Dynamic partition trees

Abstract

In this paper we study dynamic variants of conjugation trees and related structures that have recently been introduced for performing various types of queries on sets of points and line segments, like half-planar range searching, shooting, intersection queries, etc. For most of these types of queries dynamic structures are obtained with an amortized update time of O(log2 n) (or less) with only minor increases in the query times. As an application of the method we obtain an output-sensitive method for hidden surface removal in a set of n triangles that runs in time O(n log n + n · klog2(1+√5)-1) where k is the size of the visibility map obtained.