Ray shooting amidst fat convex polyhedra in 3-space

We present a data structure for ray-shooting queries in a set of disjoint convex fat polyhedra of total com- plexity n in R3. The data structure uses O(n2+") storage and preprocessing time, and queries can be answered in O(log2 n) time. A trade-off between stor- age and query time is also possible: for any m with n <m <n2, we can construct a structure that uses O(m1+") storage and preprocessing time such that queries take O((n/pm) log2 n) time