I'm looking for an algorithm, a set of algorithms, or any pointers/remarks how to solve the following problem:
Given a polygon, a central point, and a set of points scaterred around the central point inside the polygon, I want to find the nearest "edges" being created by those points with respect to the central point. One of the algorithm's parameters should be "distance sensitivity" (meaning how far two points have to be far from eachother to be considered in a different cluster and break the line).
An illustration will maybe explain it better... this could be the input, where the + denotes the central point:
The output would be the following:
I am not very well-versed in computational geometry, so any pointers would be welcome.
I'd naively like to imagine the algorithm as a growing circle spreading outwards from the central point, parts of it getting stuck on the points (larger parts get stuck if the cluster is dense enough), and tearing off at the ends of the cluster because there are no points to support it there.
I have done some research into line-sweep algorithms, which partly fit my criteria. However, what I think I need is some kind of a circle-sweep algorithm.