I suggest you explore curve reconstruction via local feature size. The following figure is essentially an "algorithm without words":
![DCGFig5.9][1]
(Figure from [this textbook](http://cs.smith.edu/~orourke/DCG/).)
![DCGFig5.9][1]
(Figure from [this textbook](http://cs.smith.edu/~orourke/DCG/).)
Joseph O'Rourke
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