Discussion of Methods and API for Splitting an Oversize Polygon

• GEOS performs poorly as a POLYGON increases in number of vertices, even in the simple cases.

• It is often desirable to "split" a POLYGON with a high number of vertices into some number of smaller POLYGONs.

• From a user's perspective, some GIS processes result in very large POLYGON, for example 10,000 or 100,000 or more, vertices. There is a case to be made that PostGIS users would benefit from standard calls to take a single POLYGON as an input, and output some GEOMETRYCOLLECTION of POLYGON that are "equivalent", disregarding the problems inherent with the numeric precision model used.

• For the sake of discussion. let us assume we are operating on a POLYGON with a single outer ring, that is formally valid.

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Rough transcript of IRC on 07Mar13:

strk: splitting / gridding … which one you mentioned was about keeping existing vertices ? I don't think it's defined, but I just hit another case in which I'd want it to be possibly defined. rationale is that "split on vertex" introduces NO spatial drift/change. while "split segment" almost _always_ introduces a spatial difference pramsey: don't you think we need a general class of "on-vertex" splitting function ? closestpoint, substring, split, … what else ? all functions that "break" any line into smaller components need a way to be invoked to specify: "no segment splitting please"

pramsey: that seems like a very narrow-bore approach to a particular prob. when the general prob is, we don't have a precision model. so I don't feel super comfortable with a complex semantic of "split, but only in this very particular way" particularly when the semantic can fall apart and look dumb so easily (hand it a very long segment)

dbb: tries to grok context here

strk: well, I've heard people saying: "every vertex has a cost" they wouldn't be happy with splitting on segments. cost of some operations is per-vertex, not per-length .. _most_ operations

dbb: isnt there a case to be made to take a very high number of vertices POLY, and simply provide a call to break it into some number of polys with max N vertices ? Arc* definitely does this with a simple dialog box, and its a common user problem I think

strk: that too. can still be done using segment-splitting as the number of added points would likely not affect the overall reduction (I've been using that) BUT, segment-splitting would introduce spatial drift so that putting the "tiles" back together they wouldn't necessarily match. of course you can't avoid that when you really want a gridded output

dbb: hmm but thats at the level of the precision model. There are lots of problems at that level

pramsey: a set-returning function that turns a big polygon into a set of tiles covering the same area

dbb: isnt splitting using existing vertices straightforward? "give me back POLY that has at most N vertices"

pramsey: not if you're trying to generate a set of things that cover the same area. that strikes me as being quite hard. it's easy to break a line into smaller lines that way

dbb: because of problems at the precision model level ? Arc* has it somehow

pramsey: and what kind of shapes do the resulting outputs have? rectangular? pieces of pie? what?

dbb: they are N vertice polys.. you say "Take this monster 100,000 vertice poly, with one outer ring I suppose.. and break it into M polys with max N vertices each" if you specify N then M is calculated

strk: they are probably clusters of triangles.. unioned

pramsey: could be strk, triangulate and then rebuild

dbb: yes, triangulate and then rebuild, that sounds right

strk: recipe goes through topology, of course

dbb: I think this is a practical addition

Methods

strk: with postgis topology you could convert to a TopoGeometry, then take its envelope and add a bisecting edge if the number of vertices in it are above your threshold, then re-do the same on each part of the now-splitted thing until every composing face is below N vertices

nhv: that should work

strk: will take forever, but it'd be a robot working… I've been actually doing "vector tiles" like that in the past.(but without support of the PostGIS Topology)

dbb: there is nothing like this in JTS now ? as a function ?

strk: there's both triangulation and topology in postgis, not a single function, you'd have to write that one, on your needs. I think plpgsql could do, it really depends on your need for speed ST_SplitByGrid() ST_SplitToMaxN() SplitToMaxN has multiple solutions, so harder to generalize. SplitToMaxN could be implemented with a sweep line, for example. a vertical line that moves from leftmost vertex toward right direction, as soon as it seen enough points it cuts. we have ST_Split already, to split a polygon by a line. sweep would be performed by taking all vertices, ordering by X and positioning the line to the Nth point…

nhv: understood but if one was to use a quadtree splitting cells where needed to satisfy maxN constraint … is best of both worlds no ? but you are very likely to end up with long skinny objects which would be avoided in a quadtree solution

dbb: I dont think people care about blazing performance for this one.. I think it is the utility that is first

strk: the characteristic would be that of max "size", not max "extent"

nhv: irregular tiles are ok I just like to avoid long skinny things when possible, they often have numerical issues

strk: maybe the sweepline could be "snapped" to the existing vertices. not sure how to identify the correct ones though

(discussion of topology line splitting, precision problems, steiner points)

dbb: so I have heard SplitToMaxN() and ST_SplitByGrid(). in the behavior of SplitToMaxN() all returned POLY use the existing vertices of the input, which are well defined of course. with SplitByGrid() the grid geometry provides the "anchor" vertices

strk: does this line have any vertex whose value is not perfectly on this grid ? what ST_SnapToGrid ensures.

nhv: exactly

strk: yes, SplitByGrid() would take a grid configuration (same as ST_SnapToGrid) which would give you anchor points.

(discussion of infinite precision)