Research Initiation: Towards Natural Quartics in Solid Modelling

当前实体建模的领域不足可以通过纳入自然四分位-四次代数曲面的一个有用子集来缓解。这样一类四分位存在于杜平环中。它们可以合理地参数化，而且它们的偏移量计算起来很简单。此外，它们是自然二次曲面和环面的超集。本研究的目标是：(i)通过纳入自然四分位数来扩展实体建模器的几何覆盖范围；（ii）在使用坐标测量机的制造单元的自动检测系统中应用这种实体建模器。

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.