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浙江大学学报(理学版)  2020, Vol. 47 Issue (2): 178-190    DOI: 10.3785/j.issn.1008-9497.2020.02.008
数学与计算机科学     
三次DP曲线定义区间的扩展及其形状优化
张迪, 查东东, 刘华勇
安徽建筑大学 数理学院,安徽 合肥 230601
Interval extension of the cubic DP curve and its shape optimization.
ZHANG Di, ZHA Dongdong, LIU Huayong
School of Sciences and Physics, Anhui Jianzhu University, Hefei 230601,China
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摘要: 为构造一种带形状参数的三次DP曲线,解决DP曲线在给定控制顶点时不具有形状修改功能的缺陷。将传统的三次DP基函数的定义区间由[0,1]推广为[0,α],重新参数化后得到一组新的含参扩展基,分析扩展基的性质并将其与固定的控制顶点进行线性组合,构造了三次α-DP曲线。讨论了曲线的性质与形状,分析了形状参数的几何意义,并给出了曲线光滑拼接的条件:当满足一定条件时,曲线可达到G1G2连续。同时,运用张量积方法将三次α-DP曲线推广到曲面。实例表明,三次α-DP曲线曲面不仅继承了传统DP曲线曲面的优良性质,而且具有形状可调性。最后给出了3种形状参数的选取方案以及相应实例。
关键词: DP曲线几何连续形状参数参数选取    
Abstract: In order that the cubic DP curve could have the shape-adjustable, a type of cubic DP curve with a shape parameter is constructed. This paper extends the definition interval of the the traditional cubic DP basis function from [0,1] to [0,α]. After reparameterization, a new set of extended basis functions with a parameter is proposed. The properties of the new basis functions are analyzed. Based on linear combination method,this paper also discusses the properties and the shape of the cubic DP curve and analyses the geometric meaning of shape parameters. Furthermore,G1 and G2 continuous conditions of the curve are given when certain conditions are met. Using the tensor product method, the curve is generalized to construct the cubic DP surface with a parameter. The new curve and surface not only inherits the excellent properties of the traditional DP curve and surface, also can adjust its shape under the fixed control points. Finally, three selection schemes of the shape parameters and the corresponding application examples are given.
Key words: DP curve    geometric continuous    shape parameters    parameter selection
收稿日期: 2019-01-14 出版日期: 2020-03-25
CLC:  TP391  
基金资助: 安徽省高等学校自然科学研究项目(KJ2018A0518).
通讯作者: ORCID:http://orcid.org/0000-0002-9330-1149 E-mail:aiaiwj@126.com.     E-mail: aiaiwj@126.com
作者简介: 张迪(1997—),ORCID:http://orcid.org/0000- 0002-9108-8401,女,硕士研究生,主要从事计算机辅助几何图形设计研究.
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张迪, 查东东, 刘华勇. 三次DP曲线定义区间的扩展及其形状优化[J]. 浙江大学学报(理学版), 2020, 47(2): 178-190.

ZHANG Di, ZHA Dongdong, LIU Huayong. Interval extension of the cubic DP curve and its shape optimization.. Journal of Zhejiang University (Science Edition), 2020, 47(2): 178-190.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2020.02.008        https://www.zjujournals.com/sci/CN/Y2020/V47/I2/178

1 施法中. 计算机辅助几何设计与非均匀有理B样条[M]. 北京:高等教育出版社, 2001: 306-454. SHIF Z. Computer Aided Geometric Design and Non-uniform Rational B-spline[M]. Beijing:Higher Education Press, 2001: 306 -454.
2 PIEGLL, TILLERM. The NURBS Book[M]. 2nd ed. Berlin: Springer, 1997: 289-311.DOI:10.1007/978-3-642-97385-7
3 韩旭里,刘圣军. 三次均匀B样条曲线的扩展[J]. 计算机辅助设计与图形学学报, 2003, 15(5): 576-578.DOI:10.1081/CEH-200044273 HANX L, LIUS J. An extension of the cubic uniform B-spline curve[J]. Journal of Computer-Aided Design & Computer Graphics, 2003, 15(5): 576-578. DOI:10.1081/CEH-200044273
4 吴晓勤.带形状参数的Bézier曲线[J]. 中国图像图形学报, 2006, 11(2): 269-274. WUX Q. Bézier curve with shape parameter[J]. Journal of Image and Graphics, 2006, 11(2): 269-274.
5 吴晓勤,韩旭里,罗善明. 四次Bézier曲线的2种不同扩展[J]. 工程图学学报, 2006, 27(5): 59-64.DOI:10.3969/j.issn.1003-0158.2006.05.011 WUX Q, HANX L, LUOS M. Two different extensions of quartic Bézier curve[J]. Journal of Engineering Graphics, 2006, 27(5): 59-64.DOI:10.3969/j.issn.1003-0158.2006.05.011
6 徐岗,汪国昭. 带局部形状参数的三次均匀B样条曲线的扩展[J]. 计算机研究与发展, 2007, 44(6): 1032-1037. DOI:10.1360/crad20070616 XUG, WANGG Z. Extensions of uniform cubic B-spline curve with local shape parameters[J]. Journal of Computer Research and Development, 2007, 44(6): 1032-1037. DOI:10.1360/crad20070616
7 刘华勇,李璐,张大明. 带形状参数的四次Ball曲线[J]. 山东大学学报(工学版), 2011, 41(2): 23-28. LIUH Y, LIL, ZHANGD M. Quadratic Ball curve with multiple shape parameters[J]. Journal of Shandong University (Engineering Science), 2011, 41(2): 23-28.
8 DELGADOJ, PEÑAJ M. A shape preserving representation with an evaluation algorithm of liner complexity[J]. Computer Aided Geometric Design, 2003, 20(1): 1-10.DOI:10.1016/S0167-8396(02)00190-5
9 DELGADOJ, PEÑAJ M. On efficient algorithms for polynomial evaluation in CAGD[J]. Monografías del Semintario Matemático García de Galdeano, 2004, 31(2): 111-120.
10 陈 杰,王国瑾. 一类带形状参数的 DP-NTP 曲线及 其应用[J]. 计算机辅助设计与图形学学报, 2011, 23(6): 1055-1060.DOI:10.1016/j.cageo.2010.07.006 CHENJ, WANGG J. A new type of DP-NTP curve with shape parameters and its application[J]. Journal of Computer-Aided Design & Computer Graphics, 2011, 23(6): 1055-1060.DOI:10.1016/j.cageo.2010.07.006
11 陈福来,吴晓勤,朱秀云. 广义三次DP曲线[J]. 计算机科学, 2012, 39(12): 264-267. CHENF L, WUX Q, ZHUX Y. Generalized cubic DP curve[J]. Computer Science, 2012, 39(12): 264-267.
12 陈福来,吴晓勤,朱秀云. 广义三次 DP 曲线的形状分析[J]. 电子设计工程, 2012, 20(12): 5-8. CHENF L, WUX Q, ZHUX Y. Shape analysis of generalized cubic DP curve[J]. Electronic Design Engineering, 2012, 20(12): 5-8.
13 彭兴璇,蒋新昕,谢宇迪. 一类带形状参数的三次DP 曲线[J]. 计算机辅助设计与图形学学报, 2018, 30(9): 1712-1718. DOI:10.3724/SP.J.1089.2018.16913 PENGX X, JIANGX X, XIEY D. A type of cubic DP curve with shape parameters[J]. Journal of Computer-Aided Design & Computer Graphics, 2018, 30(9): 1712-1718.DOI:10.3724/sp.j.1089.2018.16913
14 李军成,李兵,易叶青. 带参数的同次Ball曲线[J]. 中国图象图形学报, 2018, 23(6): 896-905. LIJ C, LIB, YIY Q. Ball curve of the same degree with a parameter[J]. Journal of Image and Graphics, 2018, 23(6): 896-905.
15 XUG,WANGG Z,CHENW Y. Geometric construction of energy-minimizing Bézier curves[J]. SCIENCE CHINA Information Sciences, 2011, 54(7): 1395-1406. DOI:10.1007/s11432-011-4294-8
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