在電腦輔助工程(Computer aided engineering)分析中，需要將CAD模型轉換成實體網格(Solid mesh)，提供求解器(Solver)進行計算，與傳統四面體網格相比，六面體網格被認為是品質最佳的網格類型，但人工構建過程耗時耗力且難以保證一致性。在建構六面體網格前需生成四邊形表面網格，因此本實驗室進行四邊形網格自動建構技術之開發，但該技術中仍有些許問題及可改進的空間。網格相交是自動建構四邊形網格的一大挑戰，該狀況會導致網格建構失敗，本研究針對各種可能的相交情形，設計了檢測和處理方法，確保網格正確無誤地建構。另外，本研究開發了一套品質計算方法，包含最小角度、展弦比、長寬比及平行偏差指標，用於評估整體網格之品質，也讓使用者能偵測品質不佳的網格並進行改善。本研究運用上述方法對建構技術的參數進行測試，比較各參數建構後之網格品質，以求得最佳參數。另外本研究也對建構完成的網格進行品質改善，透過多種方法進行改良，測試的六個案例中，最小內角及最差1%角度平均值均有顯著的提升。各案例中最小內角的數值最少有30.73°的提升，而各案例中最差1%角度平均值則提升89.7%至140.8%不等，證明本研究可有效提升整體網格之品質。

In computer aided engineering analysis, it is necessary to convert CAD models into solid meshes to provide solvers for computation. Compared to traditional tetrahedral meshes, hexahedral meshes are considered the best type. However, the manual construction process is long and laborious, and it is difficult to ensure consistency. Before constructing hexahedral meshes, it is necessary to generate quadrilateral surface meshes. Therefore, our laboratory is developing an automatic construction technique for quadrilateral meshes, but there are still some problems and room for improvement in this technique. Mesh intersection is a major challenge in automatically constructing quadrilateral meshes, which can lead to mesh generation failure or even program crashes. This study designed detection and processing methods for various possible intersection situations to ensure that meshes are generated correctly. Additionally, this study developed a set of quality calculation methods, including minimum angle, aspect ratio, edge ratio, and Parallel Deviation. This method evaluate the overall mesh quality and allow users to detect and improve poor-quality meshes. This study tested the construction technique's parameters using the above methods, comparing the mesh quality after construction with different parameters to obtain the optimal parameters. Furthermore, this study also improved the quality of the constructed meshes through various methods. Among the six test cases, the minimum angle and the average of the worst 1% angle showed significant improvements. The minimum angle increased by at least 30.73 degrees, and the average of the worst 1% angle improved by 89.7% to 140.8%, depending on the cases, proving that this study can effectively enhance the overall mesh quality.

參考文獻
[1]T. D. Blacker and M. B. Stephenson, "Paving: a new approach to automated quadratic mesh generation," International Journal for Numerical Methods in Engineering, Vol. 32, No. 4, pp. 811-847, 1991.
[2]D. R. White and P. Kinney, "Redesign of the paving algorithm: robustness enhancements through element by element meshing," Proceedings of the 6th International Meshing Roundtable, Park City, United States, Oct. 13-15, 1997.
[3]L. M. Tenkes, "Methods for generating quad-dominant and hex-dominant adaptive meshes for CFD applications," Institut Polytechnique de Paris, Master thesis, 2022.
[4]D. Bommes, B. Lévy, N. Pietroni, E. Puppo, C. Silva, M. Tarini and D. Zorin, "State of the art in quad meshing," 33rd Annual Conference of the European Association for Computer Graphics, May 13-18, 2012.
[5]P. M. Knupp, "Algebraic mesh quality metrics," Society for Industrial and Applied Mathematics Journal on Scientific Computing, Vol. 23, pp. 193-218, 2001.
[6]P. M. Knupp, "Algebraic mesh quality metrics for unstructured initial meshes," Finite Elements in Analysis and Design, Vol. 39, No. 3, pp. 217-241, 2003.
[7]R. V. Garimella, M. J. Shashkov and P. M. Knupp, "Triangular and quadrilateral surface mesh quality optimization using local parametrization," Computer Methods in Applied Mechanics and Engineering, Vol. 193, No. 9, pp. 913-928, 2004.
[8]L. F. Diachin, P. Knupp, T. Munson and S. Shontz, "A comparison of two optimization methods for mesh quality improvement," Engineering with Computers, Vol. 22, No. 2, pp. 61-74, 2006.
[9]M. S. Joun and M. C. Lee, "Quadrilateral finite-element generation and mesh quality control for metal forming simulation," International journal for numerical methods in engineering, Vol. 40, No. 21, pp. 4059-4075, 1997.
[10]H. Yagou, Y. Ohtake and A. Belyaev, "Mesh smoothing via mean and median filtering applied to face normals," Geometric Modeling and Processing. Theory and Applications, Wako, Japan, Jul. 10-12, 2002.
[11]J. Y. Lai, P. Putrayudanto, D. H. Chen, J. H. Huang, P. P. Song and Y. C. Tsai, "An enhanced paving algorithm for automatic quadratic generation of IC CAD models," The 9th IEEE International Conference on Applied System Innovation, Tokyo, Japan, Apr. 21-25, 2023.
[12]J. Y. Lai, P. Putrayudanto and Q. Wang, "Development of automatic quadratic meshing technique with unequal spreading intervals on outer and inner contours for IC CAD models," The 10th International Conference on Applied System Innovation, Kyoto, Japan, Apr. 17-21, 2024.
[13]X. Zhou, S. Sutulo and C. G. Soares, "A paving algorithm for dynamic generation of quadrilateral meshes for online numerical simulation of ship maneuvering in shallow water," Ocean Engineering, Vol. 122, pp. 10-21, 2016.
[14]ANSYS Mesh Metrics Explained. Available: https://featips.com/2022/11/2-1/ansys-mesh-metrics-explained/. [Accessed May 23, 2024]
[15]B. J. E. van Rens, D. Brokken, W. A. M. Brekelmans and F.P.T. Baaijens, "A two-dimensional paving mesh generator for triangles with controllable aspect ratio and quadrilaterals with high quality," Engineering with Computers, Vol. 14, No. 3, pp. 248-259, 1998.
[16]P. M. Knupp, "Achieving finite element mesh quality via optimization of the jacobian matrix norm and associated quantities. part I—a framework for surface mesh optimization," International Journal for Numerical Methods in Engineering, Vol. 48, No. 3, pp. 401-420, 2000.
[17]陳定輝，「應用於非結構化四邊形網格建構之輪廓撒點與網格品質改善技術發展」，國立中央大學碩士論文，2023.
[18]王齊，「四邊形網格自動建構之多尺寸輪廓撒點技術研究」，國立中央大學碩士論文，2024.
[19]李奇勳，「非結構化四邊形網格自動建構研究」，國立中央大學碩士論文，2024.
[20]吳弈翰，「IC CAD模型之混合結構化與非結構化四邊形網格自動建構技術發展」，國立中央大學碩士論文，2024.
[21]梁秉傑，「不同網格類型對於IC CAD模型模流分析之影響探討」，國立中央大學碩士論文，2024.