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广义B样条曲线的节点去除与光顺算法
  • 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：TP391.41[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, [2]合肥工业大学计算机与信息学院,合肥230009
  • 相关基金：国家自然科学基金重点项目（U1135003）;国家自然科学基金（61472466,61100126）;中国博士后科学基金面上资助项目（2015M571926）;浙江大学CAD＆CG国家重点实验室开放课题（A1607）.
作者： 张莉[1], 葛先玉[1], 檀结庆[1,2]
关键词： 广义B样条, 对偶基, 节点去除, 最佳逼近, 曲线光顺
中文摘要：

广义B 样条曲线具备了B 样条曲线的各种优良性质, 又因为其独具的核函数为形状设计带来更加丰富的可能性, 文中提出了广义B 样条曲线的节点去除与光顺算法. 首先给出了构造广义B 样条对偶基的新方法, 其时间计算复杂度得到了很好的控制; 其次摘除需去除的节点, 再利用对偶基的最佳逼近性质, 采用广义B 样条的对偶基求得新的广义B 样条曲线的控制顶点; 在广义B 样条曲线光顺中引入跳跃值的概念, 如果某个节点附近的跳跃值较大,则去除相应的节点, 从而实现在此节点处的光顺. 最后通过大量的数值实例, 展示了算法的有效性.

英文摘要：

Generalized B-splines are not only compatible with classical B-splines but also provide plentiful shapes for geometric modeling systems because of their flexible core functions. The paper focuses on knots removal and smooth method of generalized B-splines. Firstly, the dual bases of generalized B-splines are constructed, and the complexity can be reduced a lot. Secondly, jump value is introduced, if jump values of some knots are too big, the corresponding knots are removed. At last, by the aid of best approximation prop-erty of the generalized B-splines’ dual bases, control points of new approximating generalized B-splines are obtained. Thus, knots removal and smooth of curves are realized. Numerical examples are given to illustrate the effectiveness of the method.

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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