大量點資料建構B-spline曲線及曲面之逆向工程技術發展

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林冠元(Kuan-Yuan Lin) 查詢紙本館藏

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論文名稱

大量點資料建構B-spline曲線及曲面之逆向工程技術發展
(Development of B-spline Curves and Surfaces Reconstruction Techniques for Massive Point Data in Reverse Engineering)

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摘要(中)

在產品開發過程中，逆向工程一直扮演著重要角色，而所謂逆向工程係指由產品實體取得數位化曲面模型的流程方法。過程中，除了必須透過許多技術的實施與整合，往往也因為經驗導向的緣故，需要耗費大量的時間與人力，才能獲得理想的曲面模型結果。為了改善這樣的狀況，有效提升逆向曲面重建的效率與品質，本研究乃主要針對曲面自動化重建的議題，提出可能的解決方案，其中的主要特點在於：有別於過去常見的曲面自動化重建方法，乃僅以網格資料為輸入的型式，本研究另外加入了邊界輪廓曲線群為網格孔洞拘束的輸入條件，不但能節省過去需就量測網格資料完整修補所耗費的人力與時間外，亦可有效改善曲面建構品質，以落實高效率、高品質的逆向曲面重建目標。而針對自動化的曲面建構目標，本研究乃發展出特定的點、網格、曲線與曲面演算法，再加以適當串連、整合後，方能加以有效實現。除此之外，相關的曲線演算法亦延伸應用在電腦輔助製造領域的路徑轉換、插補技術方面。
具體而言，本研究所發展的各項技術可條列說明如下：(1)具誤差限制之曲線嵌方法，係考慮精度、平順性與邊界連續性條件之外，並加入容許誤差條件，以實現曲線自動化建構目標；(2)NC路徑轉換方法，係轉換大量直線插補指令為少量B-spline曲線指令，以輔助高速高精加工目標的實現；(3)曲線路徑插補方法，能在滿足弦長誤差、速度、加速度與急衝度的前提下，規劃出適當插補路徑，以實現高速高精加工目標；(4)曲面貼覆點群方法，係結合初始曲面建構與曲面變形演算法的技術，並以攤平概念求得較理想的參數初始值，可兼具較佳的運算效率與曲面品質；(5)三角網格群轉B-spline曲面之自動化方法，乃參考三角網格與邊界輪廓曲線的限制，可快速、自動產生相鄰曲面邊界具G1連續性的曲面群組，能大幅提升曲面重建的效率。

摘要(英)

Reverse engineering is a process of acquiring the sirface model from the digitized points of a physical part. It usually plays an important role on the development of new products. In addition to the implementation and integration of plenty of skills, a reverse engineering process always needs considerable time and efforts for generating satisfactory surface models as it is experience-oriented. In this study, we propose an automatic surface reconstruction method to deal with the above- mentioned problem, which can improve both the efficiency and quality of the reconstructed surfaces. Its main characteristic is as follows: different from the common methods where only a set of triangle meshes is used as the input, a set of boundary contours/curves are added for constraining the internal of external boundary of the final shape. It not only can save the efforts required for the pre-processing of the original meshes, but also can improve the surface quality and the efficiency of the entire process. For the task of automatic surface reconstruction, some specific algorithms for processing points, meshes, curves and surfaces are provided first. An intact process integrating all the related algorithms is then introduced in detail. In addition, the related algorithms for curves are further applied in computer-aided manufacturing for automatic generation of Nurbs-based NC paths from linear and circular NC paths.
Concretely speaking, the techniques developed in this study can be listed as follows: (1) An error-bounded curve fitting method is proposed to realize the goal of automatic curve construction. It not only takes the minimization of the sum of squared deviations, the strain energy minimization and the boundary continuity constraints into consideration, but also utilizes the allowed maximum and root-mean-square errors as extra constraints; (2) A method of NC code conversion is proposed for indirectly achieving the high-speed and high-precision machining under low-cost conditions. It can transform a plenty of conventional G01 codes into the less G-codes of B-spline curves; (3) A NURBS interpolator is proposed for effectively realizing the aim of high-speed and high-precision machining. It can generate sampled points on curves appropriately to meet the confined chord error, feedrate, acceleration and jerk; (4) A surface warping method is proposed for providing high-efficiency computing and suitable surface quality. It was composed of the creation of a specific initial surface and the shape-modifying operations; (5) An automatic surface reconstruction method with extra constrained boundary contours is proposed for dramatically reducing the time spent for surface reconstruction in practice. It can automatically generate a set of surface patches with G1 continuity across the shared boundaries in an efficient way according to a triangle mesh and extra boundary curves.

關鍵字(中)

★ 自動化曲面重建
★ 曲面貼覆
★ 曲線插補
★ 加工路徑轉換
★ 具誤差限制的曲線擬合

關鍵字(英)

★ Automatic surface reconstruction
★ Surface warping
★ NURBS interpolator
★ NC paths conversion
★ Error-bounded curve fitting

論文目次

摘要................................................................................... I
ABSTRACT.....................................................................II
致謝................................................................................ IV
目錄..................................................................................V
圖目錄.............................................................................IX
表目錄..........................................................................XIV
第 1章緒論....................................................................1
1-1 前言..............................................................................1
1-1-1 逆向工程技術.......................................................4
1-1-2 電腦輔助製造技術.............................................. 11
1-1-3 相關技術發展現況..............................................15
1-2 文獻回顧....................................................................16
1-3 研究目的與方法.........................................................26
1-4 論文架構....................................................................39
第 2章具誤差限制之曲線嵌合方法..........................40
2-1 前言............................................................................40
2-2 方法概要....................................................................41
2-3 初始曲線預估.............................................................44
2-4 點資料參數化.............................................................49
2-4-1 參數值初始化-弦長法........................................49
2-4-2 參數值最佳化-牛頓法........................................49
2-5 控制點位置最佳化.....................................................51
2-5-1 B-spline 曲線模型................................................52
2-5-2 PDM 嵌合............................................................52
2-5-2-1曲線一般性嵌合.......................................................52
2-5-2-2曲線平滑性嵌合.......................................................54
2-5-2-3曲線邊界拘束性嵌合................................................58
2-5-3 SDM 貼覆............................................................66
2-5-3-1曲線一般性貼覆.......................................................66
2-5-3-2曲線平滑性貼覆.......................................................72
2-5-3-3曲線邊界拘束性貼覆................................................75
2-6 控制點分佈與數量調整.............................................77
2-6-1 曲線節點新增.....................................................77
2-6-2 曲線節點移除.....................................................80
2-7 範例討論....................................................................83
2-8 結論............................................................................94
第 3章NC曲線路徑轉換與插補方法........................95
3-1 前言............................................................................95
3-2 方法概要....................................................................96
3-3 NC 路徑轉換方法.......................................................100
3-3-1 路徑點擷取.......................................................100
3-3-2 點資料處理.......................................................104
3-3-2-1雜訊濾除.................................................................104
3-3-2-2點群分段.................................................................105
3-3-3 曲線路徑產生...................................................108
3-3-3-1路徑點嵌合曲線.....................................................114
3-3-3-2曲線裁斷.................................................................115
3-3-4 曲線 NC 編碼.................................................... 117
3-4 曲線路徑插補方法...................................................123
3-4-1 插補點計算.......................................................123
3-4-1-1一般的計算方法.....................................................123
3-4-1-2修正後的計算方法..................................................124
3-4-2 預視機制階段...................................................130
3-4-3 即時打點階段...................................................138
3-4-4 多曲線插補.......................................................140
3-4-4-1決定預視的曲線數量..............................................140
3-4-4-2斜率不連續的接合條件..........................................141
3-4-4-3曲率不連續的接合條件..........................................142
3-4-4-4短節點區間的影響與處理......................................143
3-5 範例討論..................................................................149
3-5-1 實例-NC 路徑轉換............................................149
3-5-2 實例-曲線路徑插補..........................................159
3-6 結論..........................................................................173
第 4章曲面貼覆點群方法........................................174
4-1 前言..........................................................................174
4-2 方法概要..................................................................174
4-3 初始曲面建構...........................................................177
4-3-1 平面...................................................................177
4-3-2 昆氏曲面...........................................................178
4-3-3 Bicubic 昆氏曲面...............................................179
4-3-4 舉升曲面...........................................................182
4-3-5 掃掠曲面...........................................................188
4-3-6 編織曲面...........................................................205
4-4 點資料參數化........................................................... 211
4-4-1 參數值初始化-調和映射法............................... 211
4-4-2 參數值最佳化-牛頓法......................................215
4-5 控制點位置最佳化...................................................217
4-5-1 PDM 貼覆..........................................................217
4-5-2 SDM 貼覆..........................................................220
4-6 邊界拘束性條件.......................................................231
4-7 控制點分佈與數量調整...........................................233
4-8 範例討論..................................................................234
4-9 結論..........................................................................258
第 5章三角網格群轉B-spline曲面之自動化方法.259
5-1 前言..........................................................................259
5-2 方法概要..................................................................262
5-3 四邊曲線網絡規劃...................................................265
5-3-1 具邊界輪廓拘束之自動規劃............................265
5-3-1-1四邊網絡外形的產生..............................................265
5-3-1-2網格細線點群與曲線群的建構..............................270
5-3-2 手動規劃...........................................................280
5-3-2-1架構曲線與曲面法向曲線的建構..........................280
5-3-2-2網格細線點的產生..................................................281
5-4 網格分割暨曲面拓璞資訊建立...............................284
5-4-1 網格細分...........................................................290
5-4-2 區域成長...........................................................294
5-5 曲面建構..................................................................295
5-6 範例討論..................................................................301
5-7 結論..........................................................................324
第 6章結論與未來展望............................................325
6-1 結論..........................................................................325
6-2 未來展望..................................................................329
參考文獻.......................................................................332
林冠元個人簡歷..........................................................341

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指導教授

賴景義(Jiing-Yih Lai)

審核日期

2011-7-8

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