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DYNAMIC EVALUATION OF EXPONENTIAL POLYNOMIAL CURVES AND SURFACES VIA BASIS TRANSFORMATION
Yang, Xunnian1; Hong, Jialin2
2019
Source PublicationSIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN1064-8275
Volume41Issue:5Pages:A3401-A3420
AbstractIt is shown in [SIAM T. Sci. Comput., 39 (2017), pp. B424-B441] that free-form curves used in computer-aided geometric design can usually be represented as the solutions of linear differential systems and that points and derivatives on the curves can be evaluated dynamically by solving the differential systems numerically. In this paper we present an even more robust and efficient algorithm for dynamic evaluation of exponential polynomial curves and surfaces. Based on properties that spaces spanned by general exponential polynomials are translation invariant and polynomial spaces are invariant with respect to a linear transformation of the parameter, the transformation matrices between bases with or without translated or linearly transformed parameters are explicitly computed. Points on curves or surfaces with equal or changing parameter steps can then be evaluated dynamically from a start point using a precomputed matrix. Like former dynamic evaluation algorithms, the newly proposed approach needs only arithmetic operations for evaluating exponential polynomial curves and surfaces. Unlike conventional numerical methods that solve a linear differential system, the new method can give robust and accurate evaluation results for any chosen parameter steps. The basis transformation technique also enables dynamic evaluation of polynomial curves with changing parameter steps using a constant matrix, which reduces time costs significantly than computing each point individually by classical algorithms.
Keywordcurves and surfaces linear differential operator exponential polynomial dynamic evaluation basis transformation
DOI10.1137/18M1230359
Indexed BySCI
Language英语
Funding ProjectNational Natural Science Foundation of China[11290142] ; NSFC[91530118] ; NSFC[91630312] ; NSFC[91130003]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000493897100028
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/50724
Collection中国科学院数学与系统科学研究院
Corresponding AuthorYang, Xunnian
Affiliation1.Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Yang, Xunnian,Hong, Jialin. DYNAMIC EVALUATION OF EXPONENTIAL POLYNOMIAL CURVES AND SURFACES VIA BASIS TRANSFORMATION[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2019,41(5):A3401-A3420.
APA Yang, Xunnian,&Hong, Jialin.(2019).DYNAMIC EVALUATION OF EXPONENTIAL POLYNOMIAL CURVES AND SURFACES VIA BASIS TRANSFORMATION.SIAM JOURNAL ON SCIENTIFIC COMPUTING,41(5),A3401-A3420.
MLA Yang, Xunnian,et al."DYNAMIC EVALUATION OF EXPONENTIAL POLYNOMIAL CURVES AND SURFACES VIA BASIS TRANSFORMATION".SIAM JOURNAL ON SCIENTIFIC COMPUTING 41.5(2019):A3401-A3420.
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