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About 6 months ago I began writing a library[1] that focuses on topology (much of what was discussed in the article) and geospatial stats. I am by no means a ma
by morganherlocker 13y ago
About 6 months ago I began writing a library[1] that focuses on topology (much of what was discussed in the article) and geospatial stats. I am by no means a math genius, and my library does nothing too novel from a mathematical perspective. Still, it has been nearly all consuming to grok the immense amount of math that goes into this sort of thing. I can only imagine the creative energy it must have taken to actually design these algorithms from scratch.
[1] https://github.com/morganherlocker/turf https://github.com/morganherlocker/turf
- Someone 13y agoAs far as I can tell, your library does topo_graphy_, not topo_logy_. Topology ignores such things as corners, distances, and convexity. That makes it hard to combine with GIS systems.
- nathancahill 13y agoWhat? Everything about this comment is wrong. > "Topology ignores such things as corners, distances, and convexity." No, that's what topology is. > "That makes it hard to combine with GIS systems." No, GIS systems rely heavily on topology. Here are two definitions: Topology: 1. the study of geometric properties and spatial relations unaffected by the continuous change of shape or size of figures. Topography: 1. the arrangement of the natural and artificial physical features of an area.
- zodiac 13y agoThe code samples used to demonstrate that library loads a trees.geojson file with features like 'oak' and 'maple', so I think he definitely meant 'topography'. What makes you say it's a topology library?
- nathancahill 13y agoSee the authors comment above. The library does do a lot more than topology, but the see the sections titled: joins, measurement and transformation. These are all topological functions.
- bjourne 13y agoSee this video lecture for a very accessible explanation of what topology is (and is not): http://www.youtube.com/watch?v=kdpbfOzkJzI http://www.youtube.com/watch?v=kdpbfOzkJzI
- morganherlocker 13y agoYour link is referring to algebraic topology. It is one of several subfields of general topology. See the opening paragraph that lists a few others: http://en.wikipedia.org/wiki/Topology http://en.wikipedia.org/wiki/Topology
- morganherlocker 13y agoActually 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. [1] http://en.wikipedia.org/wiki/Kriging http://en.wikipedia.org/wiki/Kriging [2] http://en.wikipedia.org/wiki/Contour_line http://en.wikipedia.org/wiki/Contour_line
- j2kun 13y agoI 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.
- morganherlocker 13y ago(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).
- magicalist 13y agoNo, topology often focuses on things that are invariant under such things as corners, distances, and convexity, which can make it an extremely useful tool in a field awash in such concerns. While many would classify the GP's library as one primarily concerned with computational geometry (but certainly not topography), there are large overlaps of computational geometry with computational topology. Many topology results won't be useful in an applied field like GIS, but other results will be extremely useful as they work regardless of the mess of real world measurements. Classification of branches of mathematics is a losing game, anyway. You try to separate two bodies of work, you'll invariably find someone's extensive results that straddle the boundary.