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研究生:林震凡
研究生(外文):Cheng-Fon Lin
論文名稱:動態最小平方差三維點模型自由形變之研究
論文名稱(外文):Free-form Deformation of MLS Point Surface Models
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:2004
畢業學年度:92
語文別:英文
論文頁數:75
中文關鍵詞:動態最小平方差自由形變
外文關鍵詞:Free-form DeformationMoving Least Squares
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  在以往的電腦圖學領域中,以多邊形構成模型的電腦圖學研究一直是主要的趨勢,直到最近幾年,以點構成模型的研究主題才開始引起較多的注意,其中大多數研究主題專注於如何獲得、處理及描繪點構成模型的資訊,而較少有關對點構成模型做形變或編輯等的主題,其主要原因受限於點架構本身在表示一個大規模的幾何模型時,其龐大的點資料量會使任何對這個幾何模型所作的互動式編輯及變形的動作都會變的過分地耗時耗力。因此在本篇論文提出一個有效率降低點構成模型資料量及運算量的演算法,並解決在編輯或變形一個點構成模型中所會遇到的動態新增或減少點的問題。
  本篇論文提出一個有效率有系統的演算法,將普通一個完全以點構成的模型簡化為一個個由區域所代表的簡化點模型,而每個區域有其對應的切平面、一個參考原點及其對應的座標系和動態最小平方差多項式,這種表示法除了可以降低點的資料量還可以利用動態最小平方差多項式的連續性特性,在多項式所代表區域的正切平面上的任意點找到其投影在多項式上的對應點,因此可以動態調整每個區域的點數。
  另一個特點在於對點架構模型做自由形變時將每個區域的動態最小平方差多項式看成對應於每個區域的一個displacement map,僅需計算出每個區域參考原點的位置,並以變形前後的每個區域參考原點與其one ring鄰近區域參考原點的位置來找出變形前後的座標系對應,以這層對應關係來找出所要新增點在動態最小平方差多項式上對應的displacement,而新增點的法向量算法也是類似,運用變形前後的每個區域參考原點的法向量及其one ring鄰近區域參考原點的法向量先算出新增點的初始法向量,以這初始法向量算出一個座標系,將新增點在變形後區域座標系的位置帶入微分一次的動態最小平方差多項式中,算出該點在多項式表面的法向量,再把這個法向量值帶入以我們剛算出的新增點初始法向量座標系便可得該新增點在變形之後的法向量。
  藉由上述的兩項特點,我們可以更快速的算出點構成模型的自由變形、動態增加或減少點模型區域或全體的點,也不用為了填補變形後所產生的破洞而重新計算動態最小平方差多項式,更進一步的,因為我們將點構成模型簡化為一個個以區域代表的簡化點模型,若以region growing的方式決定只對模型的某部分區域作自由變形,本論文所提供的變形方法可即時完成,而在過度的變形及扭曲下,變形前後的區域對應會變的誤差極大而造成模型表面的破洞,這點我們可以用區域分裂來克服,把變形過大的區域分裂成兩個或多個區域來表示,減低區域對應關係的誤差。
  本篇論文提供一個快速及創新的演算法來完成點構成模型的自由形變,基本的觀念架構在多項式的特性及線性代數中的基底轉置的觀念,在資料量及運算速度上比起傳統的點構成模型變形上皆有更佳的表現,相信在不久的未來,點構成模型的即時變形也是可以達成的目標。
  This paper present an efficient and systematic algorithm, which can transform a point-based geometry model to a simplified cluster model and each cluster of this simplified model has a base plane, an origin , a coordinate system and a MLS polynomial to represent the surface of the cluster. Using this kind of representation the original points data don’t need to be recorded, which helps us to save a lot of data space. With the continuity of MLS surface, we can arbitrarily project any point anywhere inside the cluster to the MLS surface and dynamically adjust the number of point in the cluster.
  In our method, we consider every MLS polynomial of the cluster as a continuous displacement. After using FFD to deform a point-based geometry model we only compute the positions of each cluster and its one-ring neighbor clusters before and after deformations to find the corresponding relation between the original coordinate system of the cluster and the deformed coordinate system of the cluster. This corresponding relation is used to find the corresponding displacement on the original MLS surface of the new point we want to project after deformations. The normal vector of the new point is calculated from the cluster point and its one-ring neighbors with a similar algorithm.
  We present a fast and creative algorithm to achieve free-form deformation of point-based geometry; the basic concept is constructed on the characteristics of polynomial and the Linear Algebra transformation matrix. Our algorithm has better performance than the traditional point-based geometry deformation has in both saving data space and computation time. We believe that in the near future, real-time point-based geometry deformation can be achieved.
I Mandarin Abstract………………………………i
II Abstract…………………………………………iii
III Acknowledgements…………………………………v
1 Introduction………………………………………1
1.1 Motivation…………………………………………1
1.2 Our Research Pipeline………………………… 1
1.3 Contribution………………………………………3
2 Related Work………………………………………5
2.1 QSplat structure and algorithm………………8
2.2 Free-form Deformation…………………………12
3 Clustering and Moving Least Squares Projection……………………………………………………16
3.1 Clustering………………………………………17
3.2 Moving Least Squares Surface………………23
3.3 Moving Least Squares Algorithm……………24
4 Surface Reconstruction………………………29
4.1 Concept……………………………………………30
4.2 Preprocessing……………………………………32
4.3 Coordinate transformation……………………36
4.4 Deformation and re-projection of the surface………………………………………………………40
4.5 Points re-sampling……………………………51
4.6 Cluster splitting………………………………56
5 Results……………………………………………61
6 Conclusion and Discussion……………………70
6.1 Conclusion………………………………………70
6.2 Discussion and Future Work…………………70
7. References………………………………………72
[1]PAULY, M. AND GROSS, M. 2001. Spectral processing of point-sampled geometry. In Proceedings of SIGGRAPH 2001.
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[3]RUSINKIEWICZ, S. AND LEVOY, M. 2000. QSplat: A multiresolution point rendering system for large meshes. In Proceedings of SIGGRAPH 2000.
[4]ZWICKER, M., PFISTER, H., VAN BAAR, J., AND GROSS, M. 2001. Surface splatting. In Proceedings of SIGGRAPH 2001.
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[8]ZWICKER, M., PFISTER, H., VAN BAAR, J., AND GROSS, M. 2001. EWA Volume Splatting. In Proceedings of IEEE Visualization 2001
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[18]Ping-Hsien Lin, Tong-Yee Lee, “Camera- Sampling Field and Its Applications,”to appear in IEEE Transactions on Visualization and Computer Graphics, Vol. 10, No. 3, May/June, 2004.
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