Does ST_Intersects on albers geometry introduce errors

[benjaminleighton]

Presumably it doesn't because while albers projects doesn't maintain either shape nor length it should equally distort points so overlaps should be preserved

[dr-shorthair]

The lines joining adjacent points in a polygonal boundary have different shapes for different projections. So it is possible that this could introduce overlaps in some cases, especially if the points are widely spaced.

[benjaminleighton]

To clarify I mean intersection of two things both projected to albers. I imagine a surface is stretched but never folded so two points that have the relationship prior to albers projection like:
a --- b might have a relationship after albers projection like a -- b but never like b -- a

[dr-shorthair]

Yes, I understand.

If the two things do not share boundary points, then the curves interpolated between them might intersect in one projection, but not in another. I think that is most likely where node-A1 from feature-A falls close to the middle of an interval between two boundary nodes node-B1, node-B2 from the feature-B. The curve joining node-B1 to node-B2 might flip either side of node-A1 depending on the projection.

[benjaminleighton]

Looking at the world map example at https://en.wikipedia.org/wiki/Albers_projection I can't see any country boundary that looks like that happens. Shape and length are definitely distorted but all relatively.

[dr-shorthair]

It would only likely happen if big enough distances between nodes. But particularly when comparing intersections between a cylindrical projection (e.g. UTM) and a conic projection (e.g. Albers) then there will be cases where this can occur. And I don't think you could call them pathological.

[benjaminleighton]

Do you know some lat longs that would illustrate this?

[dr-shorthair]

To clarify what I wrote here: when building a boundary from a sequence of nodes, you join each one to the next using a straight line-segment in the current projection. That line-segment will be a curve in almost any other projection (particularly if comparing cylindrical vs conic).

So a point lying on one side of the line in one projection could end up on the other side of a curve in another projection. So for the same set of boundary nodes, the test for point-in-polygon can give a different result when done using different projections.

[benjaminleighton]

Yes comparing different projections definitely there is an issue but I'm jut double checking that if we convert two (potentially different) projects to a harmonized representation and then check intersections on that harmonized representation that no errors are introduced. I don't think they are.

[dr-shorthair]

It depends on what you mean by 'errors'. There can be different results testing intersection in different projections. Are these errors?

[benjaminleighton]

Postgis documents ST_Intersection here http://postgis.net/docs/ST_Intersection.html it works on a range of projections (but probably not across them) it doesn't talk about different kinds of errors.

In particular I mean the case I describe above.

Is there ever a case where if a--b in a particular projection then b--a will occur when those points are projected to albers. An example lat long should be able to illustrate such a case if it exists

[dr-shorthair]

I don't understand a--b