most recent 30 from http://mathoverflow.net 2013-05-20T20:30:55Z http://mathoverflow.net/feeds/user/25318 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/103053/techniques-for-refining-or-constraining-a-voronoi-diagram Alex Milowski 2012-07-24T22:11:48Z 2012-07-25T00:10:27Z

<p>I have a dataset coming from weather stations where each vertex used to generate the Voronoi diagram is the lat/long of the station. As such, each cell represents the area whose weather is being reported by the station. I'd like to limit the diameter of each cell to a reasonable distance and generate additional cells for areas with limited coverage. Essentially, for sparsely covered areas I want cells I can associate with either no data or estimated values.</p> <p>I'm currently using Fortune's algorithm to generate the diagram.</p> <p>What I'd like to know is what are the standard techniques for:</p> <ol> <li>limiting the diameter of a cell,</li> <li>adding points to reduce cell size?</li> </ol> <p>It seems to me that this is a refinement process of either the Voronoi diagram its dual, Delaunay triangulation. The refinement doesn't have to be ideal/optimal, just sufficiently within certain bounds (e.g. within a certain radius of the station's location).</p>

http://mathoverflow.net/questions/103053/techniques-for-refining-or-constraining-a-voronoi-diagram Alex Milowski 2012-07-25T02:40:54Z 2012-07-25T02:40:54Z

With regards to Delaunay mesh refinement, that's an interesting idea. The sharp angles aren't really a good thing either. It might be better in the long run to remove them and use some kind of averaging process to produce fabricated data for an added cell. That adds more ideas to the stack. Thanks.

http://mathoverflow.net/questions/103053/techniques-for-refining-or-constraining-a-voronoi-diagram Alex Milowski 2012-07-25T02:36:50Z 2012-07-25T02:36:50Z

I have considered adding extra points but I was curious if there was existing research or algorithms I should consider first. Given the small size of each quadrangle dataset and the relatively static nature of their locations, it would probably be reasonable to inspect every cell and add points in a systematic fashion to get the desired results. The placement of those points will affect the size of neighboring cells but I don't think the implementation I'm using will give me the neighboring cells to make wise choices.