Role of moving planes and moving spheres following Dupin cyclides

摘要

We provide explicit representations of three moving planes that form a μ-basis for a standard Dupin cyclide. We also show how to compute μ-bases for Dupin cyclides in general position and orientation from their implicit equations. In addition, we describe the role of moving planes and moving spheres in bridging between the implicit and rational parametric representations of these cyclides.