Robust boolean set operations for manifold solids bounded by planar and natural quadric surfaces

This paper describes our latest effort in robust solid modeling. An algorithm for set operations on solids bounded by planar and natural quadric surfaces, that handles all geometrically degenerate cases robustly, is described. We identify as the main reason for the lack of robustness in geometric modeling, that dependent relations are handled inconsistently by disregarding the dependencies. Instead of using explicit reasoning to make dependent decisions consistent, we show that redundant computation can be avoided by correctly ordering the operations, and redundant data can be eliminated in the set operation algorithm, so that the result is guaranteed to be a valid two-manifold solid.