I suggest you explore curve reconstruction via local feature size. The following figure is essentially an "algorithm without words":
![DCGFig5.9][1]
(Figure from [Discrete and Computational Geometry](http://press.princeton.edu/titles/9489.html).)
![DCGFig5.9][1]
(Figure from [Discrete and Computational Geometry](http://press.princeton.edu/titles/9489.html).)
Joseph O'Rourke
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