[postgis-users] Geography point to polygon st_distance for a polygon crossing the equator

[Sebastien Delaux]

Hi all,

I am new to postgis and I am interested in finding all the points that are located at x metres or less of a polygon that are stored in my postgres database.

As I am working with data located all over the world and want to work with distances in metres I decided to use the geography type.

I am trying to understand why the following query returns 0 when the point is clearly not included in the polygon:
SELECT ST_Distance(ST_GeographyFromText('SRID=4326;POINT(0. -82.)'),ST_GeographyFromText('SRID=4326;POLYGON((-90 -80, 90 -80, 90 10, -90 10, -90 -80))'));

I suspect this has something to do with the polygon crossing the equator as
SELECT ST_Distance(ST_GeographyFromText('SRID=4326;POINT(0. -82.)'),ST_GeographyFromText('SRID=4326;POLYGON((-90 -80, 90 -80, 90 -10, -90 -10, -90 -80))'));

returns a plausible distance.

Would anybody know whether my polygon is violating some assumption or whether there is any other reason that I am getting those results?

Thanks

Sebastien

[Paul Ramsey]

I don't the polygon you've draw means what you think it does. 

POLYGON((-90 -80, 90 -80, 90 10, -90 10, -90 -80))

For example, you probably figure the first segment, -90 -80, 90 -80 runs east-west between two points close to the south pole. In fact, it runs directly over the south pole, so actually to the south of your point of interest. 

P

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[Sebastien Delaux]

Thanks for your reply Paul.

Yes, that's what I thought. That would explain why (0,-82) is inside the polygon.

Nevertheless, if my first segment runs through the south pole, then I would expect both of the queries mentioned in my initial post to return 0 which is not the case.

Sebastien

[Paul Ramsey]

:) :) :)

Your second polygon has the same problem as the first, except in reverse... Your second polygon basically covers no area at all, since it consists of two arcs that both do a direct southerly run to the south pole.

P.

[Sebastien Delaux]

Thanks Paul, I get it now.

So I guess, it all comes from the fact that an arc is defined as the shortest path between 2 points which in the geometry case is a straight line and in the geography case is a great circle.

This also mean that "the polygon I had in mind" cannot be defined as a geography polygon.

S.

--

[Paul Ramsey]

That's right, we don't have a way to differentiate between great-circle edges and loxodromes on geography (or vice versa in geometry).

​You can approximate a "square"  by densifying your east-west lines in the places you want vertices to go, but the inter-vertex edges will still be great circles. You can do that by densifying in geometry land and then casting back to geography.

P.