DYNAMIC EVALUATION OF FREE-FORM CURVES AND SURFACES

doi:10.1137/16M1058911

	DYNAMIC EVALUATION OF FREE-FORM CURVES AND SURFACES
	Yang, Xunnian 1; Hong, Jialin2
	2017
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	39 期号:2 页码:B424-B441
摘要	Free-form curves and surfaces represented by control points together with well-defined basis functions are widely used in computer aided geometric design. Efficient evaluation of points and derivatives of free-form curves and surfaces plays an important role in interactive rendering or CNC machining. In this paper we show that free-form curves with properly defined basis functions are the solutions of linear differential systems. By employing typical numerical methods for solving the differential systems, points and derivatives of free-form curves and surfaces can be computed in a dynamical way. Compared with traditional methods for evaluating free-form curves and surfaces there are two advantages of the proposed technique. First, the proposed method is universal and efficient for evaluating a large class of free-form curves and surfaces. Second, the evaluation needs only arithmetic operations even when the free-form curves and surfaces are defined using some transcendental functions.
关键词	free-form curves and surfaces linear differential systems evaluation dynamic generation
DOI	10.1137/16M1058911
语种	英语
资助项目	National Natural Science Foundation of China[11290142] ; National Natural Science Foundation of China[61272300] ; NSFC[91530118] ; NSFC[91630312] ; NSFC[91130003]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000401776100009
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25499
专题	计算数学与科学工程计算研究所
通讯作者	Yang, Xunnian
作者单位	1.Zhejiang Univ, Sch Math Sci, Hangzhou 310027, 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 FREE-FORM CURVES AND SURFACES[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2017,39(2):B424-B441.
APA	Yang, Xunnian,&Hong, Jialin.(2017).DYNAMIC EVALUATION OF FREE-FORM CURVES AND SURFACES.SIAM JOURNAL ON SCIENTIFIC COMPUTING,39(2),B424-B441.
MLA	Yang, Xunnian,et al."DYNAMIC EVALUATION OF FREE-FORM CURVES AND SURFACES".SIAM JOURNAL ON SCIENTIFIC COMPUTING 39.2(2017):B424-B441.