Lupaş q-Bézier曲线的几何求值算法及其应用  

Geometric evaluation algorithms for Lupaş q-Bézier curve and its applications

作　　者：柳丽宏 左华[1] 韩力文[1,2] LIU Li-hong;ZUO Hua;HAN Li-wen(School of Mathematical Sciences,Hebei Normal University,Shijiazhuang Hebei 050024,China;Hebei Key Laboratory of Computational Mathematics and Applications,Shijiazhuang Hebei 050024,China)

机构地区：[1]河北师范大学数学科学学院,河北石家庄050024 [2]河北省计算数学与应用重点实验室,河北石家庄050024

出　　处：《图学学报》2021年第4期651-658,共8页Journal of Graphics

基　　金：国家自然科学基金项目(61573127);河北省自然科学基金项目(A2018205103);河北师范大学科研基金资助项目(L2020Z02,L2020K09);河北师范大学研究生创新资助项目(CXZZSS202053)。

摘　　要：Lupaşq-Bézier曲线是一种以q-整数作为形状参数的广义Bézier曲线。本文构造了Lupaş q-Bézier曲线的一种新型几何求值算法,该算法倒数第二层2个节点的仿射组合与曲线相切。利用算法的相切性质得到Lupaş q-Bézier曲线导矢的一种新表示,并实现了Lupaş q-Bézier曲线的细分。特别地,二次Lupaş q-Bézier曲线分割得到的2条子曲线的形状参数的乘积等于原曲线的形状参数。进一步,得到了加权Lupaş q-Bézier曲线的一种新型几何求值算法,该算法具有显式矩阵表示。The Lupaş q-Bézier curve is a generalized Bézier curve with q-integer as the shape parameter.A new geometric evaluation algorithm for Lupaş q-Bézier curve was constructed in this paper,in which the affine combination of two nodes in the penultimate layer of the algorithm is tangent to the curve.A new representation of the derivative of the Lupaşq-Bézier curve was obtained using the property of algorithm,and the subdivision of curve was realized.Particularly,a product of the shape parameters of the two subcurves produced by the subdivision of the Lupaş q-Béziercurves was equal to the shape parameter of the original curve.Furthermore,a new geometric evaluation algorithm of weighted Lupaş q-Bézier with an explicit matrix representation was gained.

关 键 词：Lupaşq-Bézier曲线 de Casteljau算法 显式矩阵表示 细分 计算复杂度 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]