李彩云
Associate Professor Supervisor of Master's Candidates
Gender:Female
Alma Mater:大连理工大学
Degree:Doctoral Degree
School/Department:大连理工大学莱斯特国际学院
Discipline:Computational Mathematics
Business Address:盘锦校区C08-304-3
E-Mail:caiyun@dlut.edu.cn
Hits:
Indexed by:期刊论文
Date of Publication:2016-04-16
Journal:中国图象图形学报
Included Journals:PKU、ISTIC、CSCD
Volume:21
Issue:4
Page Number:527-531
ISSN No.:1006-8961
Key Words:可展曲面;直纹面;Frenet标架;曲率线
Abstract:目的 曲率线在微分几何中起着非常重要的作用,它在曲面分析中是一个很有用的工具.可展曲面是曲面造型中最简单也最常用的一类曲面,目前大部分工作都是研究在给定曲面上寻找或者计算曲率线,而其反问题研究工作较少,为此,提出一种插值曲率线的可展曲面构造方法,并进一步将它应用到曲面造型中.方法 利用Frenet标架表示直纹面的母线,根据曲线为曲面曲率线以及曲面可展的充要条件,得到直纹面的母线需要满足的关系式.并引入控制函数控制曲面的形状.结果 给出了以给定曲线为曲率线的直纹面可展的具体表达式,根据可展曲面分类分析了设计曲面为柱面、锥面和空间曲线切线面的充要条件,并给出了两个代表性的实例验证该方法的有效性,实例结果表明,该方法不仅适用于一般参数曲线,对分段参数曲线也是有效的.结论 利用构造性的方法给出了插值曲率线的可展曲面的具体表达形式,并通过具体实例验证了该方法的有效性.
李彩云，女，1984年生，大连理工大学数学科学学院副教授，硕士生导师，主要从事计算几何与计算机辅助设计方向的研究工作，内容涉多元样条、曲线曲面造型的理论和应用研究等。到目前为止，在国内外重要期刊发表论文20余篇,主持1项国家自然科学基金青年基金项目，参加了包括2项国家自然科学基金面上项目在内的多个科研与教学项目建设。2017年入选大连理工大学第四届“星海骨干”人才培育计划。近年发表部分论文如下：
[1] 朱春钢, 李彩云, 王仁宏，异度隐函数样条曲线曲面, 计算机辅助设计与图形学学报, 2009, 21(7), 930-935.
[2] C.Y. Li, C.G. Zhu, A multilevel univariate cubic spline quasi-interpolation and application to numerical integration, Mathematical Methods in the Applied Sciences, 2010, 33(13), 1578-1586.
[3] 李彩云, 朱春钢, 王仁宏, 参数曲线的分段近似隐式化, 高校应用数学学报, 2010, 25(2), 202-210.
[4] C.Y. Li, R.H. Wang, C.G. Zhu, Designing and G^1 connection of developable surfaces through Bézier geodesics, Applied Mathematics and Computation, 2011, 218(7), 3199-3208.
[5] C.Y. Li, R.H. Wang, C.G. Zhu, Parametric representation of a surface pencil with a common spatial line of curvature, Computer-Aided Design, 2011, 43(9) , 1110-1117.
[6] H.Y. Liu, C.G. Zhu, C.Y. Li, Constructing N-sided toric surface patches from boundary curves, Journal of Information and Computational Science, March, 2012, 9(3), 737-743.
[7] C.Y. Li, R.H. Wang, C.G. Zhu, Designing approximation minimal surfaces with geodesics, Applied Mathematical Modelling, 2013, 37 (9), 6415-6424.
[8] C.Y. Li, R.H. Wang, C.G. Zhu, An approach for designing a developable surface through a given line of curvature, Computer-Aided Design, 2013, 45 (3) , 621-627.
[9] C.Y. Li, R.H. Wang, C.G. Zhu, A generalization of surface family with common line of curvature, Applied Mathematics and Computation, May, 2013, 219 (17), 9500-9507.
[10] Cai-Yun Li; Chun-Gang Zhu*; Ren-Hong Wang, Spacelike developable surfaces through a common line of curvature in Minkowski 3-space, Journal of Advanced Mechanical Design, Systems, and Manufacturing, 2015, 9(4), JAMDSM0050.
[11] 李彩云, 朱春钢, 王仁宏, 插值特殊曲线的曲面造型研究, 中国科学：数学，“庆贺徐利治教授95华诞专辑”，2015，45(9)，1441-1456.
[12] 李彩云, 项昕，朱春钢，一种插值曲率线的直纹面可展设计方法, 中国图像图形学报, 2016, 21(4), 527-531。
[13] 王慧，朱春钢，李彩云, 六次PH曲线G2 Hermite插值, 图学学报, 2016, 37 (2), 155-165.
[14] LI Cai-yun, ZHU Chun-gang, The classification of bi-quintic parametric polynomial minimal surfaces, Appl. Math. J. Chinese Univ, 2017, 32(1), 14-26.
[15] Cai-Yun Li*, Chun-Gang Zhu, G1 continuity of four pieces of developable surfaces with Bezier boundaries, Journal of Computational and Applied Mathematics, 2018, 329, 280-293.
[16] Hui Wang, Chungang Zhu*, Caiyun Li, Identication and Hermite interpolation of planar sextic Pythagorean-hodograph curves, Journal of Mathematical Research with Applications. 2017, 37(1), 59-72.
[17] 王慧，朱春钢，李彩云，插值有理Bezier渐近四边形的有理Bezier曲面，计算机辅助几何设计与图与形学学报，2017, 29(8), 1497-1504.
[18] Hui Wang, Chun-Gang Zhu*, Cai-Yun Li, The design of Bezeir surface through quintic Bezier asymptotic quadrilateral, Journal of Computational Mathematics, 37(5)(2019),723-740.
[19] Cai-Yun Li, Chungang Zhu*, Designing Developable C-Bézier Surface with Shape Parameters, Mathematics, 8, 402 (2020), doi:10.3390/math8030402.
[20] Caiyun Li, Chungang Zhu*, Construction of the spacelike constant angle surface family in Minkowski 3-space, AIMS Mathematics, 2020,5(6): 6341-6354.
[21] Wei Meng,Caiyun Li*, Qianqian Liu, Geometric Modeling of C-Bezier curve and surface with shape parameters, Mathematics, 2021, 9, 2651, https://doi.org/10.3390/math9212651.
