Region-based approximation of probability distributions (for visibility between imprecise points among obstacles)

Let p and q be two imprecise points, given as probability density functions on R, and let R be a set of n line segments (obstacles) in R. We study the problem of approximating the probability that p and q can see each other; that is, that the segment connecting p and q does not cross any segment of R. To solve this problem, we approximate each density function by a weighted set of polygons; a novel approach to dealing with probability density functions in computational geometry.