I suggest you explore curve reconstruction via [local feature size](http://en.wikipedia.org/wiki/Local_feature_size).
The following figure is essentially an "algorithm without words":
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![DCGFig5.9][1]
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<sup>(Figure from [this textbook](http://cs.smith.edu/~orourke/DCG/).)</sup>
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  [1]: https://i.sstatic.net/03GTJ.png