计算机应用研究2017，Vol.34Issue(1)：295-301,7.DOI:10.3969/j.issn.1001-3695.2017.01.067
三次均匀 B样条曲线的保形扩展
Conformal extension of cubic uniform B-spline curve
摘要
Abstract
This article aimed to construct an extended cubic uniform B-spline curve,which had both convex hull property and shape-preserving property,under the premise of without increasing the computational complexity.First,by adopting reverse thinking method,this paper obtained the properties of the blending function from the preset properties of the curve,and then calculated the expression of the blending function.Then,by qualitative analysis,it discussed the parameter intervals of the curve which made it has convex hull property,monotonicity-preserving,convexity-preserving,variation diminishing property respectively.The legends show the correctness of the analysis result.The intersection of the different parameter value range is the finalized feasible region of the shape parameter.Altering the shape parameter in the feasible region,it can adjust the ap-proximation degree of the curve to the control polygon under the premise that do not destroy the shape-preserving property of the curve.Finally,this paper briefly discussed the tensor product surface corresponding to the curve,and gave some legends.关键词
分段曲线曲面/全正基/保形/变差缩减性/保凸/保单调Key words
piecewise curve and surface/totally positive basis/shape-preserving/variation diminishing property/convexity-preserving/monotonicity-preserving分类
信息技术与安全科学引用本文复制引用
严兰兰,韩旭里..三次均匀 B样条曲线的保形扩展[J].计算机应用研究,2017,34(1):295-301,7.基金项目
国家自然科学基金资助项目（11261003，11271376，60970097）；江西省教育厅资助项目（GJJ14493）；江西省自然科学基金资助项目 （）
