Computing exact aspect graphs of curved objects: Solids of revolution

摘要

This paper introduces a new approach to computing the exact orthographic aspect graph of curved objects. Curves corresponding to various visual events partition the view sphere into regions where the image structure is stable. A catalog of these events for piecewise-smooth objects is available from singularity theory. For a solid of revolution whose generator is an algebraic curve, each visual event is characterized by a system of polynomial equations whose roots can be computed by continuation methods. Within each region, the stable image structure is characterized by a variation of cylindrical algebraic decomposition and ray tracing. This approach has been implemented and several examples are presented.