本研究主要目的為開發三維有限元素分析軟體中的三維實體建模及網格功能。本研究整合三維網格產生器TetGen之實作方法，並撰寫三維布林運算程式，提供整合軟體使用。

　　在程式實作上，使用Microsoft Visual Studio.Net 2003撰寫C++程式碼，將Hang Si開放原始碼給使用者的三維網格產生器TetGen，整合至以MFC開發的視窗圖形介面軟體中，使有限元素分析軟體擁有三維四面體網格化的功能。本研究參考幾何布林演算法，於視窗圖形介面軟體上提供三維幾何布林運算之程式，以補足電腦實體建模功能的齊全，與為連結布林運算及三維網格，配合網格產生器需求撰寫程式。

　　研究成果為完成有限元素軟體的三維幾何布林運算及四面體自動化網格等前處理功能。

　　The main goal of this research is to integrate three dimensional mesh generator, TetGen, into the developing of three dimensional finite element analysis software, to offer the computational geometry functionality for the software.

　　By using the C++ computer language on Microsoft Visual Studio.Net 2003, this research added three dimensional tetartohedral function to the MFC window graphic user interface software. On the window graphic user interface, this research refers to Boolean operations algorithm providing three dimensional Boolean operations codes, to complement the computational solid modeling, and combining three dimensional mesh generator with Boolean operations, to develop code for mesh generator.

　　The research result is to complete the pre-processing functions of three dimensional Boolean operations and tetartohedral auto-mesh of finite element software.

[1] L. P. Chew, Constrained Delaunay Triangulations. Algorithmica 4(1)：97-108, 1989.

[2] H. Edelsbrunner and T. S. Tan, An Upper Bound for Conforming Delaunay Triangulations. Discrete & Computational Geometry 10(2)：197-213, 1993.

[3] L. P. Chew, Guaranteed-Quality Triangular Meshes. Technical ReportTR-89-983, Department of Computer Science, Cornell University, 1989.

[4] L. P. Chew, Guaranteed-Quality Mesh Generation for Convex Surfaces. Proceedings of the Ninth Annual Symposium on Computational Geometry(San Diego, California), pages 274-280. Association for Computing Machinery, May 1993.

[5] J. Ruppert, A Delaunay Refinement Algorithm for Quality Two-Dimensional Mesh Generation. Journal of Algorithms 18(3):548-585,May 1995.

[6] G. L. Miller, D. Talmor, S. H. Teng, N. J. Walkington, A Delaunay Based Numerical Method for Three Dimensions: Generations, Formulation, and Partition. In “Proc. 27th Ann. ACM Sympos. Theory Comput,” 683-692,1995.

[7] J. R. Shewchuk, Delaunay Refinement Mesh Generation, Ph.D. thesis, School of Computer Science, Carnegie Mellon University, 1997. Available as Technical Report CMU-CS-97137.

[8] H. Edelsbrunner and D. Guoy, “An Experimental Study of Sliver Exudation,” Engineering with Computers (2002) 18: 229–240.

[9] Y. C. Lee and K. S. Fu, Integration of Solid Modeling and Data Base Management for CAD/CAM, IEEE Press Piscataway, NJ, USA, 1983.

[10] Y. D. Fougerolle, A. Gribok, S. Foufou, F. Truchetet, Member, IEEE, and M. A. Abidi, Member, IEEE, “Boolean Operations with Implicit and Parametric Representation of Primitives Using R-Functions,” IEEE Transactions on Visualization and Computer Graphics, Vol. 11, No. 5, September/October 2005.

[11] P. J. Schneider and D. H. Eberly, Geometric Tools for Computer Graphics Morgan Kaufmann Publishers ,2003.

[12] A. I. Said and D. Parker , “Design and Analysis of a New Point-in-Polyhedron Algorithm,” Department of Surveying, University of Newcastle-upon-Tyne.
[13] 張佑全,“整合電腦繪圖程式與Triangle網格產生器於有限元素程式”, 國立成功大學機械工程研究所碩士論文, 2005。

[14] M. W. Beall , An Object-Oriented Framework for the Reliable Automated Solution of Problems in Mathematical Physics, Eng. Comput. (Lond.) 15(1): 61-72, 1999.

[15] B. DolŠak, I. Bratko, and A. Jezernik, Knowledge base for finite-element mesh design learned by inductive logic programming, Cambridge University Press, 1998

[16] S. Farestam and R. Bruce Simpson, A Framework for Advancing Front Techniques of Finite Element Mesh Generation, Univ. of Waterloo, BIT 35(2):210–232, 1995, Tech. report CS-93-38, 1994.