提升内点的几何多边形距离

Question

我正在使用 boost::geometry 来处理一些几何任务。我有两个要求需要满足：

处理点 -> 多边形交点（在内部或外部）。这对 boost::geometry::within 非常有用，所以很好
获取任意点到多边形最近边的距离。虽然 boost::geometry::distance 可以正确处理多边形之外的点，但它似乎认为多边形是实体的。所以多边形内的每个点显然与多边形的距离为 0。

我尝试用 inner/outer 东西进行试验，想知道是否有可能获得多边形内外点的距离。

Answer 1

我决定使用以下方法，到目前为止似乎提供了正确的结果：

const TPolygonPoint pt{ x, y };
auto distance = std::numeric_limits<float>::max();

if(boost::geometry::within(pt, mPolygon)) {
    boost::geometry::for_each_segment(mPolygon, [&distance, &pt](const auto& segment) {
        distance = std::min<float>(distance, boost::geometry::distance(segment, pt));
    });
} else {
    distance = boost::geometry::distance(pt, mPolygon);
}

return distance;

如果有人知道更快或更好的方法，请发表评论:)

Answer 2

如果点在多边形内部，您可以使用 comparable_distance 而不是 distance 算法来加快代码速度。您不需要计算每个分段点对的确切距离。使用 comparable_distance 找到距离给定点最近的多边形线段，然后使用 distance 算法计算实际距离。

auto distance = std::numeric_limits<float>::max();
if(boost::geometry::within(pt, mPolygon)) 
{
  Segment nearestSegment;
  boost::geometry::for_each_segment(mPolygon, 
    [&distance, &pt, &nearestSegment](const auto& segment) 
     {
        double cmpDst = boost::geometry::comparable_distance(segment,pt);
        if (cmpDst < distance)
        {
          distance = cmpDst;
          nearestSegment = segment; // UPDATE NEAREST SEGMENT
        }
      });
      // CALCULATE EXACT DST
      distance = boost::geometry::distance(nearestSegment,pt);
} else {
  distance = boost::geometry::distance(pt, mPolygon);
}

Answer 3

为了获得最佳性能，您应该使用带有 boost::geometry::index 的 RTree。创建 RTree 是有成本的，但是计算一个点到任何（多）多边形环的距离会快得多。示例代码：

#include <boost/geometry.hpp>
#include <boost/geometry/geometries/geometries.hpp>
#include <boost/geometry/index/rtree.hpp>
#include <iostream>
#include <vector>

int main()
{
    namespace bg = boost::geometry;
    namespace bgi = boost::geometry::index;
    typedef bg::model::point<double, 2, bg::cs::cartesian> point;
    typedef bg::model::polygon<point> polygon;

    point p{ 0, 0 };
    // create some polygon and fill it with data
    polygon poly;
    double a = 0;
    double as = bg::math::two_pi<double>() / 100;
    for (int i = 0; i < 100; ++i, a += as)
    {
        double c = cos(a);
        double s = sin(a);
        poly.outer().push_back(point{10 * c, 10 * s});
        poly.inners().resize(1);
        poly.inners()[0].push_back(point{5 * c, 5 * s});
    }
    // make sure it is valid
    bg::correct(poly);

    // create rtree containing objects of type bg::model::pointing_segment
    typedef bg::segment_iterator<polygon const> segment_iterator;
    typedef std::iterator_traits<segment_iterator>::value_type segment_type;

    bgi::rtree<segment_type, bgi::rstar<4> > rtree(bg::segments_begin(poly),
                                                   bg::segments_end(poly));

    // get 1 nearest segment
    std::vector<segment_type> result;
    rtree.query(bgi::nearest(p, 1), std::back_inserter(result));

    BOOST_ASSERT(!result.empty());

    std::cout << bg::wkt(result[0]) << ", " << bg::distance(p, result[0]) << std::endl;

    return 0;
}

Answer 4

你可以直接使用boost::geometry::distance，如果你添加一个内边界到与外边界重合的多边形[Polygon Concept]。

#include <iostream>
#include <boost/geometry.hpp>
#include <boost/geometry/geometries/geometries.hpp>

namespace bg = boost::geometry;

int main() {
    typedef bg::model::point<int, 2, bg::cs::cartesian> point_t;
    typedef bg::model::polygon<point_t> polygon_t;

    polygon_t poly1;    

    bg::append (poly1.outer(), point_t (1, -1));
    bg::append (poly1.outer(), point_t (1, 1));
    bg::append (poly1.outer(), point_t (-1, 1));
    bg::append (poly1.outer(), point_t (-1, -1));
    bg::append (poly1.outer(), point_t (1, -1));

    poly1.inners().resize (1);
    bg::append (poly1.inners()[0], point_t (1, -1));
    bg::append (poly1.inners()[0], point_t (1, 1));
    bg::append (poly1.inners()[0], point_t (-1, 1));
    bg::append (poly1.inners()[0], point_t (-1, -1));
    bg::append (poly1.inners()[0], point_t (1, -1));


    point_t myPoint (0, 0);
    std::cout << "Minimal distance: " << bg::distance (poly1, myPoint) << std::endl;
    std::cout << "Is within: " << bg::within (myPoint, poly1) << std::endl;

    return 0;
}

-> 将 return:

    Minimal distance: 1
    Is within: 0

但是，如果您这样做，严格位于多边形内部的点将被认为位于 'outside' 多边形 boost::geometry::within 处。如果您想要这两种功能，您可以维护两个单独的多边形 - 一个有内部边界，一个没有。

提升内点的几何多边形距离

boost geometry polygon distance for inside point

c++

boost

boost-geometry