臺灣博碩士論文加值系統

本論文主要可分兩大部分，CAD系統幾何、拓樸核心之設計，以及在B-rep架構下拓樸運算之探討。
CAD系統幾何、拓樸核心之設計：
幾何與拓樸為CAD系統之核心，幾何是所有計算的重心，拓樸的發展帶給實體完整的定義，本論文將對此兩關係密切的核心進行初步的設計。
在B-rep架構下拓樸運算之探討：
對於實體運算，不採用布林運算之傳統方式，乃從拓樸的角度進行分析，將計算之重心由幾何轉至拓樸，進而完成實體邊界的表示。

There are two main goals included in the thesis: Design of geometry and topology kernel in CAD system and Method of topology operator on B-rep:
Design of geometry and topology kernel in CAD system:
Geometry and topology are the kernels of CAD system. Geometry includes many calculations, and topology gives the complete definition of solids. This thesis will implement the elementary design for the kernels of CAD system.
Method of topology operator on B-rep:
For calculation of solids, we don’t adopt Boolean Operator, we analyze the calculation from topology aspect, we put all calculations from geometry to topology, and complete the B-rep of solids.

第一章導論1
1-1.研究方向與動機1
1-2.文獻回顧2
1-3.各章摘要4
第二章軟體各模組之架構與發展流程6
2-1.前言6
2-2.各模組之架構6
2-3.軟體發展流程13
第三章座標系統之探討15
3-1.前言15
3-2.CARTESIAN座標系與HOMOGENEOUS座標系16
3-3.基本座標轉換18
3-4.綜合轉換應用21
3-5.二維與三維之轉換27
第四章實體模型系統之基本理論31
4-1.前言31
4-2.實體模型表示法32
4-3.幾何之元素架構37
4-4.拓樸之元素架構48
4-5.特徵庫54
第五章幾何交集之計算57
5-1.前言57
5-2.MAXMINTEST58
5-3.線與線的交集計算60
5-4.線與面的交集計算62
5-5.面與面的交集計算63
第六章B-REP下拓樸運算之探討69
6-1.前言69
6-2.交點的分類70
6-3.交線的分類73
6-4.交面的分類76
6-5.拓樸運算的步驟81
6-6.MERGE的法則82
6-7.資料的重建88
6-8.布林運算與拓樸運算之比較89
第七章軟體說明與介紹92
7-1.軟體介紹92
7-2.軟體操作之流程93
第八章回顧與展望99

[1] Christoph M. Hoffmann, “Geometric & Solid Modeling: An Introduction”, Morgan Kaufmann, San Mateo, California,1989.
[2] Michael E. Mortenson, “Geometric Modeling”, John Wiley & Sons, New York, Chichester, Brisbane, Toronto, Singapore, 1985.
[3] David F. Rogers, J. Alan Adams, “Mathematical Elements for Computer Graphics”, McGraw Hill International Editions(2th Edtion).
[4] Ibrahim Zeid, “CAD/CAM theory and practice”, New York, McGraw-Hill, 1991.
[5] Vera B. Anand, “Computer Graphics and Geometric Modeling for Engineers”, John Wiley & Sons, 1993.
[6] Mikell P. Groover, Emory W. Zimmers, Jr, “CAD/CAM : computer-aided design and manufacturing”, Prentice-Hall, Englewood Cliffs, N.J, 1984.
[7] Mary S. Pickett and John W. Boyse, “Solid modeling by computers :from theory to applications”, New York :Plenum Press,1984.
[8] Martti Mantyla, “An introduction to solid modeling”, Rockville, :Computer Science Press, 1988.
[9] Jami j. Shah and Martti Mantyla, “Parametric and Feature-Based CAD/CAM”, John Wiley and Sons, Inc. 1995.
[10] Tosiyasu L. Kunii (Ed.), “Modeling in Computer Graphics”, Tokyo, Japan, P.265-274(1991)
[11] Riesenfeld, R. F., “Application of B-Spline Approximation of Geometric Problems of Computer Aided Design, “ PhD dissertation, Syracuse Univ., Syracuse, NY, 1972. Also available as U. of Utah, UTEC-CSc-73-126, March 1973.
[12] J. C. Fiorot, P. Jeannin, “Rational Curves And Surfaces”, John Wiley & Sons, 1992.
[13] Jack L. Goldberg, ”Matrix Theory with Applications”McGraw-Hill, Inc. 1991.
[14] Allan J. Sieradski, “An Introduction to Topology and Homotopy”, PWS-KENT Publishing Company Boston, 1992.
[15] Robert C. Yates, “Analytic Geometry with Calculus”, Prentice Hall, 1961.