Role of moving planes and moving spheres following Dupin cyclides

Xiaohong Jia

doi:10.1016/j.cagd.2014.02.006

Role of moving planes and moving spheres following Dupin cyclides

Xiaohong Jia

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

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.

Original language	English (US)
Pages (from-to)	168-181
Number of pages	14
Journal	Computer Aided Geometric Design
Volume	31
Issue number	3-4
DOIs	https://doi.org/10.1016/j.cagd.2014.02.006
State	Published - Mar 2014

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.

ASJC Scopus subject areas

Modeling and Simulation
Computer Graphics and Computer-Aided Design
Automotive Engineering
Aerospace Engineering

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10.1016/j.cagd.2014.02.006

Cite this

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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. {\textcopyright} 2014 Elsevier B.V.",

author = "Xiaohong Jia",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: 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.",

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Role of moving planes and moving spheres following Dupin cyclides

Abstract

Bibliographical note

ASJC Scopus subject areas

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