Analytic and algebraic properties of canal surfaces

doi:10.1016/j.cam.2005.08.002

	Analytic and algebraic properties of canal surfaces
	Xu, Zhiqiang; Feng, Renzhong ; Sun, Jia-guang
	2006-10-15
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	195 期号:1-2 页码:220-228
摘要	The envelope of a one-parameter set of spheres with radii r(t) and centers m(t) is a canal surface with m(t) as the spine curve and r(t) as the radii function. This concept is a generalization of the classical notion of an offset of a plane curve. In this paper, we firstly survey the principle geometric features of canal surfaces. In particular, a sufficient condition for canal surfaces without local self-intersection is presented. Moreover, a simple expression for the area and Gaussian curvature of canal surfaces are given. We also consider the implicit equation f (x, y, z) = 0 of canal surfaces with the degree of f (x, y, z) presented. By using the degree of f (x, y, z), a low boundary of the degree of parameterizations representations of canal surfaces is presented. (c) 2005 Elsevier B.V. All rights reserved.
关键词	canal surfaces self-intersections implicit equations
DOI	10.1016/j.cam.2005.08.002
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000239258000020
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/3795
专题	计算数学与科学工程计算研究所
通讯作者	Xu, Zhiqiang
作者单位	1.Acad Sinica, Inst Computat Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Tsing Hua Univ, Sch Software, Beijing 100084, Peoples R China 3.Beijing Univ Aeronaut & Astronaut, Dept Math, Beijing 100083, Peoples R China
推荐引用方式 GB/T 7714	Xu, Zhiqiang,Feng, Renzhong,Sun, Jia-guang. Analytic and algebraic properties of canal surfaces[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2006,195(1-2):220-228.
APA	Xu, Zhiqiang,Feng, Renzhong,&Sun, Jia-guang.(2006).Analytic and algebraic properties of canal surfaces.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,195(1-2),220-228.
MLA	Xu, Zhiqiang,et al."Analytic and algebraic properties of canal surfaces".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 195.1-2(2006):220-228.