Let $p$ and $q$ be two imprecise points, given as probability density functions on $\mathbb R^2$, and let $\cal R$ be a set of $n$ line segments (obstacles) in $\mathbb R^2$. 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 $\cal R$. 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.
|Number of pages||13|
|Publication status||Published - 2014|
Buchin, K., Kostitsyna, I., Löffler, M., & Silveira, R. I. (2014). Region-based approximation of probability distributions (for visibility between imprecise points among obstacles). (arXiv.org; Vol. 1402.5681 [cs.CG]). s.n.