I've just come up with a better example of the straight skeleton's ambiguity:
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)
This is probably similar to the ambiguity problem in 3d, described in Straight Skeletons of Three-Dimensional Polyhedra ( doi | pdf | 2008 )