Computing exact aspect graphs of curved objects: Algebraic surfaces

摘要

This article presents an algorithm for computing the exact aspect graph of an opaque solid bounded by a smooth algebraic surface. Orthographic projection is assumed. The algorithm is based on a catalog of visual events available from singularity theory. It uses curve tracing, cell decomposition, homotopy continuation, and ray tracing to construct the regions of the view sphere delineated by visual-event curves. The algorithm has been fully implemented, and examples are presented.