Hierarchical geometric models for visible-surface algorithms

The research described in this paper addresses the problems associated with the design of systems for efficiently producing computer-generated pictures and picture sequences of very complex, three-dimensional environments. The thesis of the research is that the geometric structure inherent in the definition of the shapes of three-dimensional objects and environments must be used not just to define their relative motion and placement but also to assist in solving many other problems of systems for producing pictures by computer.The implications are that by using an extension of traditional structure information, or a geometric hierarchy, five significant improvements to current techniques are possible. First, the range of complexity of an environment is greatly increased while the visible complexity of any given scene is kept within a fixed upper limit. Second, a meaningful way is provided to vary the amount of detail presented in a scene both according to the screen area occupied by the objects in the scene and according to camera and object motions. Third, by using the geometric hierarchy, "clipping" becomes a very fast logarithmic search for the resolvable parts of the environment within the field-of-view. Fourth, by using this positional hierarchy in conjunction with a storage hierarchy of the sort used in virtual memory computing systems, frame-to-frame coherence and clipping define a graphical "working set", or fraction of the total structure that should be present in primary store for immediate access by the visible-surface algorithms. Finally, the proposed structural framework suggests a new recursive descent visible-surface algorithm in which the computation time grows almost linearly with a scene's visible complexity rather than as a worse than linear function of its object-space complexity.