Approximate mu-bases of rational curves and surfaces

CSpace

	Approximate mu-bases of rational curves and surfaces
	Shen, Liyong ; Chen, Falai ; Juettler, Bert ; Deng, Jiansong
	2006
发表期刊	GEOMETRIC MODELING AND PROCESSING - GMP 2006, PROCEEDINGS
ISSN	0302-9743
卷号	4077 页码:175-188
摘要	The mu-bases of rational curves and surfaces are newly developed tools which play an important role in connecting parametric forms and implicit forms of curves and surfaces. However, exact mu-bases may have high degree with complicated rational coefficients and are often hard to compute (especially for surfaces), and sometimes they are not easy to use in geometric modeling and processing applications. In this paper, we introduce approximate mu-bases for rational curves and surfaces, and present an algorithm to compute approximate mu-bases. The algorithm amounts to solving a generalized eigenvalue problem and some quadratic programming problems with linear constraints. As applications, approximate implicitization and degree reduction of rational curves and surfaces with approximate mu-bases are discussed. Both the parametric equations and the implicit equations of the approximate curves/surfaces are easily obtained by using the approximate mu-bases. As indicated by the examples, the proposed algorithm may be a useful alternative to other methods for approximate implicitization.
关键词	approximate mu-bases approximate implicitization
语种	英语
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Theory & Methods ; Mathematics, Applied
WOS记录号	WOS:000239567900013
出版者	SPRINGER-VERLAG BERLIN
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/2890
专题	中国科学院数学与系统科学研究院
通讯作者	Shen, Liyong
作者单位	1.Univ Sci & Technol China, Dept Math, Chengdu, Peoples R China 2.Johannes Kepler Univ Linz, Inst Appl Geometry, A-4040 Linz, Austria 3.Chinese Acad Sci, AMSS, Inst Syst Sci, KLMM, Beijing 100864, Peoples R China
推荐引用方式 GB/T 7714	Shen, Liyong,Chen, Falai,Juettler, Bert,et al. Approximate mu-bases of rational curves and surfaces[J]. GEOMETRIC MODELING AND PROCESSING - GMP 2006, PROCEEDINGS,2006,4077:175-188.
APA	Shen, Liyong,Chen, Falai,Juettler, Bert,&Deng, Jiansong.(2006).Approximate mu-bases of rational curves and surfaces.GEOMETRIC MODELING AND PROCESSING - GMP 2006, PROCEEDINGS,4077,175-188.
MLA	Shen, Liyong,et al."Approximate mu-bases of rational curves and surfaces".GEOMETRIC MODELING AND PROCESSING - GMP 2006, PROCEEDINGS 4077(2006):175-188.