DYNAMIC EVALUATION OF EXPONENTIAL POLYNOMIAL CURVES AND SURFACES VIA BASIS TRANSFORMATION
文献类型：期刊论文
| 作者 | Yang, Xunnian2; Hong, Jialin1 |
| 刊名 | SIAM JOURNAL ON SCIENTIFIC COMPUTING
 |
| 出版日期 | 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 |
| WOS记录号 | WOS:000493897100028 |
| 出版者 | SIAM PUBLICATIONS |
| 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.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 2.Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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