A fundamental problem in computational geometry is determining whether it is possible to travel between two points in the plane while avoiding a set of obstacles. If the obstacles are known in advance, they can be preprocessed so that path-existence queries can be performed efficiently.
In this thesis, we consider a variation of the path-existence query problem where each query contains an additional set of obstacles that must be avoided. We show how to preprocess a simple polygon so that given a source and a destination within that polygon, as well as a set of pairwise disjoint convex
polygon or disk obstacles, we can efficiently determine whether there is an obstacle-avoiding path between the source and the destination.