基于Lupas q-拟Bernstein算子的G^2样条曲线  

G^2 Spline Curves Based on Lupas q-analogue of Bernstein Operator

作　　者：杨军[1] 王青燕 YANG Jun;WANG Qing-yan(School of Mathematics and Information Sciences,Nanchang Hangkong University,Nanchang 330063,China)

机构地区：[1]南昌航空大学数学与信息科学学院,南昌330063

出　　处：《南昌航空大学学报（自然科学版）》2018年第4期24-31,共8页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：国家自然科学基金(51865039)

摘　　要：为增加自由型曲线形状调控能力,以Lupas q-Bernstein算子的性质为基础,给出了Lupas q-拟Bezier曲线的新性质;进一步,在控制顶点给定的情况下,通过引入新的形状参数获取额外自由度,对分段Lupas q-Bezier曲线进行光滑拼接构造G2样条曲线。特别地,当选取特殊形状参数时,曲线可退化为Gamma样条曲线。理论分析和计算实例表明G2样条曲线较Gamma样条曲线在形状控制方面具有更多的灵活性。To improve the shape control ability of freeform curves,based on the properties of the Lupas q-Bernstein operator,new properties of the Lupas q-Bezier curve are given. Further,additional degrees of freedom are obtained by introducing new shape parameters for given control points,and a G2 spline curve is constructed by joining piecewise Lupas q-Bezier curves smoothly. In particular,when the shape parameters are selected specially,the curve degenerates into the Gamma spline curve. Theoretical analysis and calculation examples show that the G2 spline curve has more flexibility in shape control than the Gamma spline curve.

关 键 词：q-拟Bernstein算子 Lupas q-Bezier曲线 几何连续 样条 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]