A-splines: local interpolation and approximation using G(k)-continuous piecewise real algebraic curves

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	A-splines: local interpolation and approximation using G(k)-continuous piecewise real algebraic curves
	Bajaj, CL ; Xu, GL
	1999-07-01
发表期刊	COMPUTER AIDED GEOMETRIC DESIGN
ISSN	0167-8396
卷号	16 期号:6 页码:557-578
摘要	We provide sufficient conditions for the Bernstein-Bezier (BB) form of an implicitly defined bivariate polynomial over a triangle, such that the zero contour of the polynomial defines a smooth and single sheeted real algebraic curve segment. We call a piecewise G(k)-continuous chain of such real algebraic curve segments in BE-form as an A-spline (short for algebraic spline). We prove that the degree n A-splines can achieve in general G(2n-3) continuity by local fitting and still have degrees of freedom to achieve local data approximation. As examples, we show how to construct locally convex cubic A-splines to interpolate and/or approximate the vertices of an arbitrary planar polygon with up to G(4) continuity, to fit discrete points and derivatives data, and approximate high degree parametric and implicitly defined curves. Additionally, we provide computable error bounds. (C) 1999 Elsevier Science B.V. All rights reserved.
关键词	algebraic curve G(k)-continuous interpolation and approximation BB-form on triangle
语种	英语
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Mathematics, Applied
WOS记录号	WOS:000081366300005
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/14226
专题	中国科学院数学与系统科学研究院
通讯作者	Bajaj, CL
作者单位	1.Univ Texas, Dept Comp Sci, Austin, TX 78712 USA 2.Chinese Acad Sci, ICMSEC, State Key Lab Sci & Engn Comp, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Bajaj, CL,Xu, GL. A-splines: local interpolation and approximation using G(k)-continuous piecewise real algebraic curves[J]. COMPUTER AIDED GEOMETRIC DESIGN,1999,16(6):557-578.
APA	Bajaj, CL,&Xu, GL.(1999).A-splines: local interpolation and approximation using G(k)-continuous piecewise real algebraic curves.COMPUTER AIDED GEOMETRIC DESIGN,16(6),557-578.
MLA	Bajaj, CL,et al."A-splines: local interpolation and approximation using G(k)-continuous piecewise real algebraic curves".COMPUTER AIDED GEOMETRIC DESIGN 16.6(1999):557-578.