三角網格資料定位整合與平滑性補洞之研究

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許聖函(Shen-Han Shu) 查詢紙本館藏

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機械工程學系

論文名稱

三角網格資料定位整合與平滑性補洞之研究
(On the Development of Registration and Hole Filling for Triangular Meshes)

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摘要(中)

本研究的目的在發展關於定位搜尋的演算法以篩檢出網格的重疊資料，再將定位過程分成粗定位及精定位兩個層次，用疊代的方式以期能使兩筆資料越來越趨近密合，並且將定位完之重疊資料做刪減重複部份的工作，而整合成單一筆完整的三角網格模型，以做為整個逆向工程建構流程的前導。在掃描的過程中，常會發生各種原因而導致失去了部份掃描資料而使得三角網格模型產生了孔洞，導致資訊的喪失，為了讓實體得以展現本來的風貌，在補孔洞的過程中，除了以正確的網格拓樸關係將孔洞補齊外，補好的孔洞平滑性與接合處的平順也是不可忽略的課題，在本文中發展拓樸完整修補流程與曲面嵌合結合的孔洞修補演算法，並求得初始的補洞新增點，再應用局部的移動性最小平方法求得最終新增點，以再次調整網格頂點的位置。

摘要(英)

When an object is scanned from different views in reverse engineering, the coordinate systems are usually different. Registration is a process to find the coordinate transformation between the multiple sets of data sets that the data can be merged. The objective of this study was to develop an algorithm for the registration of multiple sets of scan data. The proposed algorithm included two stages, a rough registration stage and a fine registration stage. Iteration methods were proposed for each of the two stages. Once the data were merged, overlapping would happen and the overlapped data must be eliminated. An algorithm was also proposed for the removal of the overlapped data. Examples were presented to illustrate the overall process and the feasibility of the
proposed approach.
Hole-filling is a process to repair the holes of a triangular model with
additional meshes and to keep the accuracy of the topology and the
smoothness of the new meshes with the original meshes. We proposed a
hole-filling algorithm by fitting the vicinity vertices of the hole into a
B-spline surface and planned the new vertices on the u-v domain
corresponding to such a surface. The main advantage of such a method
was that the u-v domain, instead of a 3D plane conventionally used in
many approaches, can better be used to represent the shape of any curves
hole. The new vertices planned were thus distributed appropriately on the
entire hole. The points on the u-v domain can thus be mapped onto the
B-spline surface to yield the 3D vertices. Since the surface did not pass
through the boundary vertices of the hole completely, a modification
algorithm base on the local moving least squares (LMLS) method was
proposed to modify the 3D vertices. A detail discussion of the entire
algorithm was described in this paper. Successful examples were
presented also to illustrate the feasibility of the proposed method.

關鍵字(中)

★ 定位
★ 資料整合
★ 補洞
★ 三角網格
★ 平滑
★ 移動性最小平方

關鍵字(英)

★ Smooth
★ Moving Least Squares
★ Merge Hole Filling
★ Triangular Meshes
★ Registration

論文目次

目錄
摘要.....................................................................I
英文摘要.................................................................II
致謝.....................................................................IV
目錄.....................................................................V
圖目錄.................................................................. VIII
第一章緒論..............................................................1
1.1 前言............................................................1
1.2 文獻回顧........................................................2
1.3 研究目的與方法..................................................7
1.4 論文架構........................................................11
第二章搜尋演算法........................................................12
2.1 前言.................................................................12
2.2 點群資料搜尋.........................................................12
2.3 線段資料搜尋.........................................................17
2.4 三角網格資料搜尋.....................................................18
2.4.1點搜尋對應網格.............................................20
2.4.2網格搜尋對應網格...........................................26
第三章網格資料定位整合..................................................30
3.1 前言.................................................................30
3.2 奇異值矩陣分解法.....................................................30
3.3 利用SVD求旋轉矩陣與平移矩陣..........................................31
3.4 初始定位.............................................................34
3.5 粗定位...............................................................34
3.6 精定位...............................................................38
3.7 網格資料重新整合.....................................................43
3.8 定位結果分析.........................................................46
3.9 結論.................................................................47
第四章平滑性孔洞修補....................................................53
4.1 前言.................................................................52
4.2 孔洞定義.............................................................55
4.3 映射三維頂點到二維空間...............................................59
4.4 孔洞點判斷...........................................................62
4.5 孔洞分割.............................................................64
4.6 孔洞點成長...........................................................68
4.7 網格自交判斷.........................................................70
4.8 二維空間映射回三維空間...............................................73
4.8.1 移動性最小平方法...................................................74
4.8.2 局部移動性最小平方法...............................................76
4.9 補洞結果分析.........................................................81
4.10 結論................................................................82
第五章結論與未來展望....................................................87
5.1 結論.................................................................87
5.2 未來展望.............................................................88
參考文獻.................................................................91

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指導教授

賴景義(Jiing-Yih Lai)

審核日期

2005-7-11

推文