Repetitive Hidden Surface Removal for Polyhedra

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. We assume that a polyhedral scene in 3-space is given in advance and is preprocessed off-line into a data structure. Afterward, the data structure is accessed repeatedly with viewpoints given on-line and the portions of the polyhedra visible from each viewpoint are produced on-line. This mode of operation is close to that of real interactive display systems. The main difficulty is to preprocess the scene without knowing the query viewpoints. In this paper, we present a novel approach to this problem. Letnbe the total number of edges, vertices and faces of the polyhedral objects and letkbe the number of vertices and edges of the image. The main result of this paper is that, using an off-line data structure of sizemwithn^1+ϵ≤m≤n^2+ϵ, it is possible to answer on-line hidden-surface-removal queries in timeO(k log n+min{n log n, kn^1+ϵ/m^{$\text{1}\text{2}$}}), when the scene is composed ofc-oriented polyhedra. This data structure allows dynamic insertion and deletion of polyhedral objects. The polyhedra may intersect and may have cycles in the dominance relation. We also improve worst-case time and storage bounds for the repetitive hidden surface removal problem when the polyhedral scene is composed of unrestricted polyhedra.