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Does anyone know an algorithm to solve the following problem:
Given a sequence of points in the plane that represent a polygon (not necessarily convex), output the maximum possible radius of a circle that can fit inside this polygon.
It would be good if it was below O(n2), but any references are welcome. Thanks ahead.
Auto comment: topic has been updated by kowalsk1 (previous revision, new revision, compare).
If it was convex, you could make inequalities of form Ax+By+Cr>=0. For non-convex you need something different.
Binary search for R. if you choose R to be your radius check if size R circle fits inside.
You probably will need veronoi diagrams.
How do you determine in which point should be center of the circle?
All right, I already understand how. If somebody still curious — visit this article.
In each vertex with reflex angle generate two new polygons without that vertex. Black is non-convex. Red and green are new polygons. And after having only convex ones get maximum of circles in each polygon. Algorithm at emaxx for convex.
Where's O(2^n) subpolygons...
Btw, why did you not just google your question? I found answer for that in few minutes.