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研究生： 廖偉智
Wei-Zhi Liao
論文名稱： 基於粒子系統之流體表面追蹤法
Particle-based Fluid Surface Tracking
指導教授： 張鈞法
Chun-Fa Chang
口試委員:
學位類別： 碩士
Master
系所名稱： 電機資訊學院 - 資訊工程學系
Computer Science
論文出版年： 2006
畢業學年度： 94
語文別： 英文
論文頁數： 60
中文關鍵詞： 基於粒子系統 、有號數距離函式 、立方體行進演算法
外文關鍵詞： Particle-based, signed distance function, marching cube algorithm
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    • 在流體模擬的領域中，有許多現成的流體表面追蹤的方法。而這些方法大致上可以分為階層法、粒子系統法、以及上面兩者合一的方法。在我的論文中，主要是以粒子系統法為主，它的好處就是非常適合模擬複雜的流體表面移動。然而，此粒子系統法卻有潛在性的問題。比如說，很難單純只用粒子系統去求得流體表面的三角片拓樸，更別提表面垂直向量及曲度。為了解決這問題，我使用一個表單去記錄每個格子的狀態，並且去對「有號數距離函式」做取樣存入每個格子點上。最後，我們使用「立方體行進演算法」重建液體表面，以及使用以物理為基礎的繪圖方式呈現。

    In fluid simulation, there are many surface tracking methods proposed which can be classified as level set based methods, particle based methods and their hybrid combination. In this thesis, I focus on the particle based methods which are ideal for animating violent phenomena. However, a particle based method has some potential problems. For example, it is hard to get triangle meshes from particles, not to mention to compute the surface normals and curvatures. My proposed method incorporates a table to store the state of the cell and samples the signed distance function on each grid point to solve this problem. Finally, I use the marching cube algorithm to construct fluid surface and render it with a physically- based rendering method.

    摘要 i Abstract ii Acknowledgements iii Table of Contents iv Chapter 1 Introduction 1 1.1 Thesis Overview 3 Chapter 2 Previous Works 5 2.1 Improvement on Data Structure 6 2.2 Improvement on Velocity Update 10 2.3 Improvement on Surface Tracking 11 Chapter 3 Fundamental of Fluid Dynamics 15 3.1 Navier-Stokes Equations 15 3.1.1 Reynolds Transport Theorem 16 3.1.2 Conservation of Mass 21 3.1.3 Conservation of Linear Momentum 24 3.1.4 Navier-Stokes Equations 28 3.1.5 Inviscid Flow – Euler Equation 30 3.2 Solving Navier-Stokes Equations 31 3.2.1 Explicit Method 31 3.2.2 Implicit Method 35 Chapter 4 Particle-based Surface Tracking 40 4.1 Algorithm Overview 40 4.2 Data Structure 42 4.3 Velocity Field Update 45 4.4 Particle Position Update 47 4.5 Sampling Signed Distance Function 51 4.6 Surface Construction 52 4.7 Rendering 53 Chapter 5 Conclusion and Future Work 58 Reference 59

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