Repetitive Hidden Surface Removal for Polyhedra

Marco Pellegrini
1996 Journal of Algorithms  
The repetitive hidden-surface-removal problem can be rephrased as the problem of nding the most compact representation of all views of a polyhedral scene that allows e cient on-line retrieval of a single view. In this paper we present a novel approach to this problem. We assume that a polyhedral scene in 3-space is given in advance and is preprocessed o -line into a data structure. Afterwards, the data structure is accessed repeatedly with view-points given on-line and the portions of the
more » ... dra visible from each view-point are produced on-line. This mode of operation is close to that of real interactive display systems. The main di culty is to preprocess the scene without knowing the query view-points. 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 that, using an o -line data structure of size m with n 1+ m n 2+ , it is possible to answer on-line hidden-surface-removal queries in time O(k log n + minfn log n; kn 1+ =m 1=2 g), when the scene is composed of c-oriented polyhedra. This data structure accommodates 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/storage bounds for the repetitive hidden surface removal problem when the polyhedral scene is composed of unrestricted polyhedra.
doi:10.1006/jagm.1996.0038 fatcat:gxu7rvkqdjdqhihmw4tvie4fjm