Efficient Point Location in a Convex Spatial Cell-Complex

In this paper a new approach is proposed to point-location in a three-dimensional cell-complex 7 , which may be viewed as a nontrivial generalization of a corresponding two-dimensional technique due to Sarnak and Tarjan. Specifically, in a space-sweep of 7), the intersections of the sweep-plane with P occurring in a given slab, i.e., between two consecutive vertices, are topologically conformal planar subdivisions. If the sweep direction is viewed as time, the descriptions of the various slabs are distinct "versions" of a two-dimensional point-location data structure, dynamically updated each time a vertex is swept. Combining the persistence-addition technique of Driscoll,