Repetitive hidden-surface-removal for polyhedral scenes

Abstract

The repetitive hidden-surface-removal problem can be rephrased as the problem of finding the most compact representation of all views of a polyhedral scene that allows efficient on-line retrieval of a single view. In this paper we present a novel approach to the hidden surface removal problem in repetitive mode. We assume that a polyhedral scene in 3-space is given in advance and is preprocessed off-line into a data structure independently from any viewpoini. Afterwards, the data structure is accessed repeatedly with view-points given on-line and the portions of the polyhedra visible from each view-point are produced on-line. This mode of operation is close to that of real interactive display systems. Let n be the number total of edges, vertices and faces of the polyhedral objects and let k be the number of vertices and edges of the image. The main result of this paper is a collection of data structures answering hidden-surface-removal queries in almost-optimal output-sensitive time O(k log2n) using O(n2+ε) storage for the case of axis oriented polyhedra, or more generally for c-oriented polyhedra. If only linear storage is allowed, hidden-surface-removal queries are answered in time O(k log n+ min{n log n, kn1/2+ε). A continuous trade off between storage and query time is given and the data structures are made dynamic under insertion and deletion of polyhedral objects. The polyhedra may intersect and may have cycles in the dominance relation. For general polyhedral scenes we answer queries in time O(k log2n), using O(n4+ε) storage.