Computing exact aspect graphs of curved objects: solids of revolution
David Kriegman, Jean Ponce · 2003
An approach to computing the exact orthographic aspect graph of curved objects is introduced. Curved corresponding to various visual events partition the Gaussian 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 polynomials 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.>