曲面模型轉換三角網格模型之研究

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姓名

楊聿宏(Yu-hung Yang) 查詢紙本館藏

畢業系所

光機電工程研究所

論文名稱

曲面模型轉換三角網格模型之研究
(On the study of converting CAD models into Triangular models)

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摘要(中)

三角網格可以建構為各種型態之模型，因此被廣泛應用於CAD/CAM系統、電腦圖學、醫學影像、虛擬實境等領域。而在逆向工程與快速原型之應用中，將CAD模型轉換為網格模型為非常重要之技術。網格模型之建構必須在維持精度之前提下進行，否則轉換出之網格模型即無法精準表示原始CAD模型。減少三角網格數量亦為另一項重點，過多的三角網格數量將減低資料運算之效能。本論文提出精確且快速之精度控制方式，以及藉由四元樹資料結構作為曲面細分之輔助，以期確實減少三角網格數量。為建構水密且合理之網格模型，本論文提出以B-Rep資料結構輔助剪切曲面建立曲面邊界關連性，使由多片曲面構成之CAD模型經由三角網格化後，在原曲面接合處之網格皆能正確被建立，而避免破洞或自交等不合理情況發生，藉此建構出理想之網格模型。

摘要(英)

All types of the models could be structured by triangle meshes which have been widely used in CAD/CAM systems, computer graphics, medical images, Virtual Reality, etc. For applications of the reverse engineering and the rapid prototyping processes, the converting CAD models into triangular meshes is a very important technique. Keeping the accuracy is the prerequisite for the process of the model structuring, or the result triangular meshes can’t be indicated the original CAD model. Reducing the triangular mesh quantity of the model is another important procedure. Excess triangle meshes would make the efficiency of data programming be reduced. We provide an exactly and efficiently accurate controlling method and the surface subdivision method assisted by the quadtree data structure which would help to reduce the amounts of meshes. In order to structure the watertight and manifold triangular mesh, we provide the applications of the B-Rep data structure to help the trimmed NURBS surfaces establish the relationships of boundaries between surface and surface. When the CAD model structured by trimmed surfaces has been triangulated, the triangle meshes in the boundary connecting with neighbor surfaces would be structured exactly. The wrong cases such as holes or self-intersection would not be occurred. Therefore, the ideal polygon-based model has been structured.

關鍵字(中)

★ 逆向工程
★ 三角網格化
★ 網格產生
★ 四元樹
★ 弦長誤差值
★ 曲面偏差值
★ B-Rep資料結構

關鍵字(英)

★ Reverse Engineering
★ Triangulation
★ Mesh Generation
★ Quadtree
★ Chord Error
★ Surface Deviation
★ B-Rep Data Structure

論文目次

摘要 I
ABSTRACT II
致謝 III
目錄 V
圖目錄 VIII
表目錄 XI
第一章緒論 1
1.1 前言 1
1.2 文獻回顧 5
1.2.1 曲面之剪切與三角網格化 5
1.2.2 資料結構應用與參數對應 6
1.2.3 網格模型之邊界密合處理 7
1.3 研究目的與方法 8
1.3.1 研究目的 8
1.3.2 研究方法 9
1.4 論文架構 12
第二章　NURBS曲面之三角網格化 14
2.1 前言 14
2.2 曲線與曲面之數學模型概論 15
2.2.1 NURBS曲線之概論 15
2.2.2 NURBS曲面之概論 16
2.3 四元樹資料結構 20
2.3.1 樹狀結構之簡介 20
2.3.2 四元樹之簡介與應用 23
2.3.3 四元樹之程式資料類別 25
2.3.4 四元樹之建構流程與資料搜尋 27
2.3.4.1 四元樹建構流程暨前期之相鄰資料搜尋 28
2.3.4.2 後期之相鄰資料搜尋 31
2.4 曲面偏差值演算法 34
2.5 密鋪方塊三角網格建構法 39
2.6 範例分析與討論 41
第三章　剪切曲面之三角網格化 47
3.1 前言 47
3.2 剪切曲面之概論 49
3.3 剪切曲線多邊形化 52
3.3.1 曲線弦長誤差之概論 52
3.3.2 等分內插式弦長誤差演算法與折線之建構 55
3.3.3 逐點追跡式弦長誤差演算法與折線之建構 56
3.3.4 內插式與追跡式弦差演算法之比較與分析 56
3.4 空間域與參數域之數值映射及資料對應 60
3.5 剪切曲面之三角網格化流程 63
3.5.1 基底曲面與剪切曲線之處理 63
3.5.2 基底網格與剪切多邊形之合併處理 63
3.6範例分析與討論 68
第四章　多曲面模型轉換為網格模型之技術 75
4.1 前言 75
4.2 B-Rep資料結構 78
4.3 套用B-Rep資料結構之新三角網格化流程 82
4.4 範例分析與討論 85
第五章　範例實測與分析探討 89
5.1 前言 89
5.2 本研究之曲面網格化流程 89
5.3 商用軟體與本研究之範例測試比較 91
5.3.1 範例一：機車後照鏡 91
5.3.2 範例二：維納斯女神頭像 94
5.3.3 範例三：人體左手 99
5.3.4 範例四：人體右耳 99
5.3.5 範例五：巨石像 104
5.4 分析與討論 107
第六章　結論與未來展望 111
6.1 結論 111
6.2 未來展望 113
參考文獻 115

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指導教授

賴景義(Jing-yi Lai)

審核日期

2009-7-6

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