Abstract：This paper proposes a new class of shape-preserving piecewise cubic polynomial curves with both local and global shape control parameters. By presetting the properties of its basis functions and then solving equations, a set of polynomial basis functions with two shape parameters are derived, including the cubic uniform B-spline basis functions as a special case. Based on the relationship between the new basis functions and the cubic Bernstein basis functions, the totally positive property of the new basis functions is proved and a new class of piecewise cubic polynomial curves is therefore defined. The effect of the relative position of the control polygons' side vectors onto the shape characteristic of the corresponding curve segments is analyzed. Necessary and sufficient conditions are obtained for the curve segments containing single or double inflection points, a loop or a cusp, or be locally or globally convex, which provide a theoretical guide for adjusting the shape of curve segments.
基金资助:Supported by the NSFC(11261003, 11761008), the Natural Science Foundation of Jiangxi Province (20161BAB211028) and the Science Research Foundation of Jiangxi Province Education Department (GJJ160558).
作者简介: YAN Lanlan(1982-),ORCID:http://orcid.org/0000-0002-5472-9986,female,Ph.D,associate professor,the field of interest is CAGD,E-mail:yxh821011@aliyun.com.
引用本文:
严兰兰, 樊继秋. 保形分段三次多项式曲线的形状分析[J]. 浙江大学学报（理学版）, 2018, 45(1): 44-53.
YAN Lanlan, FAN Jiqiu. Construction and analysis of a new class of shape-preserving piecewise cubic polynomial curves. Journal of ZheJIang University(Science Edition), 2018, 45(1): 44-53.
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