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Piecewise rational approximations of real algebraic curves
Bajaj, CL; Xu, GL
1997
Source PublicationJOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN0254-9409
Volume15Issue:1Pages:55-71
AbstractWe use a combination of both algebraic and numerical techniques to construct a C-1-continuous, piecewise (m, n) rational epsilon-approximation of a real algebraic plane curve of degree d. At singular points we use the classical Weierstrass Preparation Theorem and Newton power series factorizations, based on the technique of Hensel lifting. These, together with modified rational Pade approximations, are used to efficiently construct locally approximate, rational parametric representations for all real branches of an algebraic plane curve. Besides singular points we obtain an adaptive selection of simple points about which the curve approximations yield a small number of pieces yet achieve C-1 continuity between pieces. The simpler cases of C-1 and C-0 continuity are also handled in a similar manner. The computation of singularity, the approximation error bounds and details of the implementation of these algorithms are also provided.
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:A1997WD52300005
PublisherVSP BV
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/28956
Collection中国科学院数学与系统科学研究院
Affiliation1.PURDUE UNIV,DEPT COMP SCI,W LAFAYETTE,IN 47907
2.CHINESE ACAD SCI,STATE KEY LAB SCI & ENGN COMP,ICMSEC,BEIJING,PEOPLES R CHINA
Recommended Citation
GB/T 7714
Bajaj, CL,Xu, GL. Piecewise rational approximations of real algebraic curves[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,1997,15(1):55-71.
APA Bajaj, CL,&Xu, GL.(1997).Piecewise rational approximations of real algebraic curves.JOURNAL OF COMPUTATIONAL MATHEMATICS,15(1),55-71.
MLA Bajaj, CL,et al."Piecewise rational approximations of real algebraic curves".JOURNAL OF COMPUTATIONAL MATHEMATICS 15.1(1997):55-71.
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