I am trying to find the first intersection of a line with anything else.

By first intersection I mean the first intersection, if you follow the line in its direction from start to end.

Check the image below, it should make it clear. Black is a line, blue is another geometry, here a polygon, red is the point I am looking for.

Line, Polygon and first intersection

Maybe there is some standard algorithm for this that I am not aware of? Or maybe a combination of multiple ones?

I am not interested in solutions of closed-source software.

  • 1
    As Mac and Tosh discovered in the classic Looney Toons short, the definition of "first" is dependent on order of execution.
    – Vince
    Nov 9 '16 at 21:31
  • Yeah but a linestring has a start and an end if you consider a standard Simple Feature ordered list of points as its "body". Nov 9 '16 at 22:07
  • 1
    If you break the line at the Polygon boundaries, wont the polyline containing the start point have the first node at it's end?
    – klewis
    Nov 9 '16 at 23:04
  • It can be more complicated than that. Computationally, there may be an advantage to fiipping the coordiate stream.
    – Vince
    Nov 9 '16 at 23:20
  • Oh, I like that idea @klewis! I think that should be bug free or does someone see a problem with that approach? Nov 9 '16 at 23:39

Piece-wise example about how to do it with PostGIS functions http://postgis.net/docs/ST_Intersection.html and http://www.postgis.org/docs/ST_Line_Locate_Point.html

  1. Find intersection points of the linestring and the exterior of the polygon.
select ST_AsText(
ST_GeomFromText('LINESTRING ( 440 280, 760 480 )'),
ST_geomFromText('POLYGON (( 500 400, 620 480, 740 360, 640 280, 500 400 ))'))))
"MULTIPOINT(555.66265060241 352.289156626506,673.846153846154 426.153846153846)"
  1. Find the distance to each intersection point
ST_GeomFromText('LINESTRING ( 440 280, 760 480 )'),St_GeomFromText('Point (555.66265060241 352.289156626506)'))


ST_GeomFromText('LINESTRING ( 440 280, 760 480 )'),St_GeomFromText('Point (673.846153846154 426.153846153846'))


The first point is located at length of 36.14% from the start point and it is closer that the latter (73.07%).


However, if the aim is to get the shortest direct distance to the intersection points, it can be found with http://postgis.net/docs/ST_StartPoint.html and http://postgis.net/docs/ST_Distance.html. Example with the same points as above.

ST_GeomFromText('LINESTRING ( 440 280, 760 480 )')),St_GeomFromText('Point (555.66265060241 352.289156626506)'))

ST_GeomFromText('LINESTRING ( 440 280, 760 480 )')),St_GeomFromText('Point (673.846153846154 426.153846153846)'))
  • Thanks! Unfortunately this will fail if the shapes of the geometries are such that the first intersection actually is further away than others. Think many meandering curves. Nov 9 '16 at 23:00
  • The function ST_Line_Locate_Point is measuring the distance by following the line. Isn't that just what you want: If you follow the path, how long have you walked when you cross the border for the first time? Or do you want to know the shortest direct distance?
    – user30184
    Nov 10 '16 at 6:18
  • Oh ouch, I misread it. Yes, ST_Line_Locate_Point seems perfect. Thanks! Nov 10 '16 at 9:35

Alternative SQL method based on the suggestion of @klevis.

  • Split linestring with the outer ring of the polygon
  • Result is a GeometryCollection, select the first part of the collection
  • First part should be the one with the original starting point, so select the last point of that first part and you have found the answer.
select ST_AsText(
ST_GeomFromText('LINESTRING ( 440 280, 760 480 )'),
ST_ExteriorRing(ST_GeomFromText('POLYGON (( 500 400, 620 480, 740 360, 640 280, 500 400 ))'))),1)));

"POINT(555.66265060241 352.289156626506)"

I am not sure if ST_Split is guaranteed to keep the order of the parts and it might be good to add a test that the start points of the original line and the selected part are equal. If not, select next part with ST_GeometryN and loop as long as needed.


I have a solution in theory which always should work, but require multiple queries and I only provide for postgis:

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