How to find the largest circle that lies within a sampled boundary?

Question

Given sets of 2D points which are the boundaries of an irregular shape, a shape which may not be convex and may have internal holes, is there an algorithm to find the larges

Answer 1

Problem is not good defined since set of points don't bound any area. Boundary you mention should be some curve, probably polygon. Without that you can't say that there are internal holes, and also can't ask for circle to be within boundary. With this definition, you can create circle of any size on "outside" that touches few set points.

If you use polygon to specify boundary, Aioobe's link is good one. If you redefine problem to find maximal radius circle touching at least 3 points of given set, than it is same as checking for circumcircles of Dalaunay triangulation.