Bezier型曲线内能极小化的通用方法及其应用  

General methods for minimizing the internal energy of Bezier-like curves and their applications

作　　者：李军成 刘成志 LI Jun-cheng;LIU Cheng-zhi(College of Mathematics and Finance,Hunan University of Humanities,Science and Technology,Loudi 417000,China)

机构地区：[1]湖南人文科技学院数学与金融学院,湖南娄底417000

出　　处：《高校应用数学学报（A辑）》2024年第3期291-302,共12页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：湖南省自然科学基金(2024JJ7254);国家自然科学基金(12101225)。

摘　　要：虽然Bezier型曲线中包含的形状参数可提高其形状表现能力,但如何通过确定形状参数的最佳取值对Bezier型曲线的形状进行优化也值得关注.该文提出了通过对三种常见内能极小化来确定Bezier型曲线中所含形状参数最优值的通用方法,该方法包括极小化一种内能,同步极小化其中两种内能以及同步极小化三种内能等情形.最后利用一种被称为三次替代曲线的Bezier型曲线对文中所提出的方法进行了检验,结果表明这些方法是可行的.Although the shape parameters contained in Bezier-like curves can indeed improve their shape representation ability,it is also worth paying attention to how to optimize the shape of Bezier-like curves by determining the optimal values of the shape parameters.In this paper,the general methods for determining the optimal values of the shape parameters contained in Bezier-like curves by minimizing the three well known internal energy of the curves are proposed.The general methods include minimizing one of the internal energy,synchronously minimizing two of the internal energy,and synchronously minimizing all the internal energy.Then a Bezier-like curve called cubic alternative curve is used to check the proposed general methods,and the results show that these methods are feasible.

关 键 词：Bezier型曲线 形状参数 形状优化 能量极小化 

分 类 号：O241.5[理学—计算数学]