利用带形状参数的有理势函数构造基于Metaball的过渡曲线  

Construction of transition curves based on Metaball technique using rational potential function with a shape parameter

作　　者：李军成[1] 宋来忠[2] 

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 [2]三峡大学理学院,湖北宜昌443002

出　　处：《浙江大学学报（理学版）》2017年第3期307-313,共7页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(11171181);湖南省教育厅资助科研项目(14B099)

摘　　要：利用现有势函数构造基于Metaball的过渡曲线,此过渡曲线无法兼具拟高阶连续性与形状可调性.针对这一问题,巧妙地从一种带形状参数的曲线模型出发,构造一类带形状参数的有理势函数,并研究该势函数的性质.所构造的有理势函数具有统一的数学模型,不仅能使过渡曲线在端点处达到拟Ck连续,而且还可通过修改形状参数的值调整过渡曲线的形状.实例表明,通过调整有理势函数的次数及形状参数的取值可构造出满足不同拟连续性且形状不同的过渡曲线,以满足实际应用需要.Using the existing potential functions to construct transition curve based on Metaball technique,it can not have both quasi high order continuity and shape adjustability.To solving this problem,a rational potential function with a shape parameter is constructed ingeniously from a curve with shape parameters.Some properties of the rational potential function are studied.The rational potential function is expressed as a unified mathematical model,which can not only make the transition curve achieve quasi Ck continuity at the end points,but also adjust the shape of the transition curve by modifying the value of the shape parameter.Some examples showed that the transition curves with different continuities and shapes could be constructed by changing the degree and the shape parameter of the rational potential function,which could be used to meet different needs of the practical application.

关 键 词：势函数 形状参数 Metaball技术 过渡曲线 形状调整 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]