The domain inadequacy of current solid modellers can be alleviated by incorporating the natural quartics - a useful subset of degree four algebraic surfaces. Such a class of quartics exist in the Dupin cyclides. They can be rationally parameterized and their offsets are trivial to compute. Furthermore, they are a superset of the natural quadrics and the torus. The objectives of this research are: (i) to extend the geometric coverage of solid modellers by incorporating the natural quartics; (ii) to enable the application of such solid modellers in automated inspection systems of manufacturing cells employing coordinate measuring machines.
