一类带三个形状参数的三角曲面

摘要/Abstract

摘要： 为在控制顶点固定的情况下，仍能够调整三角曲面的外形，三个形状参数被引入到多项式基函数中，从而得到一类新的三角曲面。这类三角曲面具有几何不变性、仿射不变性、凸包性、对称性、表示唯一性、角点插值性和角点切平面性等特点，是三角Bézier曲面的扩展。形状参数对曲面外形的影响直观可见，其中一个形状参数更是能够在修改曲面时保持边界不变。文中的几个数值实例展示了利用形状参数进行外形调整的方便有效，这表明新的表达方式对三角Bézier曲面而言是一种有力的补充。

关键词: 计算机辅助设计, 二元基函数, 三角曲面, 形状参数

Abstract: To adjust the triangular surface with the fixed control points,three shape parameters are brought into the bivariate polynomial basis functions,and a new class of triangular surface is constructed.The new surface has the properties of the geometric and affine invariability,convex hull,symmetry,unique presentation,interpolation at the corners as well as tangent plane at the endpoints,which is the extensions of the triangular Bézier surface.The obvious geometric significance of shape parameters is proposed.The new surface can adjust the shape by changing the value of shape parameters,even if when the boundaries are fixed.The obvious geometric significance of shape parameters is proposed.Several numerical examples show the efficiency for operation,which indicates that the new surface is a powerful supplement for triangular Bézier surface.

Key words: computer aided design, bivariate basis functions, triangular surface, shape parameter

中图分类号:

TP391.7

陈军. 一类带三个形状参数的三角曲面[J]. .

CHEN Jun. Class of triangular surface with three shape parameters[J]. .

参考文献

［1］FARIN G.Triangular Bernstein-Bézier patches［J］.Computer Aided Geometric Design,1986,3(2);83-127.
[2]FARIN G,PIPER B,WORSEY A.The octant of a sphere as a non-degenerate triangular Bézier patch［J］.Computer Aided Geometric Design,1987,4(4);329-332.
[3]HAHMANN S,BONNEAU G P.Polynomial surfaces interpolating arbitrary triangulations［J］.IEEE Transactions on Visualization and Computer Graphics,2003,9(1):99-109.
[4]FARIN G.Curves and surfaces for CAGD,a practical guide.［M］.5th ed.San Francisco,Cal.,USA;Morgan Kaufmann,2001.
[5]HAN Xuli.Cubic trigonometric polynomial curves with a shape parameter［J］.Computer Aided Geometric Design,2004,21(6);535-548.
[6]WU Hongyi,XIA Chenglin.Extensions of Bézier curves and surfaces with multiple shape parameters［J］.Journal of Computer-Aided Design & Computer Graphics,2005,17(12);2607-2612(in Chinese).［邬弘毅,夏成林.带多个形状参数的Bézier曲线与曲面的扩展［J］.计算机辅助设计与图形学学报,2005,17(12);2607-2612.］
[7]HAN Xi’an,MA Yichen,HUANG Xili.Shape modification of cubic quasi-Bézier curve［J］.Journal of Xi’an Jiaotong University,2007,41(8):903-906(in Chinse).［韩西安,马逸尘,黄希利.拟三次Bézier曲线的形状调整［J］.西安交通大学学报,2007,41(8):903-906.］
[8]HU Gang,LIU Zhe,QIN Xinqiang,et al.New extension of uniform cubic B spline curve with multiple local shape parameters［J］.Journal of Xi’an Jiaotong University,2008,42(10):1245-1249(in Chinese).［胡钢,刘哲,秦新强,等.带多局部形状参数的三次扩展均匀B样条曲线［J］.西安交通大学学报,2008,42(10):1245-1249.］
[9]CHEN Jie,WANG Guojin.A new type of the generalized Bézier curves［J］.Applied Mathematics;A Journal of Chinese Universities(Series B),2011,26(1);47-56.
[10]CHEN Jie,WANG Guojin.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(in Chinse).［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.］
[11]YAN Lanlan,LIANG Jiongfeng.An extension of the Bézier model［J］.Applied Mathematics and Computation,2011,218(6);2863-2879.
[12]HU Gang,QIN Xinqiang,HAN Xi’an,et al.Continuity conditions for cubic quasi-Bézier curves and surfaces［J］.Journal of Xi’an Jiaotong University,2010,44(11):46-50(in Chinse).［胡钢,秦新强,韩西安,等.拟三次Bézier曲线曲面的拼接技术［J］.西安交通大学学报,2010,44(11);46-50.］
[13]CAO Juan,WANG Guozhao.Extension of the cubic bernstein-Bézier surfaces over the triangular domain［J］.Journal of Computer-Aided Design & Computer Graphics,2006,18(9);1403-1407(in Chinese).［曹娟,汪国昭.三角域上三次Bernstein-Bézier参数曲面的扩展［J］.计算机辅助设计与图形学学报,2006,18(9);1403-1407.］
[14]WU Xiaoqin,HAN Xuli.Bézier triangular patch with a shape parameter［J］.Journal of Computer-Aided Design & Computer Graphics,2006,18(11);1735-1740(in Chinse).［吴晓勤,韩旭里.带有形状参数的Bézier三角曲面片［J］.计算机辅助设计与图形学学报,2006,18(11);1735-1740.］
[15]CAO Juan,WANG Guozhao.An extension of bernstein–Bézier surface over the triangular domain［J］.Progress in Natural Science,2007,17(3);352-357.
[16]LIU Zhi,TAN Jieqing,CHEN Xiaoyan.Cubic bézier triangular patch with shape parameters［J］.Journal of Computer Research and Development,2012,49(1);152-157(in Chinese).［刘植,檀结庆,陈晓彦.三角域上带形状参数的三次Bézier曲面［J］.计算机研究与发展,2012,49(1);152-157.］

[1]	王耀,王春香,周国勇,纪康辉,刘流,郝林文. 快速成型技术中分层算法的研究综述[J]. 计算机集成制造系统, 2021, 27(3): 828-841.
[2]	何援军. 国产CAD软件重启之路[J]. 计算机集成制造系统, 2021, 27(11): 3057-3075.
[3]	郑华栋,丛明,刘毅,董航,刘冬. 面向增材制造的机器人轨迹自动生成技术[J]. 计算机集成制造系统, 2018, 24(第4): 956-963.
[4]	徐昌鸿,张树生,黄波,李秀玲. 面向数控工艺重用的三维CAD模型局部结构检索[J]. 计算机集成制造系统, 2017, 23(第8期): 1652-1661.
[5]	胡钢,吉晓民,白晓波. 广义带多参Bézier-like曲面及其拼接条件[J]. 计算机集成制造系统, 2016, 22(第2期): 501-515.
[6]	张旭,张冉,张学昌. 基于辅助装置的多视点云精确配准方法[J]. 计算机集成制造系统, 2014, 20(5): 1029-.
[7]	孙长乐,宁大勇,熊伟,王海涛. 基于特征的工程领域CAD模型检索技术[J]. 计算机集成制造系统, 2014, 20(4): 747-.
[8]	孙宇航,黄运保+,陈立平. 基于启发式图匹配的模板形状搜索方法[J]. , 2013, 19(12): 0-0.
[9]	朱林森. 四坐标船模曲面对称加工集成制造系统[J]. , 2013, 19(12): 0-0.
[10]	成彬,张树生. 基于视图模型的产品设计信息重用检索系统[J]. 计算机集成制造系统, 2013, 19(08 ): 1975-1983.
[11]	陈成军,洪军,杨国庆. 基于三维CAD模型的复杂机械设备拆装智能诱导系统[J]. 计算机集成制造系统, 2013, 19(08 ): 2026-2035.
[12]	李鹏,张旭,马孜,陈余庆,胡英,刘传龙. 加工中心在线复合式检测定位技术[J]. 计算机集成制造系统, 2013, 19(07 ): 1595-1605.
[13]	程云勇,朱真真,李维亮,张定华. 面向叶片弯扭变形分析的测量采样方法[J]. 计算机集成制造系统, 2013, 19(06 ): 1329-1335.
[14]	王延平,李原,张杰. 三维CAD模型模块划分的蚁群聚类图分割方法[J]. 计算机集成制造系统, 2013, 19(05 ): 926-934.
[15]	段黎明1,2，王侃1,2，陈中1,2. 工业CT重建模型与原始CAD模型粗配准的改进[J]. , 2013, 19 (04 ): 0-0.