建構規則網格分佈的網格簡化技術

Regular Mesh Simplification

施詠禎(YONG-JHEN SHIH)

指導教授 ： ARRAY(0xa508f98)

中原大學/工學院/資訊工程研究所/碩士(2010年)

https://doi.org/10.6840/cycu201000335

摘要

隨著電腦運算能力日漸強大的幫助下，由三角片組成的3D模型已經普遍應用在不同領域之中。然而，為了讓3D模型能夠勝任線上虛擬實境系統所需要即時顯像功能，3D模型必須經過網格簡化的過程，藉由移除模型上較不重要的部分來產生出保留重要外形特徵但幾何資料量大幅降低的簡化模型。過往的網格簡化研究著重於如何在簡化過程中正確保留外形特徵，卻忽略的簡化模型網格分佈的規則性而產生出網格散亂的簡化結果，造成簡化模型的後續應用受到限制。
本論文針對這個目的提出同時考慮外形特徵保留程度以及簡化後網格分佈規則程度的三角網格簡化演算法。在外形特徵的保留工作上，為了能夠有效地保留原始模型之外形特徵，本論文透過模型表面法向量差異度的分析，自動的將模型表面分割成多個平坦的表面區域，並保證這些區域的邊界會落在表面特徵的位置。藉由此表面分群技術可以自動且正確的萃取出原始模型的外形特徵，並以此特徵作為後續簡化過程中的限制條件來完成簡化模型的特徵保留工作。在網格簡化的過程中，本論文加入了區域性網格鬆弛技術有效率的調整簡化網格的分佈情形，讓簡化後的網格除了具有較少的幾何資料之外，同時擁有規則的網格分佈。

關鍵字

網格簡化

並列摘要

Along with computer operational capability day after day under formidable help, The 3D model which is composed of triangles already generally applied in the different domain. However, in order to enable the 3D model to be competent on-line hypothesized solid boundary system to need the immediate developing function, the 3D model must the process which simplifies the mesh. The unimportant part produces the simplified model which because of the detachment model on the retention important contour characteristic but geometry material quantity largely reduces. Passing mesh simplification research emphatically in how in simplified process correct retention contour characteristic, actually neglects the simplified model mesh distributed regularity has the grid scattered in disorder simplification result, causes the simplified model the following application to be restricted.
The present paper after this goal proposed simultaneously considers the contour characteristic retention degree as well as the simplification grid distribution rule degree triangle mesh simplification algorithm. In contour characteristic retention work, for can retain contour of characteristic effectively the pilot model, The present paper by the model surface normal vector difference's analysis, automatic divides into the model surface many smooth superficial regions, and guaranteed that these regions the boundary will fall on the character of surface position. The affiliation surface hives off the technology to be possible from this automatic and the correct extract leaves the pilot model the contour characteristic, and takes in the following simplified process by this characteristic the limiting condition to complete the simplified model the characteristic retention work. Simplifies in the mesh in the process, the present paper has joined the regional mesh relaxation technology effectiveness adjustment simplification grid distributed situation, After letting simplified the mesh besides has the few geometry material, simultaneously has the rule grid distribution.

並列關鍵字

Mesh Simplification

參考文獻

[Chiang06] C. H. Chiang “3D Model Remeshing Using Shape Approximation Partition”, In published by Chung Yuan Christian University, 2006.

[BCPT10] B. S. Jong, , C. H. Chiang, P. F. Lee, and T. W. Lin “High Quality Surface Remeshing with Equilateral Triangle Grid”, The Visual Computer, Vol. 26, No.2, pages 121 – 136, 2010.

[BJW06] B. S. Jong, J. L. Tseng, W. H. Yang “An Efficient and Low-Error Mesh Simplification Method Based on Torsion Detection”, The Visual Computer, Vol. 22, No.1, pages 56 – 67, 2006.

[BSNJ02] B. Lévy, S. Petitjean, N. Ray, and J. Maillot “Least Squares Conformal Maps for Automatic Texture Atlas GeneRation”, In Proceedings of ACM SIGGRAPH, pages 362 – 371, 2002.

[Ciarlet91] P. G. Ciarlet “Basic Error Estimates for Elliptic Problems”, Handbook of Numerical Analysis, Vol. 2, pages 17–351, Finite Element Methods (Part 1), 1991.