Role of moving planes and moving spheres following Dupin cyclides
KAUST DepartmentVisual Computing Center (VCC)
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AbstractWe 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. © 2014 Elsevier B.V.
SponsorsThe author is grateful to professor Falai Chen and professor Ron Goldman for their guidance on the topic of A-bases through years. Zhouwang Yang at the University of Science and Technology of China proposed the original idea in Section 6 two years ago in another project. This work is supported by a National Key Basic Research Project of China (2011CB302404), by grants from NSFC (11201463), (60821002) and (91118001). The author is also supported by the National Center for Mathematics and Interdisciplinary Sciences in the Chinese Academy of Sciences and KAUST base funding.
JournalComputer Aided Geometric Design