computational geometry - Small circle inside simple polygon -

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i've been working on computational geometry problem , ran across following problem (which needed subroutine) failed find references or algorithms.

given simple (possibly concave) polygon p, goal compute center , radius of smallest circle contained in p (empty circle) touches polygon in @ least 2 places (point or edge). if 2 "places" happen points of polygon there no constraints. no constraints if hit point , edge. if hit 2 edges should not consecutive (assuming clockwise or counter-clockwise order).

i aiming implementable algorithm running in order of n^3 or better. pointers, references, or ideas helpful.

thanks! amer

since you're looking pointers or ideas, i'll brief. medial axis of polygon set of centers of circles touch boundary in 2 or more locations (https://en.wikipedia.org/wiki/topological_skeleton#centers_of_bi-tangent_circles). known skeleton, medial axis consists of tree-like graph made of lines , parabolas. if check circles @ vertices of graph (ignoring graph vertices coincide polygon vertices), can find both largest , smallest circles. you'll have fine tune accommodate "no consecutive edges" requirement.


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