Actually it deals with both. Primarily it deals with topology and statistics in the context of topography and geography. The concepts addressed by topology are essential to any GIS engine. There are actually several definitions of topology, and turf actually touches on most of them:
- basic topology like detecting whether or not a point lies within a complex polygon
- topological morphology, such as smoothing a line or polygon while maintaining boundaries (this is probably the most common definition in the GIS world)
- topological interpolation, such as estimating z values over a 3d mesh[1][2] (there are a number of methodologies here, and this represents probably the most interesting intersection of topology and statistics)
Also note that turf is geared towards GIS, but most of the underlying operations are not GIS specific and apply to geometry more generally. You will find many of the same algorithms in applications like game engines, for example.
I think the point is that none of these are topology in the mathematical sense. They're computational geometry. In my view that's still one of the most difficult fields of mathematics (precisely because the algorithms rely on extremely complicated data structures), but it's not topology.
If you are groking topology in the mathematical sense, you'd be talking about concepts like (co)homology and homotopy groups, and be doing quite a lot of commutative algebra. You definitely would not care about statistics and point location.
(co)homology and homotopy are specific to algebraic topology. There are several other types. Regardless, these sorts of discussions have convinced me that the semantics regarding these subjects are extremely muddy. I am by no means an expert, and tend to try to stick to the meanings conveyed by colleagues with more experience and/or wikipedia :)
My library is definitely not a topology library. I tend to describe it as a geospatial processing engine. My first comment was really only meant to speak to some overlap I noticed with the topology described in the article, and to convey my deep respect for the people who have a more full understanding of the low level mathematics involved (which it sounds like you might possess).
- basic topology like detecting whether or not a point lies within a complex polygon
- topological morphology, such as smoothing a line or polygon while maintaining boundaries (this is probably the most common definition in the GIS world)
- topological interpolation, such as estimating z values over a 3d mesh[1][2] (there are a number of methodologies here, and this represents probably the most interesting intersection of topology and statistics)
Also note that turf is geared towards GIS, but most of the underlying operations are not GIS specific and apply to geometry more generally. You will find many of the same algorithms in applications like game engines, for example.
[1] http://en.wikipedia.org/wiki/Kriging [2] http://en.wikipedia.org/wiki/Contour_line