Re: boost::geometry: intersection of a point with a linestring

From: Mateusz Loskot (mateusz_at_[hidden])
Date: 2019-10-03 17:30:30

On Thu, 3 Oct 2019 at 18:04, Giorgino R via Boost-users
<boost-users_at_[hidden]> wrote:
>
> Is there any boost functionality to "split" a linestring with an intersecting point?

I'm not aware of any such algorithm in Boost.Geometry.

> I was expecting that boost::geometry::intersection could return a multi-linestring (of size two) or a vector of linestrings (size two).

That would be a different algorithm, presumably split, but not
intersection according to OGC.

Mind you, the Boost.Geometry documentation at
https://www.boost.org/libs/geometry/doc/html/geometry/reference/algorithms/intersection/intersection_3.html
says "The function intersection implements function Intersection from
the OGC Simple Feature Specification.",
what is similar to PostGIS, https://postgis.net/docs/ST_Intersection.html.
The OGC Simple Feature Specification says the algorithm returns
point set intersection of input geometries.

> For example, please see a very simple case below which doesn't compile:
>
>>   point_2d pt(0.5, 0);
>>   linestring_2d ls({ point_2d(0, 0), point_2d(1, 0), point_2d(3, 0), point_2d(5, 0) });
>>   std::vector<linestring_2d> inter;
>>   bg::intersection(pt, ls, inter);
>
>
> Is there any way to get inter vector with two linestrings (...) or any multi geometry container
> that will hold the spatial information of two lines connected in this point?
> Or should I create these two lines myself by working out which points of the linestring
> are left and right of the intersecting point?

There is a way and yes you need to build a solution your self,
but it should be not a hair-pulling experience using the building blocks
provided by Boost.Geometry.

For example, here is a quick example with possible solution:

```
#include <boost/geometry.hpp>
#include <algorithm>
#include <iostream>
#include <vector>
namespace bg = boost::geometry;
using point_2d = bg::model::d2::point_xy<double>;
using linestring_2d = bg::model::linestring<point_2d>;

int main()
{
    point_2d pt(2.5, 0);
    linestring_2d ls({{0, 0}, {1, 0}, {2, 0}, {3, 0}, {4, 0}, {5, 0}});

    auto split_begin = std::find_if(bg::segments_begin(ls),
bg::segments_end(ls),
        [&pt](auto const& segment) { return bg::intersects(segment, pt); });

    linestring_2d line1;
    std::for_each(bg::segments_begin(ls), split_begin, [&line1](auto const& s)
    {
        bg::append(line1, s.first);
    });
    bg::append(line1, split_begin->first);
    bg::append(line1, pt);

    linestring_2d line2;
    bg::append(line2, pt);
    bg::append(line2, split_begin->second);
    std::for_each(++split_begin, bg::segments_end(ls), [&line2](auto const& s)
    {
        bg::append(line2, s.second);
    });

    std::cout << bg::dsv(line1) << std::endl;
    std::cout << bg::dsv(line2) << std::endl;
}
```

It does take some time to get familiar with Geometry LEGO, but the docs are good
and the .cpp files with examples should be useful as well.

Best regards,
-- 
Mateusz Loskot, http://mateusz.loskot.net