两个多边形之间的交叉点

Question

我有两个多边形（一个矩形和一个曲线），如下图所示：

我正在使用boost::geometry::intersection函数使用以下代码获取交叉点：

#include "boost\geometry\geometries\point_xy.hpp"
#include "boost\geometry\geometries\polygon.hpp"
typedef boost::geometry::model::d2::point_xy<float> point_xy;
typedef boost::geometry::model::polygon<point_xy> polygon;

void Gating::createEllipsePolygon(int i_popId, polygon & i_ellipse)
{
    float *pointX = nullptr, *pointY = nullptr;
    size_t size = 0;
    switch (i_popId)
    {
    case Stromal:
        pointX = &m_ellipseXG2[0];
        pointY = &m_ellipseYG2[0];
        size = m_ellipseXG2.size();
        break;
    case Tumor:
        pointX = &m_ellipseXG1[0];
        pointY = &m_ellipseYG1[0];
        size = m_ellipseXG1.size();
        break;
    default:
        break;
    }

    for (size_t i = 0; i < size; ++i)
    {
        bg::append(i_ellipse, bg::make<point_xy>(pointX[i], pointY[i]));
    }
}

void Gating::createRectanglePolygon(int i_popId, polygon & i_rectangle)
{
    Ranges *range = nullptr;
    size_t size = 0;
    switch (i_popId)
    {
    case Stromal:
        range = &m_intermediateRangePop2;
        bg::append(i_rectangle, bg::make<point_xy>(0., range->yLowerBound));
        bg::append(i_rectangle, bg::make<point_xy>(0., range->yUpperBound));
        bg::append(i_rectangle, bg::make<point_xy>(range->xUpperBound, range->yUpperBound));
        bg::append(i_rectangle, bg::make<point_xy>(range->xUpperBound, range->yLowerBound));
        bg::append(i_rectangle, bg::make<point_xy>(0., range->yLowerBound));
        break;
    case Tumor:
        range = &m_intermediateRangePop1;
        bg::append(i_rectangle, bg::make<point_xy>(range->xLowerBound, 0.));
        bg::append(i_rectangle, bg::make<point_xy>(range->xLowerBound, range->yUpperBound));
        bg::append(i_rectangle, bg::make<point_xy>(range->xUpperBound, range->yUpperBound));
        bg::append(i_rectangle, bg::make<point_xy>(range->xUpperBound, 0.));
        bg::append(i_rectangle, bg::make<point_xy>(range->xLowerBound, 0.));
        break;
    default:
        break;
    }
}

bool Gating::checkIntersectionBetweenEllipseAndRect(int i_popId)
{
    std::vector<float> *polyPointX = nullptr, *polyPointY = nullptr;
    bool intersection = false;
    polygon ellipse, rectangle;
    std::vector<polygon> output;
    createEllipsePolygon(i_popId, ellipse);
    createRectanglePolygon(i_popId, rectangle);

    switch (i_popId)
    {
    case Stromal:
        polyPointX = &m_polyPointXG2;
        polyPointY = &m_polyPointYG2;
        break;
    case Tumor:
        polyPointX = &m_polyPointXG1;
        polyPointY = &m_polyPointYG1;
        break;
    default:
        break;
    }


    if (bg::within(ellipse, rectangle))
    {
        for (auto it = bg::points_begin(ellipse); it != bg::points_end(ellipse); ++it)
        {
            polyPointX->push_back(it->x());
            polyPointY->push_back(it->y());
        }
    }
    else
    {
        intersection = bg::intersection(rectangle, ellipse, output);
        for (polygon const& poly : output)
        {
            for (auto it = bg::points_begin(poly); it != bg::points_end(poly); ++it)
            {
                polyPointX->push_back(it->x());
                polyPointY->push_back(it->y());
            }
        }
        polyPointX->erase(polyPointX->begin(), polyPointX->begin() + 5);
        polyPointY->erase(polyPointY->begin(), polyPointY->begin() + 5);
        polyPointX->push_back((*polyPointX)[0]);
        polyPointY->push_back((*polyPointY)[0]);
    }

    return intersection;
}

boost::geometry::intersection的输出是两个多边形的vector，如下图中的红色所示：

相反，我想得到这样的东西（绿线）：

我是否以错误的方式使用boost::geometry::intersection？ boost::geometry::intersection不是正确的使用方法吗？是否有其他功能可以得到我想要的东西？非常感谢任何帮助！