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浙江大学学报(理学版)  2017, Vol. 44 Issue (3): 307-313    DOI: 10.3785/j.issn.1008-9497.2017.03.011
数学与计算机科学     
利用带形状参数的有理势函数构造基于Metaball的过渡曲线
李军成1, 宋来忠2
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
Construction of transition curves based on Metaball technique using rational potential function with a shape parameter
LI Juncheng1, SONG Laizhong2
1. College of Mathematics and Finances, Hunan University of Humanities, Science and Technology, Loudi 417000, Hunan Province, China;
2. College of Science, China Three Gorges University, Yichang 443002, Hubei Province, China
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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.
关键词: 势函数形状参数Metaball技术过渡曲线形状调整    
Abstract: 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.
Key words: potential function    shape parameter    Metaball technique    transition curve    shape adjustment
收稿日期: 2016-01-26 出版日期: 2017-03-01
CLC:  TP391  
基金资助: 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).
作者简介: 李军成(1982-),ORCID:http://orcid.org/0000-0002-1904-4068,男,博士,副教授,主要从事计算机辅助几何设计及其应用研究,E-mail:lijuncheng82@126.com.
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引用本文:

李军成, 宋来忠. 利用带形状参数的有理势函数构造基于Metaball的过渡曲线[J]. 浙江大学学报(理学版), 2017, 44(3): 307-313.

LI Juncheng, SONG Laizhong. Construction of transition curves based on Metaball technique using rational potential function with a shape parameter. Journal of Zhejiang University (Science Edition), 2017, 44(3): 307-313.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.03.011        https://www.zjujournals.com/sci/CN/Y2017/V44/I3/307

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