Sunday, July 22, 2012

[fxrrntwi] Voronoi puzzle and most general position

Create a Voronoi diagram of some points in general position.  Cut along the partition boundaries to create a puzzle.  General position makes this puzzle fairly easy because an edge can match up with exactly one other edge of the same length, and exactly three pieces meet at a vertex, so the corners sum to 360 degrees.

The challenge is to find points to make the puzzle as easy as possible.  Find points that maximize the minimum difference between edges of different lengths.  Maximize the minimum angular defect of 3 corners which don't sum to 360 degrees.  Also, avoid very short edges.

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