如何使用 C++ boost geometry 从两个多边形创建环（甜甜圈）？

Question

我正在尝试计算 2 个多边形之间的差异（实际上，为简单起见，是直线形状）。例如，shape1 有点列表 {0 0, 100, 0, 100 100, 0 100}，shape2 有点列表 {25 25, 75 25, 75 75, 25 75}。所以从概念上讲，我希望 "shape1 - shape2" 会为我提供 4 个矩形框，可以做成环形或甜甜圈形状。我不知道如何做到这一点，但我在网上找到了 "boost" 库并试了一下：

#include <iostream>
#include <list>

#include <boost/geometry.hpp>
#include <boost/geometry/geometries/point_xy.hpp>
#include <boost/geometry/geometries/polygon.hpp>

#include <boost/foreach.hpp>


int main()
{
    typedef boost::geometry::model::polygon<boost::geometry::model::d2::point_xy<double> > polygon;

    polygon green, blue;

    boost::geometry::read_wkt( "POLYGON((0 0 100 0 100 100 0 100))", green);

    boost::geometry::read_wkt( "POLYGON((25 25 75 22 75 75 25 75))", blue);

    std::list<polygon> output;
    boost::geometry::difference(green, blue, output);

    int i = 0;
    std::cout << "green - blue:" << std::endl;
    BOOST_FOREACH(polygon const& p, output)
    {
        std::cout << i++ << ": " << boost::geometry::area(p) << std::endl;
    }


    output.clear();
    boost::geometry::difference(blue, green, output);

    i = 0;
    std::cout << "blue - green:" << std::endl;
    BOOST_FOREACH(polygon const& p, output)
    {
        std::cout << i++ << ": " << boost::geometry::area(p) << std::endl;
    }


    return 0;
}

然而，什么也没有打印出来......我的计划是想办法将输出结果转换为矩形框 {0 0 100 0 100 25 0 25} {0 75 100 75 100 100 0 100} {0 25 25 25 25 75 0 75} 和 {75 25 100 25 100 75 75 75}，但令我感到沮丧的是，上面的代码根本没有打印出任何内容。谁能给我一些指导？我附上了一张图片，展示了我想要做什么。事实上，我已经有了表示这个甜甜圈的所有点坐标，所以也许我可以跳过 "difference() function" ？如果是这种情况，困难的部分将是将甜甜圈转换为矩形段。（让我们假设这里的所有多边形都是直线形状。）谢谢

Answer 1

您的起始多边形没有所需的方向。您可以使用 is_valid 自行找出答案。方便的是，您可以使用 correct 来修复输入数据的最常见问题：

std::string reason;
if (!bg::is_valid(geometry, reason))
{
    std::cout << "Correcting " << bg::wkt(geometry) << " to ";
    bg::correct(geometry);
    std::cout << bg::wkt(geometry) << "\n";

    if (!bg::is_valid(geometry, reason))
        std::cout << "UNCORRECTIBLE: " << reason << "\n";
}

当你这样做时，你会发现：

Correcting POLYGON((0 0,100 0,100 100,0 100,0 0)) to POLYGON((0 0,0 100,100 100,100 0,0 0))
Correcting POLYGON((25 25,75 22,75 75,25 75,25 25)) to POLYGON((25 25,25 75,75 75,75 22,25 25))

现在，当你得到差异时，你将得到预期的结果：

auto do_diff = [](std::string caption, auto const& a, auto const& b) {
    multi output;
    bg::difference(a, b, output);

    std::cout << caption << bg::wkt(output) << std::endl;
};

do_diff("green - blue:", green, blue);
do_diff("blue - green:", blue, green);

完整演示

Live On Coliru

#include <iostream>
#include <fstream>

#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/foreach.hpp>

namespace bg = boost::geometry; 

int main() {
    typedef bg::model::d2::point_xy<double> point;
    typedef bg::model::polygon<point> polygon;
    typedef bg::model::multi_polygon<polygon> multi;

    polygon green, blue;

    bg::read_wkt("POLYGON((0 0 100 0 100 100 0 100))", green);
    bg::read_wkt("POLYGON((25 25 75 22 75 75 25 75))", blue);

    auto test = [](polygon& geometry) {
        std::string reason;
        if (!bg::is_valid(geometry, reason))
        {
            std::cout << "Correcting " << bg::wkt(geometry) << " to ";
            bg::correct(geometry);
            std::cout << bg::wkt(geometry) << "\n";

            if (!bg::is_valid(geometry, reason))
                std::cout << "UNCORRECTIBLE: " << reason << "\n";
        }
    };

    test(green);
    test(blue);

    auto do_diff = [](std::string caption, polygon const& a, polygon const& b) {
        multi output;
        bg::difference(a, b, output);

        std::cout << caption << bg::wkt(output) << std::endl;
    };

    do_diff("green - blue:", green, blue);
    do_diff("blue - green:", blue, green);

    {
        std::ofstream svg("output.svg");
        boost::geometry::svg_mapper<point> mapper(svg, 400, 400);
        mapper.add(blue);
        mapper.add(green);

        mapper.map(blue, "fill-opacity:0.5;fill:rgb(0,0,153);stroke:rgb(0,0,200);stroke-width:2");
        mapper.map(green, "fill-opacity:0.5;fill:rgb(0,153,0);stroke:rgb(0,200,0);stroke-width:2");
    }
}

版画

Correcting POLYGON((0 0,100 0,100 100,0 100,0 0)) to POLYGON((0 0,0 100,100 100,100 0,0 0))
Correcting POLYGON((25 25,75 22,75 75,25 75,25 25)) to POLYGON((25 25,25 75,75 75,75 22,25 25))
green - blue:MULTIPOLYGON(((0 0,0 100,100 100,100 0,0 0),(25 25,75 22,75 75,25 75,25 25)))
blue - green:MULTIPOLYGON()

并为以下内容编写 svg：

Answer 2

The will end your frustration/confusion, this answer will make you more productive :)

而且，是的，您可以跳过差异函数：

bg::read_wkt("POLYGON((0 0 0 100 100 100 100 0 0 0) (25 25 75 22 75 75 25 75 25 25))", donut);

这指定了内圈（反方向！）。

结果：

由此程序生成：

Live On Coliru

#include <boost/geometry.hpp>
#include <boost/geometry/geometries/point_xy.hpp>
#include <boost/geometry/geometries/polygon.hpp>

#include <iostream>
#include <fstream>

namespace bg = boost::geometry; 

int main() {
    typedef bg::model::d2::point_xy<double> point;
    typedef bg::model::polygon<point> polygon;

    polygon donut;
    bg::read_wkt("POLYGON((0 0 0 100 100 100 100 0 0 0) (25 25 75 22 75 75 25 75 25 25))", donut);

    std::ofstream svg("output.svg");
    boost::geometry::svg_mapper<point> mapper(svg, 400, 400);
    mapper.add(donut);

    mapper.map(donut, "fill-opacity:0.5;fill:rgb(0,0,153);stroke:rgb(0,0,200);stroke-width:2");
}

如何使用 C++ boost geometry 从两个多边形创建环（甜甜圈）？

How can I use C++ boost geometry to create ring (donut) from two polgons?

c++

geometry

boost

boost-geometry

完整演示