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基于插值细分的逼近细分法
  • ISSN号：1003-9775
  • 期刊名称：《计算机辅助设计与图形学学报》
  • 时间：0
  • 分类：TP391[自动化与计算机技术—计算机应用技术;自动化与计算机技术—计算机科学与技术]
  • 作者机构：[1]合肥工业大学数学学院,合肥230009
  • 相关基金：国家自然科学基金.广东联合基金重点项目（U1135003）;国家自然科学基金（61472466,61070227）.
作者： 檀结庆[1], 童广悦[1], 张莉[1]
关键词： 插值细分法, 逼近细分法, 生成多项式, Ck连续性, interpolating subdivision, approximating subdivision, Laurent polynomial, C-continuity
中文摘要：

通过在Hassan的四点三重插值细分法中引入一个偏移变量,推导出了一种逼近细分法,从而使三重逼近细分和插值细分统一到一个细分格式.该方法利用细分格式的生成多项式,在理论上分析了提出的细分格式的一致收敛性和Ck连续性;通过对细分格式中参数u取不同的值,可对生成的极限曲线形状进行控制.数值实验结果表明,文中方法是合理有效的.

英文摘要：

This paper presents a new method for constructing approximating subdivision, which is obtained by introducing an offset variable to the interpolating four-point ternary subdivision schemes proposed by Hassan. The new scheme unifies the ternary approximating subdivision and interpolation subdivision. The uniform convergence and Ck smoothness of the limit curve produced by our subdivision scheme are analyzed by means of the Laurent polynomials. It is pointed out that the parameter in the subdivision can be adjusted to control the shape of the limit curve. Numerical experiments show that the proposed method is effective.

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期刊信息
  • 《计算机辅助设计与图形学学报》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学技术协会
  • 主办单位:中国计算机学会
  • 主编：鲍虎军
  • 地址：北京2704信箱
  • 邮编：100190
  • 邮箱：jcad@ict.ac.cn
  • 电话：010-62562491
  • 国际标准刊号：ISSN：1003-9775
  • 国内统一刊号：ISSN：11-2925/TP
  • 邮发代号:82-456
  • 获奖情况:
  • 第三届国家期刊奖提名奖
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,荷兰文摘与引文数据库,美国工程索引,英国科学文摘数据库,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:24752