mu-Bases for rational canal surfaces

doi:10.1016/j.cagd.2018.12.001

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	mu-Bases for rational canal surfaces
	Yao, Shanshan 1,2; Jia, Xiaohong1,2
刊名	COMPUTER AIDED GEOMETRIC DESIGN
	2019-02-01
卷号	69 页码:11-26
关键词	Canal surface mu-basis Syzygy Parametrization Inversion formula
ISSN号	0167-8396
DOI	10.1016/j.cagd.2018.12.001
英文摘要	We 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.
资助项目	National 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研究方向	Computer Science ; Mathematics
语种	英语
出版者	ELSEVIER SCIENCE BV
WOS记录号	WOS:000459845600002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/34168]
专题	系统科学研究所
通讯作者	Jia, Xiaohong
作者单位	1.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
推荐引用方式 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.