使用`boost :: geometry :: difference`的精度问题

Question

大多数时候，当我使用boost::geometry::difference时，它会做我期望的事情。但是，当我有两个边缘几乎重合的多边形时，我会得到一些奇怪的行为。考虑这个例子：

#include <iostream>
#include <fstream>
#include <list>

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

using PointType = boost::geometry::model::d2::point_xy<double>;
using PolygonType = boost::geometry::model::polygon<PointType>;
using MultiPolygonType = boost::geometry::model::multi_polygon<PolygonType>;

template <typename TPolygon>
void printValidity(const TPolygon& polygons)
{
    boost::geometry::validity_failure_type failure;
    bool valid = boost::geometry::is_valid(polygons, failure);

    if(!valid) {
        std::cout << "not valid: " << failure << std::endl;
    }
    else {
        std::cout << "valid." << std::endl;
    }
}

template <typename TPolygon>
void WritePolygonsToSVG(const std::vector<TPolygon>& polygons, const std::string& filename)
{
    std::ofstream svg(filename);

    boost::geometry::svg_mapper<PointType> mapper(svg, 400, 400);

    for(size_t polygonID = 0; polygonID < polygons.size(); ++polygonID) {
        mapper.add(polygons[polygonID]);
        int redValue = 50 * polygonID; // NOTE: This will break with more than 5 polygons
        mapper.map(polygons[polygonID], "fill:rgb(" + std::to_string(redValue) + ",128,0);stroke:rgb(0,0,100);stroke-width:1");
    }
}

int main()
{
    MultiPolygonType polygon1;
    boost::geometry::read_wkt("MULTIPOLYGON(((-23.8915 -12.2238,-23.7604 -10.2739,-23.1774 -7.83411,-22.196 -5.52561,-20.8436 -3.41293,-19.7976 -2.26009,-19.8108 -2.00306,24.8732 2.51519,26.0802 -9.42191,-23.6662 -14.452,-23.8915 -12.2238)))", polygon1);
    WritePolygonsToSVG(polygon1, "polygon1.svg");

    MultiPolygonType polygon2;
    boost::geometry::read_wkt("MULTIPOLYGON(((-8.85138 -12.954,-8.89712 -12.7115,-8.9307 -12.5279,-3.35773 -12.078,-3.42937 -11.5832,-3.50013 -11.0882,-3.57007 -10.5932,-3.63925 -10.098,-3.70775 -9.60273,-3.77561 -9.10737,-3.84289 -8.61192,-3.90967 -8.1164,-3.976 -7.62081,-4.04194 -7.12517,-4.10756 -6.62948,-4.17291 -6.13375,-4.23805 -5.63799,-4.30305 -5.14222,-4.36797 -4.64643,-4.43287 -4.15064,-4.49781 -3.65485,-4.56285 -3.15909,-4.62806 -2.66331,-4.69349 -2.16756,-4.75921 -1.67185,-4.82528 -1.17619,-4.89175 -0.680597,-4.91655 -0.497015,17.8166 1.80166,17.8143 1.61653,17.8078 1.11656,17.8009 0.61658,17.7937 0.116605,17.7863 -0.383369,17.7786 -0.883343,17.7707 -1.3833,17.7627 -1.88324,17.7545 -2.38318,17.7463 -2.88312,17.7381 -3.38307,17.7299 -3.88301,17.7218 -4.38295,17.7139 -4.8829,17.706 -5.38285,17.6984 -5.88279,17.6911 -6.38274,17.684 -6.88269,17.6772 -7.38265,17.6709 -7.8826,17.6649 -8.38256,17.6595 -8.88251,17.6545 -9.38247,17.6501 -9.88244,17.6471 -10.2746,-8.85138 -12.954)))", polygon2);
    WritePolygonsToSVG(polygon2, "polygon2.svg");

    MultiPolygonType differencePolygon;

    boost::geometry::difference(polygon1, polygon2, differencePolygon);
    WritePolygonsToSVG(differencePolygon, "difference.svg");

    printValidity(differencePolygon);

    MultiPolygonType realDifference;
    boost::geometry::read_wkt("MULTIPOLYGON(((-23.8915 -12.2238,-23.7604 -10.2739,-23.1774 -7.83411,-22.196 -5.52561,-20.8436 -3.41293,-19.7976 -2.26009,-19.8108 -2.00306,24.8732 2.51519,26.0802 -9.42191,-23.6662 -14.452,-23.8915 -12.2238),(-8.85138 -12.954,17.6471 -10.2746,17.6501 -9.88244,17.6545 -9.38247,17.6595 -8.88251,17.6649 -8.38256,17.6709 -7.8826,17.6772 -7.38265,17.684 -6.88269,17.6911 -6.38274,17.6984 -5.88279,17.706 -5.38285,17.7139 -4.8829,17.7218 -4.38295,17.7299 -3.88301,17.7381 -3.38307,17.7463 -2.88312,17.7545 -2.38318,17.7627 -1.88324,17.7707 -1.3833,17.7786 -0.883343,17.7863 -0.383369,17.7937 0.116605,17.8009 0.61658,17.8078 1.11656,17.8143 1.61653,17.8166 1.80166,-4.91655 -0.497015,-4.89175 -0.680597,-4.82528 -1.17619,-4.75921 -1.67185,-4.69349 -2.16756,-4.62806 -2.66331,-4.56285 -3.15909,-4.49781 -3.65485,-4.43287 -4.15064,-4.36797 -4.64643,-4.30305 -5.14222,-4.23805 -5.63799,-4.17291 -6.13375,-4.10756 -6.62948,-4.04194 -7.12517,-3.976 -7.62081,-3.90967 -8.1164,-3.84289 -8.61192,-3.77561 -9.10737,-3.70775 -9.60273,-3.63925 -10.098,-3.57007 -10.5932,-3.50013 -11.0882,-3.42937 -11.5832,-3.35773 -12.078,-8.9307 -12.5279,-8.89712 -12.7115,-8.85138 -12.954)))", realDifference);
    WritePolygonsToSVG(realDifference, "realDifference.svg");
    printValidity(realDifference);

    return 0;
}

在此代码中使用boost::geometry::difference计算的'differencePolygon'是“有效的”，尽管它有一个无限小的区域：

'realDifference'多边形是我从“真实代码”输出的（由于（我猜的是）WKT编写器的精度，输入略有不同）。你可以看到这个多边形有两个无限小的区域，实际上返回无效（21：failure_self_intersections）：

是否有某种公差参数可以设置为在差异操作期间避免这些无限小的区域（显然有时会破坏多边形）？或者是否有通过删除这些自交叉来“校正”多边形的功能？ （我知道正确的（）函数只能修复环的排序。）