Solving the Range Searching Problem for Region Bounded by a Convex Surface

In this paper we consider one of the approaches to solving the range searching problem for a range which is bounded by a convex surface in Euclidean d-dimensional space. In particular, we propose a method of range searching which gives query time O(logN) and uses O(NlogN) memory where N is cardinality of an input data set. It is enabled by applying optimal data structures for storing points in nodes of a quadtree.