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

林冠元(Kuan-Yuan Lin)

指導教授 ： 賴景義

國立中央大學/工學院/機械工程學系/博士(2011年)

摘要

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。

關鍵字

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

並列摘要

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.

並列關鍵字

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

參考文獻

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