Techniques for refining or constraining a Voronoi diagram? 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.
I'm currently using Fortune's algorithm to generate the diagram.
What I'd like to know is what are the standard techniques for:


*

*limiting the diameter of a cell,

*adding points to reduce cell size?


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).
 A: Delaunay refinement is centered on exactly this purpose: adding mesh vertices as far away from existing mesh vertices as possible. While the analysis of Delaunay refinement algorithms typically focuses on cell/triangle quality bounds, the key idea (from the seminal paper by Ruppert [1]) is that controlling mesh size (both above and below) is equivalent to controlling mesh quality. 
If you go back to this earlier Delaunay refinement algorithm by L.P. Chew, you don't see angle quality in the algorithm at all: the algorithm has a constant size for the mesh and inserts Delaunay circumcenters until none exist with a circumradius larger than that size. 
The relationship with refinement an cell size is even more apparent in [2]. In that analysis of a Delaunay refinement algorithm, the size of the Voronoi cells (both the inner and outer radii of the cells) is emphasized and angles do not directly appear. 
Many Delaunay refinement codes allow the user to control the maximum size of cells / triangles created. In Triangle, this is provided through a bound on triangle area is provided. But CGAL and Tetgen have more direct control over the volume of the cells/tets created.
Most of the research is focused on figuring out how to add as few vertices as possible and still produce a quality mesh. Once that coarsest quality mesh is created, it is relatively straightforward to continue adding circumcenters to further reduce the size.
[1] Ruppert, Jim, A Delaunay refinement algorithm for quality 2-dimensional mesh generation, J. Algorithms 18, No. 3, 548-585 (1995). ZBL0828.68122.
[2] Hudson, Benoît; Miller, Gary L.; Phillips, Todd, Sparse Voronoi Refinement, Proceedings of the 15th international Meshing Roundtable, Seattle, (2006). pdf.
