Role of moving planes and moving spheres following Dupin cyclides

Jia, Xiaohong

Type

Article

Authors

Jia, Xiaohong

KAUST Department

Visual Computing Center (VCC)

Date

2014-03

Permanent link to this record

http://hdl.handle.net/10754/563427

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Abstract

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. © 2014 Elsevier B.V.

Sponsors

The 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.