臺灣博碩士論文加值系統

現今三維模型在各個領域中普遍被使用，其中模型的產生方式，大多是使用三維建模軟體或三維掃描，然而透過三維掃描得到的三維模型，其混亂和不規則的網格結構讓後續應用上不太方便，因此，必須對網格進行重製。網格重製一直是電腦圖學領域核心研究對象之一，目的是要讓原始模型的混雜網格結構可以重新計算並得到整齊、規律和漂亮的網格結構。在本研究中，提出新的方法來改善現有根據骨架資訊並以六面體方塊拼裝後投影回原始模型的網格重製方法，由於該方法在拼湊六面體方塊是需要互相連接的，因此當改變任一方塊時，其餘方塊皆需要重新計算，此外容易發生六面體方塊扭轉(torsion)的問題，若無妥善處理就直接投影回原始模型上，就會發生網格摺疊(fold over)的問題。而本研究利用骨架資訊得到模型分區，根據不同的分區種類進行流場設計以及網格線鋪設，而全程皆在原始模型上處理，一方面可省去六面體方塊鋪設的麻煩，另一方面毋須投影可避免錯誤產生。

3D models are widely used in every field today. The most common ways to create 3D models are 3D modeling softwares and scanning. However, the models acquired with scanning have the issue of irregular geometric structure, limiting their applicability. A remeshing process is needed to make those models more applicable. Remeshing has been one of the popular subjects in computer graphics. The purpose of remeshing is to reconstruct a mesh into a more uniformly and orderly shaped mesh. In this paper, a new method is proposed to improve the remeshing process that
computing a coarse quad structure that fits with skeleton by subdivided boxes and projecting this structure onto origin model. The problem with the method is that all subdivided boxes have to be recalculated when any single box is changed due to the boxes being interconnected. Another issue is that the fold-overs tend to happen on the result mesh when the torsions of boxes are not properly handled. In the proposed method, models are first divided into partitions based on skeleton data, and then line fields and mesh grid are generated according to the types each partition. Because the method only considers the original mesh, errors caused by projection and the complex process of place subdivided boxes are avoided.

中文摘要 i
Abstract ii
第一章 介紹 1
第二章 相關研究 4
第三章 系統架構 6
第四章 骨架擷取與模型分區 8
第五章 分區網格重製 13
第六章 實驗結果與討論 30
第七章 結論與未來工作 36
參考文獻 37

[1] C.Y. Yao, H. K. Chu, T. Ju, T. Y. Lee, Compatible quadrangulation by sketching, Computer Animation and Virtual Worlds, vol. 20, pp. 101-109, 2009.
[2] F. Usai, M. Livesu, E. Puppo, M. Tarini, R. Scateni, Extraction of the quad layout of a triangle mesh guided by its curve skeleton, ACM Trans. Graph., vol. 35, no. 1, pp. 6:1-6:13, 2015.
[3] C. Y. Yao, M. T. Chi, T. Y. Lee, T. Ju, Region-based line field design using harmonic functions, IEEE Transactions on Visualization and Computer Graphics, vol. 18, no. 6, pp. 902-913, 2012.
[4] S. Dong, P. T. Bremer, M. Garland, V. Pascucci, J. C. Hart, Quadrangulating a mesh using laplacian eigenvectors, Technical Report, 2005.
[5] S. Dong, P. T. Bremer, M. Garland, V. Pascucci, J. C. Hart, Spectral surface quadrangulation, pp. 1057-1066, 2006.
[6] B. Jobard, W. Lefer, Creating evenly-spaced streamlines of arbitrary density, Visualization in Scientific Computing, pp. 43-55, 1997.
[7] O. K. C. Au, C. L. Tai, H. K. Chu, D. Cohen-Or, T. Y. Lee, Skeleton extraction by mesh contraction, ACM Trans. Graph., vol. 27, no. 3, pp. 44:1-44:10, 2008.
[8] D. Kirsanov, Minimal discrete curves and surfaces. PhD thesis, Applied Math, Harvard University, 2004.
[9] S. Dong, S. Kircher ,M. Garland, Harmonic functions for quadrilateral remeshing of arbitrary manifolds, Computer Aided Geometric Design, vol. 22, no. 5, pp. 392-423, 2005.
[10] O. Sorkine, D. Cohen-Or, Least-squares meshes," pp. 191-199, 2004.
[11] M. Marinov, L. Kobbelt, Direct anisotropic quad-dominant remeshing, No. 10, pp. 207-216, 2004.