三角網格模型之平滑化研究

對於複雜幾何外型或細微特徵的物體，曲面模型往往無法快速、精確的表達，以三角網格來表達實物模型是一個直接、簡單的方式。由於具有完整的拓樸結構與計算簡單的優點，因此受到許多工業界的重視。三角網格模型在電腦圖學、有限元素分析、快速原型製作、逆向工程、CAD/CAM等領域中受到廣泛的應用，STL為常見的檔案交換格式。在逆向工程中，大部分的網格模型都透過各種雷射掃描設備擷取表面的點資料得到，由於環境或儀器精度等因素，網格在建立之後時常會產生許多雜訊而增加後續曲面建構的處理困難度，因此網格的前處理有其必要性。本研究利用RevCAD逆向工程軟體之網格平滑化功能測試、探討軟體的應用性，並利用其他平滑化方法加以作比較。最終目的為探討平滑化流程及改善網格的品質。

關鍵字

保留特徵；非等向性；三角網格平滑化；網格品質

並列摘要

The surface model is generally unable to describe complicated geometric shape or tiny feature object quickly and exactly. The triangular model is an alternative to express it in a direct and simple method. Because of the complete topology structure and simple computation, the triangular model plays an important role in industrial application. It also used wildly in computer graphics, finite element analysis, rapid prototyping, reverse engineering, and CAD/CAM field, the STL format is a common file exchange format. In reverse engineering, most of triangular models are generated from various laser scanner by collecting points from the model surface, however, because of environment or equipment precision, noise is produced which increases the difficulties in follow-up reverse procedure. Therefore, a pre-processing of the meshes is very important. This study employs mesh smoothing function in a reverse engineering software to test and evaluate its applications and employs other mesh smoothing methods to compare each other. The smoothing procedure and the method to improve mesh quality are discussed, too.

並列關鍵字

mesh quality ； feature preserve ； anisotropic ； triangular mesh smoothing

參考文獻

[1]G. Taubin, “A Signal Processing Approach to Fair Surface Design”, Proceedings of ACM SIGGRAPH 1995, pp. 351-358, 1995.

[2]M. Desbrun, M. Meyer, P. Schröder and A.Barr, “Implicit Fairing of Irregular Meshes Using Diffusion and Curvature Flow”, Proceedings of ACM SIGGRAPH 1999, pp. 317-324, 1999.

[3]M. Meyer, M. Desbrun, P. Schroder and A. H. Barr, “Discrete Differential-Geometry Operators for Triangulated 2-Manifolds”, Visualization and Mathematics III, pp. 35-57, 2002.

[4]H. Yagou, Y. Ohtake and A. Belyaev, “Mesh Smoothing via Mean and Median Filtering Applied to Face Normals”, Proceedings of Geometric Modeling and Processing, pp. 124-131, 2002.

[6]S. Fleishman, I. Drori and D. Cohen-Or, “Bilateral Mesh Denoising”, Proceedings of ACM SIGGRAPH 2003, pp. 950-953, 2003.

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三角網格模型之平滑化研究

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