometries/polygon.hpp>
#include <boost/geometry/geometries/multi_polygon.hpp>
#include <boost/geometry/io/io.hpp>
#include <boost/geometry/algorithms/intersection.hpp>
#include <boost/geometry/algorithms/correct.hpp>
#include <boost/geometry/algorithms/is_valid.hpp>

namespace bg = boost::geometry;

int main(){
    typedef bg::model::d2::point_xy<double> TPoint;
    typedef bg::model::polygon<TPoint>      TPoly;
    TPoly first, second;

    bg::read_wkt("POLYGON(( 1.504477611940313 3.761194029850755, 1.504477611940305 3.573134328358203, 1.316417910447765 3.573134328358206, 1.316417910447769 3.761194029850752))", first);
    bg::read_wkt("POLYGON(( 1.504477611940313 3.761194029850755, 1.504477611940305 3.573134328358203, 1.316417910447765 3.573134328358206, 1.316417910447751 3.761194029850769))", second); 

    std::string reason;
    // polys not closed!
    if (!bg::is_valid(first, reason))  std::cout << "First polygon not valid: "  << reason << "\n";
    if (!bg::is_valid(second, reason)) std::cout << "Second polygon not valid: " << reason << "\n";

    bg::correct(first);
    bg::correct(second);

    // no more output!
    if (!bg::is_valid(first, reason))  std::cout << "First polygon not valid: "  << reason << "\n";
    if (!bg::is_valid(second, reason)) std::cout << "Second polygon not valid: " << reason << "\n";

    std::vector<TPoly> out;
    bg::intersection(first, second, out);

    for (auto& g : out)
        std::cout << "\nresult: " << bg::wkt(g) << "\n";
}

打印:

First polygon not valid: Geometry is defined as closed but is open
Second polygon not valid: Geometry is defined as closed but is open

糟糕。 geos 没有关闭! correct(poly) 自动修复了这个问题:

result: POLYGON((1.50448 3.57313,1.31642 3.57313,1.31642 3.76119,1.50448 3.76119,1.50448 3.57313))

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¹ 外圈必须逆时针，内圈顺时针，多边形必须闭合...诸如此类。