Hierarchical geometric models for visible surface algorithms

TLDR

The geometric structure inherent in the definition of the shapes of three‑dimensional objects and environments is 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 study proposes using a geometric hierarchy to enable five significant improvements to current visible surface algorithms. The algorithm extends traditional structure information into a geometric hierarchy, using frame‑to‑frame coherence and clipping to define a working set and enabling a recursive‑descent visible surface algorithm whose time grows linearly with visible complexity. The approach yields five key benefits: it expands environmental complexity while keeping visible complexity bounded, allows adjustable detail levels, turns clipping into a fast logarithmic search, defines a working set for efficient frame‑to‑frame coherence, and supports a recursive‑descent algorithm whose runtime scales linearly with visible complexity.

Abstract

The geometric structure inherent in the definition of the shapes of three-dimensional objects and environments is 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. 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. Third, “clipping” becomes a very fast logarithmic search for the resolvable parts of the environment within the field of view. Fourth, 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 algorithm. Finally, the geometric structure suggests a recursive descent, visible surface algorithm in which the computation time potentially grows linearly with the visible complexity of the scene.