A-splines: local interpolation and approximation using G(k)-continuous piecewise real algebraic curves
文献类型：期刊论文
| 作者 | Bajaj, CL; Xu, GL |
| 刊名 | COMPUTER AIDED GEOMETRIC DESIGN
 |
| 出版日期 | 1999-07-01 |
| 卷号 | 16期号:6页码:557-578 |
| 关键词 | algebraic curve G(k)-continuous interpolation and approximation BB-form on triangle |
| ISSN号 | 0167-8396 |
| 英文摘要 | 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. |
| WOS研究方向 | Computer Science ; Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000081366300005 |
| 出版者 | ELSEVIER SCIENCE BV |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/14225]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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