Tuesday, May 12, 2009

ambiguous weighted skeleton



I've just come up with a better example of the straight skeleton's ambiguity:

ambig_neu

The top figure shows a situation where we need to make a decision. The bottom figures, a,b,c are examples of different resolution methods, that might be one of the following:
  • use the nearest intersection (raytracing!)
  • invent a priority system that pleases us (artist driven)
  • use an average weighting of the two edges (b, above)
Of course this follows from the fact that a weighted skeleton with consecutive parallel edges of different gradients is invalid. I'm not certain there's a clean way to resolve it...I'm looking...

This is probably similar to the ambiguity problem in 3d, described in Straight Skeletons of Three-Dimensional Polyhedra ( doi | pdf | 2008 )

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