DYNAMIC EVALUATION OF EXPONENTIAL POLYNOMIAL CURVES AND SURFACES VIA BASIS TRANSFORMATION

doi:10.1137/18M1230359

	DYNAMIC EVALUATION OF EXPONENTIAL POLYNOMIAL CURVES AND SURFACES VIA BASIS TRANSFORMATION
	Yang, Xunnian 1; Hong, Jialin 2
刊名	SIAM JOURNAL ON SCIENTIFIC COMPUTING
	2019
卷号	41 期号:5 页码:A3401-A3420
关键词	curves and surfaces linear differential operator exponential polynomial dynamic evaluation basis transformation
ISSN号	1064-8275
DOI	10.1137/18M1230359
英文摘要	It 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.
资助项目	National Natural Science Foundation of China[11290142] ; NSFC[91530118] ; NSFC[91630312] ; NSFC[91130003]
WOS研究方向	Mathematics
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000493897100028
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/50723]
专题	中国科学院数学与系统科学研究院
通讯作者	Yang, Xunnian
作者单位	1.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
推荐引用方式 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.