[1]刘雄伟,彭维,郑海波.边界表示的拓扑与几何一致性[J].华侨大学学报(自然科学版),2000,21(1):51-56.[doi:10.3969/j.issn.1000-5013.2000.01.011]
　Liu Xiongwei,Peng Wei,Zheng Haibo.The Consistency in Topology and Geometry of Boundary Representation[J].Journal of Huaqiao University(Natural Science),2000,21(1):51-56.[doi:10.3969/j.issn.1000-5013.2000.01.011]
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边界表示的拓扑与几何一致性()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第21卷
期数:
2000年第1期
页码:
51-56
栏目:
出版日期:
2000-01-20

文章信息/Info

Title:
The Consistency in Topology and Geometry of Boundary Representation
文章编号:
1000-5013(2000)01-0051-06
作者:
刘雄伟; 彭维; 郑海波
华侨大学机电工程系, 泉州362011; 西北工业大学CAD/CAM研究中心, 西安710072
Author(s):
Liu Xiongwei1;  Peng Wei2;  Zheng Haibo1
1.Dept. of Electromech. Eng., Huaqiao Univ., 362011, Quanzhou; 2.CAD/CAM Res. Cent., Northwest. Polytechn. Univ., 710072, Xian
关键词:
简单闭路理论;  欧拉公式;  Gauss-Bonnet定理;  边界表示;  角度超出量;  总曲率
Keywords:
simple closed path theory;  Euler′s formula;  Gauss Bonnet Theorem;  boundary representation;  angle excess;  total curvature
分类号:
O189.1
DOI:
10.3969/j.issn.1000-5013.2000.01.011
摘要:
闭路拓扑原理和欧拉公式是检验实体模型边界表示的拓扑与几何一致性的重要工具 .有关文献对此问题的论述不妥 .文中在总结前人研究工作的基础上,给出曲面上简单闭路总旋转角的精确定义,并以球面为例分析曲面上简单闭路总旋转角的计算方法,从而导出角度超出量的概念 .对多面体进行严格的定义,给出欧拉公式及 Gauss- Bonnet定理对多面体的应用条件 .最后给出多面体的广义欧拉特征值、广义 Gauss- Bonnet定理及广义欧拉公式 .这些理论和方法,共同构成实体模型边界表示的拓扑与几何一致性检验的有效工具 .
Abstract:
For inspecting topological and geometrical unanimity of a solid model,principle of closed path topology and Euler′s formula are important tools.On which the exposition of related literatures was inappropriate.Starting from the summation of predecessors′ studies,the authors put forward their theory and method to make up effective tool for its inspection.Firstly,a precise definition is given to the angle of resultant rotation of a simple closed path on a curved surface,and an analysis is made on its calculation with spherical surface as example,and thus a concept of angle excess is derived.Secondly,a strict definition is given to polyhedra,and the conditions are given for applying Euler′s formula and Gauss Bonnet Theorem to polyhedra.Finally,the generalized Euler eigenvalue and the generalized Gauss Bonnet Theorem and the generalized Euler′s formula are given to polyhedra.

参考文献/References:

[1] Mortenson M E. Geometric modeling:chapter 9--solid modeling fundamentals [M]. New York:John Wiley·Sons Inc, 1985.372-430.
[2] 欧阳春梅. 实体造型技术 [M]. 北京:国防工业出版社, 1991.28-89.
[3] 孙家广, 陈玉键, 辜凯宁. 计算机辅助几何造型技术 [M]. 北京:清华大学出版社, 1990.65-90.
[4] Armstrong M A, 孙以丰. 基础拓扑学 [M]. 北京:北京大学出版社, 1983.2-30.

备注/Memo

备注/Memo:
福建省自然科学基金资助项目
更新日期/Last Update: 2014-03-23