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研究生:郭川竹
研究生(外文):Chuan-Chu Kuo
論文名稱:創新之組合方法於散亂點資料的模型重建與應用
論文名稱(外文):A novel combinatorial approach to surface reconstruction from unorganized points and its applications
指導教授:姚宏宗姚宏宗引用關係
指導教授(外文):Hong-Tzong Yau
學位類別:博士
校院名稱:國立中正大學
系所名稱:機械系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:176
中文關鍵詞:逆向工程CAD/CAM模型重建狄龍尼三角形火龍尼圖形區域成長STL模型
外文關鍵詞:reverse engineeringCAD/CAMsurface reconstructionDelaunay triangulationVoronoi diagramregion growingSTL model
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電腦幾何模型的建構通常是藉由電腦輔助設計(CAD)與逆向工程(RE)二種技術所產生。近年來,由於三維掃瞄硬體設備的快速發展,逆向工程的應用已經逐漸受到重視,尤其是在具複雜幾何造型之電腦幾何模型的建構上,更顯得其重要地位。一般而言,逆向工程包括物體表面數位化(Surface Digitizing)與模型重建(Surface Reconstruction)二項主要技術。物體表面數位化是指藉由接觸式探頭掃瞄機或非接觸式雷射掃瞄機,來掃瞄實際物體(黏土、木頭模型或工件)表面以擷取其點資料;而模型重建是指利用擷取的點資料建構出一個能夠代表原始物體的電腦幾何模型。本論文將專注於模型重建之問題的處理。
在逆向工程中,模型重建的主要困難點在於如何建構出一個具正確幾何與拓樸且與原來物體形狀相同的電腦模型。在本論文中,假設所處理的數位掃瞄資料除了具有三維的點座標以外,將不具任何其它可利用的幾何資訊。在這樣的假設條件下,此模型重建問題將變成”廣泛性的模型重建問題”。能夠處理此種問題的方法將能一致且單一的解決所有模型重建的問題。換句話說,僅需要一種能夠處理”廣泛的模型重建問題”的演算法,即可解決各式各樣的模型重建問題。此外,因為輸入掃瞄點資料的限制條件較少,這樣的演算法將有更廣泛的應用。
近年來,在電腦繪圖上皆依賴網格模型(Polygonal model)進行模擬與彩現(Rendering)等應用。此外,在生產製造上,網格模型亦受到相當的重視,特別是在快速原型製造(Rapid prototyping and manufacturing)與實體切削上,更是扮演主要角色。因此,在逆向工程與CAD/CAM領域的應用,網格模型已經變得愈來愈重要了。在所有網格模型的格式中,所謂的三角網格模型(Triangular mesh),或立體印刷模型(STL model)是邊界表達模型(B-rep model)中最簡單的一種。本論文將以”三角網格曲面”(Triangulated surface)來稱呼這種立體印刷模型;而此三角網格曲面亦將用來表達本論文所提出之模型重建演算法的輸出結果。
在本論文中,將提出一種新穎的組合方法來處理上述廣泛的模型重建問題。這種組合方法主要是以狄龍尼三角形(Delaunay triangulation)與火龍尼圖形(Voronoi diagram)二種著名的幾何結構為基礎。首先,本論文提出適應性雕刻演算法(Delaunay-based adaptive sculpturing algorithm, DBAS al-gorithm)來處理廣泛的模型重建問題。此演算法的輸出可以是網格實體模型,也可以是具邊界的網格曲面;其亦能夠處理點資料具有雜訊的問題,以及重建尖邊、尖角特徵與進行網格最佳化。接著,繼續提出一種所謂狄龍尼區域成長演算法(Greedy Delaunay-bBased region-growing algorithm, greedy DBRG algorithm)來彌補雕刻演算法之計算效率的不足。這種greedy DBRG演算法是繼承了以狄龍尼為基礎(Delaunay-based approach)與以區域成長為基礎(Region-growing approach)的二種演算法的優點,相當穩地且快速。只是這種greedy DBRG缺乏處理具雜訊點資料的能力,亦無法重建尖邊、尖角特徵與進行網格最佳化。因此,本論文最後結合DBAS演算法與greedy DBRG演算法二者的觀念,開發出以幾何組合結構為基礎的適應性DBRG演算法(Adaptive DBRG algorithm),能夠穩定且有效率的重建網格模型,並具有前述二種演算法的所有優點與能力。為了有效證明上述三種廣泛性模型重建演算法能夠從無順性掃瞄點資料中穩定且快速的重建網格模型,本論文提出並驗證了數種點資料模型的重建。實驗結果證明,此三種演算法具相當高的執行效率,並且與現存著名的演算法的效率不相上下。
就具複雜曲面之物件而言,其幾何設計上經常以B-rep的幾何模型來表示。然而,在快速原型製造或實體切削時,B-rep模型需要轉換為STL模型。但是因為B-rep模型本身拓樸或幾何的誤差與缺陷,經常造成轉換後之STL模型具有不正確的縫隙或網格重疊的現象,甚至產生網格法向量不一致的現象。本論文亦提出一種演算法來修正這種不正確的STL模型。此演算法應用了前述廣泛性模型重建的技術,以達到整體性縫補STL模型的效果。被縫補的STL模型可以是來自掃瞄實際物體的掃瞄點資料,亦可以是來自B-rep模型的轉換。本論文所提出具系統性的演算法能夠同時克服上述二種不同情況所產生的STL模型。經實驗結果顯示,此演算法能夠穩定且有效率的縫補具極複雜之幾何外型的STL模型。

A computer geometrical model can generally be created using computer-aided design (CAD) tools or reverse engineering (RE) techniques. However, due to the rapid development of 3D scanning technology, the RE approach has gained wide popularity especially for the model creation of complex sculptured objects. Re-verse engineering consists of two major processes, surface digitizing and surface reconstruction. The surface digitizing process is to acquire the dada set from a physical object, such as clay or wooden models or parts, by laser range scanners or contact probe digitizers. The surface reconstruction process is to reconstruct the shape of the object from the data set. This dissertation is focusing on the problem of surface reconstruction.
The major issue of surface reconstruction is how to generate a geometrical model with a correct topology and geometry that is faithful to the original object which is complex in shape. In this dissertation, the surface reconstruction is treated as a “general surface reconstruction problem” by assuming that the sam-ple points contain no additional information other than the three-dimensional co-ordinates. The approach to the general surface reconstruction problem is capable of unifying and governing various surface reconstruction algorithms. In other words, only with a general surface reconstruction algorithm, various surface re-construction problems can be readily solved. In addition, such approach also has more extensive applications since the input points have fewer restrictions.
Recently, numerous applications in computer graphics rely on the polygonal model for both simulation and display. Besides, in manufacturing production, the polygonal model has received serious attentions in recent years; especially it is playing a leading role in the rapid prototyping (RP) and the polygonal model ma-chining. Therefore, the polygonal model is becoming more and more important in the applications of RE and CAD/CAM. Among all the polygonal models, the triangular mesh, or more specifically, an STL (stereo-lithography) model, is the simplest one of B-Rep (Boundary-Representation) models. In the dissertation, the STL model is referred to as the “triangulated surface” model to represent the re-sult of the surface reconstruction.
In the dissertation, a combinatorial approach is proposed to solve the general surface reconstruction problem. Such combinatorial approach is based on both well-known geometrical structures, Delaunay triangulation and Voronoi diagram. With these both structures, a Delaunay-based adaptive sculpturing (DBAS) algo-rithm is proposed to reconstruct a complex surface from a set of unorganized points. The DBAS algorithm can not only reconstruct a surface with and without boundary, but also has the ability to deal with the tough problems such as sample points with noises, sharp feature retrieval, and mesh optimization. Furthermore, combining the Delaunay-based approach and the region-growing technique, a greedy Delaunay-based region-growing (DBRG) algorithm is proposed to en-hance the computation efficiency of the sculpturing algorithm. The greedy DBRG algorithm maintains the advantages of both Delaunay-based and region-growing approaches. Finally, integrating the DBAS algorithm and the greedy DBRG algo-rithm, an adaptive DBRG algorithm is proposed to robustly and efficiently recon-struct a complex surface from a set of unorganized points; and it really inherits all the advantages of the two above-mentioned algorithms. To validate the proposed DBAS, greedy DBRG, and adaptive DBRG algorithms, some detailed illustrations are given. Experimental results show that they are highly efficient compared with other existing algorithms.
In the design of complex parts involving free-form or sculptured surfaces, the design is usually represented by a B-Rep model. But in production involving rapid prototyping or solid machining, the B-Rep model is often converted to the popular STL model. Due to defects such as topological and geometric errors in the B-Rep model, the resulting STL model may contain gaps, overlaps, and in-consistent orientations. This dissertation also presents the extension of a surface reconstruction algorithm to the global stitching of STL models for rapid proto-typing and solid machining applications. The model to be stitched may come from the digitization of physical objects by 3D laser scanners, or the triangulation of trimmed surfaces of a B-Rep model. Systematic procedures have been developed for each of these two different but equally important cases. The result shows that the proposed method can robustly and effectively solve the global stitching prob-lem for very complex STL models.

Abstract (Chinese) i
Abstract (English) iv
Acknowledgements (Chinese) vii
List of Figures xii
List of Tables xvii
List of Symbols and Abbreviations xviii
Chapter 1: Introduction 1
1.1 Motivation ………………………………………………………….. 2
1.2 Problem statement ………………………………………………….. 2
1.3 Previous work ………………………………………………………. 5
1.3.1 Dealunay-based approach ……………………………………. 5
1.3.2 Region-growing approach ……………………………………. 9
1.3.3 Implicit surface approach ……………………………………. 11
1.3.4 Warping approach ……………………………………………. 13
1.3.5 Clustering approach ……………….…………………………. 14
1.4 Overview of proposed surface reconstruction algorithm …………... 15
1.5 Contributions ……………………………………………………….. 16
1.6 Dissertation organization …………………………………………… 17
Chapter 2: Geometrical Structures and Definitions 18
2.1 Convex hull ………………………………………………………… 18
2.2 Voronoi diagram and Delaunay triangulation ……………………… 19
2.3 Medial axis …………………………………………………………. 20
2.4 Pole ………………………………………………………………… 21
2.5 Local feature size …………………………………………………… 23
2.6 Sampling criterion — r-sample ……………………………………… 23
2.7 Skinnyness formula ………………………………………………… 25
2.8 Triangulated surface representation ………………………………... 25
Chapter 3: DBAS Algorithm 28
3.1 Geometrical definitions………………………………………….….. 28
3.1.1 Power diagram ……………………………………………….. 28
3.1.2 Labeling algorithm of Amenta et al. ………………………….. 29
3.2 Overview of DBAS algorithm ………………………….………….. 30
3.3 DBAS algorithm …………………………...……….………………. 33
3.3.1 Determination of outer concave poles …………………..……. 33
3.3.2 Sculpting of concave regions ……..…………………………... 37
3.4 Extension to Surface Reconstruction of Bordered Surfaces ………… 41
3.4.1 Extraction of resulting triangulated surface …………………… 41
3.5 General Discussion …………………………………………………... 44
3.5.1 Sampling requirement …………………………………………. 44
3.5.2 Non-uniform distribution ……….……………………………… 44
3.5.3 Sharp edges ……….……………………………………………. 47
3.6 Implementation and Experiments …….…………………………….... 47
3.7 Comparison ………………………………………………….……….. 52
3.7.1 Comparisons with the original crust algorithm ……..………….. 52
3.7.2 Comparisons with the power crust algorithm …………...……… 53
3.7.3 Comparisons with the co-cone algorithm …………..………….. 55
3.8 Summary ……..………………………………………………………. 58
Chapter 4: Greedy DBRG Algorithm 60
4.1 Overview of greedy DBRG algorithm ……………………………… 60
4.2 Greedy DBRG algorithm ………………………………………….. 63
4.2.1 Initializations …………………………………………………... 64
4.2.2 Region Growing ……………………………………………….. 68
4.2.3 Demonstrations ………………………………………………… 72
4.3 Open Surface Reconstruction ……………………………………….. 73
4.4 Small Holes Filling ………………………………………………….. 74
4.5 Circumradius of a Delaunay triangle ………………………………… 77
4.6 Treatment of Poor Data ……………………………………………… 79
4.6.1 Non-uniform distribution ……………………………………… 79
4.6.2 Sharp edges ……………………………………………………. 79
4.7 Implementation and Experiments …………………………………… 81
4.8 Summary …………………………………………………………….. 85
Chapter 5: Adaptive DBRG Algorithm 86
5.1 Overview of adaptive DBRG algorithm …………………………….… 86
5.2 Effects of poles ………..……………………………………………... 90
5.2.1 Sharp feature reconstruction …..……………………………….. 90
5.2.2 Mesh fairing …….………………………………………..……. 92
5.2.3 Noise filtering ……..…………………………………………… 94
5.3 Adaptive DBRG Algorithm ……………..……………………………. 97
5.3.1 Computing characteristic vertices and poles ……..…………… 98
5.3.2 Determining initial and candidate triangle ……...……………… 101
5.3.3 Demonstrations …...……………………………………………. 105
5.4 Implementation and Experiments …………………………………….. 108
5.5 Summary ……………………………………………………………… 111
Chapter 6: Extension of Surface Reconstruction Algorithm to the Global Stitching and Repairing of STL Models 113
6.1 Introduction …………………………………………………………… 113
6.2 Stitching of STL Model from Multiple Scan Data ……………………. 116
6.2.1 Registration of Multiple Scan Data Sets ………………………... 117
6.2.2 Removal of Overlapped Data Set ………………………………. 118
6.2.3 Reconstruction of an STL Solid Model from the Complete Data Set ………………………………………………………………. 119
6.3 Automatic Stitching of STL Model from Complex B-rep Surface Model …………………………………………………………………. 122
6.3.1 Digitization/Triangulation of Trimmed Surfaces ……………….. 124
6.3.2 Triangle Subdivision Using LFS Principle ……………………… 124
6.3.3 Reconstruction of the STL Solid Model from Scattered Triangle Vertices ………………………………………………………… 125
6.3.4 Triangle Reduction Based on Accuracy Constraint ……………… 127
6.4 Summary ………………………………………………………………. 129
Chapter 7: Conclusions and Future Development 131
7.1 Summary and contributions ……………………………………………. 131
7.2 Future development ……………………………………………………. 135
Bibliography 139
Resume (Chinese) 152
List of Publications 153

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