如何在boost::geometry::intersection(ring1, ring2, vector_of_linestring)中返回相交的线字符串？

Question

我有两个环A和B，我想使用boost::geometry::intersection()来返回线串（橙色箭头）：

但是我的代码只返回相交点P1和P2。我应该修改哪一部分？

#include <boost/geometry.hpp>
#include <boost/geometry/geometries/point_xy.hpp>
#include <boost/geometry/geometries/register/ring.hpp>
#include <boost/geometry/geometries/register/point.hpp>
#include <iostream>

namespace bg = boost::geometry;
typedef bg::model::point<double, 2, bg::cs::cartesian> point_t;
typedef bg::model::linestring<point_t> linestring_t;
typedef bg::model::ring<point_t> ring_t;
typedef bg::model::polygon<point_t> polygon_t;

typedef bg::model::multi_point<point_t> mpoint_t;
typedef bg::model::multi_linestring<linestring_t> mlinestring_t;
typedef bg::model::multi_polygon<polygon_t> mpolygon_t;

int main() {
    point_t ptA0(0, 0);
    point_t ptA1(10, 0);
    point_t ptA2(10, 10);
    point_t ptA3(0, 10);
    ring_t ringA;
    bg::append(ringA, ptA0);
    bg::append(ringA, ptA1);
    bg::append(ringA, ptA2);
    bg::append(ringA, ptA3);
    bg::append(ringA, ptA0);
    
    point_t ptB0(5, -5);
    point_t ptB1(15, -5);
    point_t ptB2(15, 5);
    point_t ptB3(5, 5);
    ring_t ringB;
    bg::append(ringB, ptB0);
    bg::append(ringB, ptB1);
    bg::append(ringB, ptB2);
    bg::append(ringB, ptB3);
    bg::append(ringB, ptB0);  

    std::vector<linestring_t> resline;      
    bg::intersection(ringB, ringA, resline);
    for (int i = 0; i < resline.size(); i++) {
        std::cout << bg::dsv(resline[i]) << std::endl;
    }   
    return 0;
}

以下是输出结果：(10, 5) 是 P1，(5, 0) 是 P2，这不是我预期的。

((10, 5), (10, 5)) 
((5, 0), (5, 0))

- hwx

---

在我看来，输出结果是我所期望的。我不知道你是否期望得到其他结果（但你肯定有你的理由）。对我来说，交点被表示为0长度的线段有些令人惊讶，但经过第二次查看后也是合理的（由于给定的输出类型）。然而，如果你期望得到环B的相交线，为什么不同时得到环A的相交线呢？ - Scheff's Cat

也许，你可以逐个检查linestring B的线路与linestring A（在循环中）相交。我不确定性能影响如何，但至少这样可以确保你获得了linestring B哪条线路与A相交... - Scheff's Cat

Answer 1

我尝试使用Boost Geometry实现的DE-9IM来解决这个问题：https://godbolt.org/z/KWzvzExr7，输出结果为https://pastebin.ubuntu.com/p/9ck6gcPK5P/。

---- void do_test(Input, Input) [with Input = boost::geometry::model::ring<boost::geometry::model::point<int, 2, boost::geometry::cs::cartesian> >]
a: POLYGON((0 0,0 10,10 10,10 0,0 0))
b: POLYGON((5 -5,5 5,15 5,15 -5,5 -5))
MULTIPOINT((10 5),(5 0))
MULTIPOLYGON(((10 5,10 0,5 0,5 5,10 5)))
Segment of ringB LINESTRING(5 -5,5 5) relates to ringA 
['F', 'F', '2']
['F', 'F', '1']
['F', 'F', '2']
Segment of ringB LINESTRING(5 5,15 5) relates to ringA 
['F', 'F', '2']
['F', 'F', '1']
['F', 'F', '2']
Segment of ringB LINESTRING(15 5,15 -5) relates to ringA 
['F', 'F', '2']
['F', 'F', '1']
['F', 'F', '2']
Segment of ringB LINESTRING(15 -5,5 -5) relates to ringA 
['F', 'F', '2']
['F', 'F', '1']
['F', 'F', '2']
 ---- void do_test(Input, Input) [with Input = boost::geometry::model::linestring<boost::geometry::model::point<int, 2, boost::geometry::cs::cartesian> >]
a: LINESTRING(0 0,0 10,10 10,10 0,0 0)
b: LINESTRING(5 -5,5 5,15 5,15 -5,5 -5)
MULTIPOINT((10 5),(5 0))
Segment of ringB LINESTRING(5 -5,5 5) relates to ringA 
['F', 'F', '1']
['F', 'F', 'F']
['F', 'F', '2']
Segment of ringB LINESTRING(5 5,15 5) relates to ringA 
['F', 'F', '1']
['F', 'F', 'F']
['F', 'F', '2']
Segment of ringB LINESTRING(15 5,15 -5) relates to ringA 
['F', 'F', '1']
['F', 'F', 'F']
['F', 'F', '2']
Segment of ringB LINESTRING(15 -5,5 -5) relates to ringA 
['F', 'F', '1']
['F', 'F', 'F']
['F', 'F', '2']
 ---- void do_test(Input, Input) [with Input = boost::geometry::model::polygon<boost::geometry::model::point<int, 2, boost::geometry::cs::cartesian> >]
a: POLYGON((0 0,0 10,10 10,10 0,0 0))
b: POLYGON((5 -5,5 5,15 5,15 -5,5 -5))
MULTIPOINT((10 5),(5 0))
MULTIPOLYGON(((10 5,10 0,5 0,5 5,10 5)))
Segment of ringB LINESTRING(5 -5,5 5) relates to ringA 
['F', 'F', '2']
['F', 'F', '1']
['F', 'F', '2']
Segment of ringB LINESTRING(5 5,15 5) relates to ringA 
['F', 'F', '2']
['F', 'F', '1']
['F', 'F', '2']
Segment of ringB LINESTRING(15 5,15 -5) relates to ringA 
['F', 'F', '2']
['F', 'F', '1']
['F', 'F', '2']
Segment of ringB LINESTRING(15 -5,5 -5) relates to ringA 
['F', 'F', '2']
['F', 'F', '1']
['F', 'F', '2']

但据我所见，所有结果至少都是完全不相交的。因此，您可能需要放大点而不是线段：

在Wandbox上实时运行

#include <boost/geometry.hpp>
#include <boost/geometry/geometries/ring.hpp>
#include <boost/geometry/iterators/segment_iterator.hpp>
#include <iostream>

namespace bg = boost::geometry;
using point_t  = bg::model::point<int, 2, bg::cs::cartesian>;
using ring_t   = bg::model::ring<point_t>;
using mpoint_t = bg::model::multi_point<point_t>;

void do_test(ring_t ringA, ring_t ringB)
{
    std::string reason;
    if (!bg::is_valid(ringA, reason)) { std::cout << "warning ringA: " << reason << "\n"; bg::correct(ringA); }
    if (!bg::is_valid(ringB, reason)) { std::cout << "warning ringB: " << reason << "\n"; bg::correct(ringB); }

    std::cout << "ringA: " << bg::wkt(ringA) << std::endl;
    std::cout << "ringB: " << bg::wkt(ringB) << std::endl;

    mpoint_t result;
    bg::intersection(ringA, ringB, result);
    std::cout << bg::wkt(result) << std::endl;

    for (auto seg : boost::make_iterator_range(bg::segments_begin(ringB),
                                               bg::segments_end(ringB))) {
        for (auto& p : result)
            if (bg::intersects(p, seg))
                std::cout << bg::wkt(p) << " intersects " << bg::wkt(seg) << "\n";
    }
}

int main() {
    do_test({{0, 0}, {0, 10}, {10, 10}, {10, 0}/*, {0, 0}*/},
            {{5, -5}, {5, 5}, {15, 5}, {15, -5}/*, {5, -5}*/});
}

打印

warning ringA: Geometry is defined as closed but is open
warning ringB: Geometry is defined as closed but is open
ringA: POLYGON((0 0,0 10,10 10,10 0,0 0))
ringB: POLYGON((5 -5,5 5,15 5,15 -5,5 -5))
MULTIPOINT((10 5),(5 0))
POINT(5 0) intersects LINESTRING(5 -5,5 5)
POINT(10 5) intersects LINESTRING(5 5,15 5)

- sehe