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mu-Bases for rational canal surfaces
Yao, Shanshan1,2; Jia, Xiaohong1,2
AbstractWe show an efficient approach to computing a mu-basis for a rational canal surface defined by two rational generating curves. By simple geometry we can directly write down three moving planes whose intersection contains the canal surface. The degrees of the three moving planes are much lower than the degree of the surface parametrization, and their outer product retrieves the exact parametrization of the surface, with only a univariate extraneous factor. A matrix factorization technique is applied to these three moving planes to derive a mu-basis for the canal surface, whose outer product is exactly the parametrization of the canal surface. An inversion formula of a given point is also provided by mu-basis representations. (C) 2018 Elsevier B.V. All rights reserved.
KeywordCanal surface mu-basis Syzygy Parametrization Inversion formula
Funding ProjectNational Natural Science Foundation of China[61872354] ; open funding project of State Key Laboratory of Virtual Reality Technology and Systems of Beihang University[BUAA-VR17KF-06] ; Open Projects Program of National Laboratory of Pattern Recognition (NLPR)[201700020] ; Tsinghua University[2015THZ02-2] ; Tsinghua University[2015THZ01]
WOS Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Software Engineering ; Mathematics, Applied
WOS IDWOS:000459845600002
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Document Type期刊论文
Corresponding AuthorJia, Xiaohong
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Yao, Shanshan,Jia, Xiaohong. mu-Bases for rational canal surfaces[J]. COMPUTER AIDED GEOMETRIC DESIGN,2019,69:11-26.
APA Yao, Shanshan,&Jia, Xiaohong.(2019).mu-Bases for rational canal surfaces.COMPUTER AIDED GEOMETRIC DESIGN,69,11-26.
MLA Yao, Shanshan,et al."mu-Bases for rational canal surfaces".COMPUTER AIDED GEOMETRIC DESIGN 69(2019):11-26.
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