臺灣博碩士論文加值系統

我們提出一個可以建造多個網格模型間一致性規則四角化網格的方法，提出這個方法的原因有三點：第一點，普遍得到的網格模型都不是規則分部的，在幾何的處理上，規則網格比不規則網格容易處理，因此如何以規則網格表示不規則網格在電腦圖學的應用上是很有幫助的一個題目；第二點，在電腦圖學的應用上，大部分的網格都是以三角形構成，所以大多的研究也是建立在以三角形為基礎的處理上，但是某些應用中四角形網格較能有較良好的效果，例如流體力學或是貼圖的應用上等等；第三點，在現今的研究中，有越來越多的研究不只是專注在處理單一網格模型，而是希望在多個網格模型間找到更有趣的應用，但是多個網格模型間的應用絕大部分需要仰賴一致性的網格模型。有鑒於以上三種需要，我們設計一個方法，可以在多個非genus 0的網格模型間找出對應的四角化參數空間，用以建造一致性網格。

We propose a novel approach to build consistent regular and quadrilateral meshes among many input mesh models. The major contributions of this thesis are described as follows. First, the general mesh models are always not regular. However, it is well-known that the regular meshes are much easier to manipulate than the irregular meshes. So, the conversion from an irregular mesh to a regular mesh is very useful in today digital geometry processing. Second, most of mesh models are comprised of triangles in computer graphics. In contrast, the quadrilateral mesh models can facilitate many important applications such as PDEs, fluid dynamic, texturing and etc. Finally, many people are concentrated on manipulating multi-models, so a common consistent mesh model is required. In this thesis, we design a novel method to create consistent quadrangulation among input irregular meshes. In particular, this novel cross-surface quadrangulation method is not limited by the genus of input models.

中文摘要 III
Abstract IV
誌謝 V
目錄 VI
圖表目錄 IX
第一章 導論 1
1.1 研究動機 1
1.2 研究內容與流程 2
1.3 主要研究貢獻 4
第二章 相關研究 6
2.1 網格四角化 6
2.2 一致性網格參數化 10
2.3 Sweep曲面 14
第三章 主要架構及演算法 16
3.0 代表符號定義 16
3.1 架構與流程 17
3.1.1 架構 17
3.1.2 流程 19
3.2 建構基礎網格 21
3.2.1 問題描述 21
3.2.2 骨架素描 23
3.2.3 產生堆疊方塊與整合 27
3.2.4 表面掃描 39
3.3 參數化 45
3.3.1 問題描述 45
3.3.2 初始參數化 47
3.3.3 Relaxation （Smoothing） 53
3.3.4 頂點的移動計算 58
3.3.5 網格重建 & AGIM 62
3.3.6 一致性參數化 67
第四章 實驗結果與討論 69
4.1 實驗結果 69
4.2 討論 79
第五章 結論與未來展望 81
參考文獻 83

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