Determining whether polygon crosses the antimeridian

Question

I'm working on a system that uses bounding boxes as a fast first check for a point-in-polygon filter. My current naive implementation (just taking the min/max lat and long for all points) fails on polygons that cross the antimeridian (180 longitude).

I've done enough research to determine that the Right Way is probably to use spherical polygons, but I'm hoping to avoid the complexity of this approach (code complexity and time complexity). I think I can ignore issues at the poles, at least for the present, so the problem is relatively simple if I can accurately identify polygons that cross the antimeridian, set the appropriate east/west values, and then change the bbox check if east < west. But I'm stuck on identification.

Constraints:

• I don't control the format of the input polygons.
• I assume all longitudes in the polygon are in the range -180 - 180
• I assume that all input polygons follow the right-hand rule, i.e. have a counter-clockwise winding order.

Given these constraints, what's the easiest way to identify a polygon that crosses 180 longitude?

Answer 1

The easiest way to identify a polygon that crosses 180 longitude is:

1. Create polyline vector file with antimeridian line that crosses 180 (for test purposes I used GCS_WGS_1984 WKID: 4326 Authority: EPSG coordinate system).
2. Use select by location tool to select polygon features that intersect antimeridian line.

This method is tested with ArcGIS Desktop:

Picture 1: Picture 2:

Answer 2

I think that you have to make assumptions that constrain the polygon in some way. Consider that if you are at a defined point on the globe, and you want to get to another defined point, you assume that the edge to that point is a straight line. On a globe, that will be a great circle path. But you can go either direction on the great circle and still be on a straight line! This leads to all sorts of possibilities of edges that cross over one another and so forth. The topology of an "area" that is defined by four connected vertices on a globe is pretty complex. And there of course are the singularities at the poles.

Answer 3

Detecting Antimeridian Crossings

• Take your polygon's coordinates (in GeoJSON format), then check if the absolute value of the longitudinal difference between two consecutive vertices of the polygon is greater than a certain threshold. Practically, 180 degrees could be a sensible threshold default to start with (you can increase this of course).

For most practical purposes, after you've detected antimeridian crossings, you probably want to split your polygon in order to allow further geospatial operations. Here's the full tutorial + code snippets using Python and Shapely.