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研究生:蘇志盛
研究生(外文):Chih-Cheng Su
論文名稱:以有權重的質心范諾圖作漸進式三維模型重新網格化
論文名稱(外文):Adaptive 3D Remeshing Scheme Using Weighted Centroidal Voronoi Diagram
指導教授:李同益李同益引用關係
指導教授(外文):Tong-Yee Lee
學位類別:碩士
校院名稱:國立成功大學
系所名稱:資訊工程學系碩博士班
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:中文
論文頁數:80
中文關鍵詞:多層解析度網格三維物體重新網格化網格細分
外文關鍵詞:decompositionmultiresolutionsubdivisionremeshmeshessnake
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  三維物體在電腦的應用相當廣泛,而三角網格是用來表示三維物體常用的方法,其來源通常為3D scanners、商用軟體,或者經電腦視覺演算法由二維影像重構而來。但是三角上述方法所得之三角網格普遍存在二個問題:不規則(irregular)與不一致(non-uniform)。這二個問題導致三角網格有許多狹長三角形的存在,使三角網格的應用,如貼圖、變形等,其困難度增加。
  流程一開始讓使用者將幾何模型作切割,切割的路徑會盡量經過物體的特徵,形成若干盤子狀(disk-like)的表面區域,之後透過有權重的質心范諾圖(Weighted Centroidal Voronoi Diagram)自動將每個表面區域細分為更多三角形表面區域,並將其各別攤平與重新三角化。此方法將三維物體重新網格化,去除狹長三角形,整個流程是接近自動化,而且低誤差的,並且能控制重新網格化後三維物體的三角形個數,可應用於多層解析度網格。
In computer graphics and geometric modeling, surfaces are often represented by triangular meshes. Somehow, the triangular meshes are often irregular and complicate processing such as numerical analysis, texturing, and storage.
We present a novel method to decompose an arbitrary 3D model, and then resample vertices in the model by low-distortion parameterization. There are two goals of this decomposition process: automatic and size-equally. We first need to cut a 2-manifold mesh into several disk-like patches. For each patch, we automatically partition it into more triangular patches. With the help of weighted centroidal Voronoi diagram (WCVD), these triangular patches are equally sized. Recursivelly subdividing these triangular patches, we finally get a regular model.
摘要………………………………………………………………………………………….I
目錄………………………………………………………………………………………..IV
圖目錄……………………………………………………………………………………..VI
第1章 導論1
1.1 研究動機與目的1
1.2 本論文之系統架構2
1.3 本論文之貢獻4
第2章 相關研究6
2.1 網格簡化6
2.2 網格精緻化10
2.3 網格細化13
2.4 網格特徵保存15
第3章 Snake應用於三維幾何模型17
3.1 Snake: Active Contour Model 簡介17
3.1.1 內在能量定義(Internal Energy):17
3.1.2 外在能量定義(External Energy):20
3.2 逼近最短路徑21
3.2.1 幾何模型上的最短路徑21
3.2.2 逼近最短路徑24
3.3 將Snake應用在三維幾何模型25
3.3.1 曲率計算25
3.3.2 Principal Direction29
3.3.3 Snake on 3D Surfaces34
第4章 表面區域自動切割45
4.1 WCVD(Weighted Centroidal Voronoi Diagram)45
4.1.1 范諾圖之特性與加速方法45
4.1.2 CVD(Centroidal Voronoi Diagram)49
4.1.3 WCVD之作法51
4.2 攤平圖與WCVD54
4.2.1 攤平方法54
4.2.2 攤平之誤差值與WCVD57
4.3 幾何模型重新組合59
4.3.1 決定相連關係59
4.3.2 三角形表面區域60
第5章 幾何模型重新網格化62
5.1 網格細分62
5.2 微調取樣點63
第6章 實驗結果與討論65
6.1 老人頭模型65
6.2 實驗數據68
6.3 討論70
第7章 未來展望71
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