李照宏,郑红婵,廉慧芬,金明娅.可再生混合高阶指数多项式的插值细分法[J].计算机科学,2018,45(3):51-57, 66
可再生混合高阶指数多项式的插值细分法
Interpolatory Subdivision Schemes for Mixed Higher-order Exponential Polynomials Reproduction
投稿时间:2017-07-18  修订日期:2017-08-08
DOI:10.11896/j.issn.1002-137X.2018.03.008
中文关键词:  非静态,插值细分法,再生性,指数多项式,指数B样条
英文关键词:Non-stationary,Interpolatory subdivision schemes,Reproduction,Exponential polynomials,Exponential B-spline
基金项目:本文受陕西省自然科学基金项目:基于细分法的可控分形生成及自然景物模拟研究(S2016YFJM1161)资助
作者单位E-mail
李照宏 西北工业大学应用数学系 西安710129  
郑红婵 西北工业大学应用数学系 西安710129 zhenghc@nwpu.edu.cn 
廉慧芬 西北工业大学应用数学系 西安710129  
金明娅 西北工业大学应用数学系 西安710129  
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中文摘要:
      通过引入新的形状控制参数,提出一类可以精确插值混合型指数多项式的非静态插值细分法。其基本思想是,通过生成指数多项式空间的指数B样条细分法,得到具有相同空间再生性的插值细分法。与具有相同再生性的其他插值细分法相比,所提细分法具有更小的支撑与更大的自由度。从理论上对细分法的再生性进行了分析,并进一步通过图例分析了初始形状控制参数及自由参数对极限曲线的影响。最后展示了取特殊的初始形状控制参数时,所提细分法对于一些特殊曲线的再生性。
英文摘要:
      By introducing new shape control parameter,this paper presented a family of unified interpolatory subdivision schemes which can accurately interpolate mixed and high-order exponential polynomials.The basic idea is to obtain new interpolatory subdivision schemes with the same spare reproducing through generating exponential B-spline subdivision schemes exponential polynomial space.These schemes have smaller support and greater freedom degree than other schemes with the same reproduction.This paper analyzed the reproduction property of the interpolatory schemes in theo-ry.Finally,the influence of initial shape control parameters and free parameters on the limit curve was analyzed.For specific initial control parameter,the presented schemes can be used to reproduce some special curves which are represented by mixed and high-order exponential polynomials.This paper further showed that variety of schemes will be obtained by choosing different free parameters.
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