採用小波轉換加速的即時布料動態模擬

Abstract

物理方面的模擬，例如動態布料模擬，對於增加應用軟體的視覺效果上有相當大的助益。之前有關於這方面的研究大多致力於更穩定的數值積分方法，以及更快速的系統架構。本篇論文提出一個節省更多時間的系統架構：基於根據重要性採樣的概念，先將質點的法向量資料做小波轉換，藉由查詢轉換過的階層資訊，找出法向量差別較小的區域，然後以內插法代替數值積分法來計算區域內的質點位置。此外，為了配合以上的前處理方式，我們修改近似隱積分法，使得不需要內插的質點能經由穩定而快速的計算得到正確的結果。同時因為內插帶來的改變，許多在質量-彈簧系統中形成困擾但不易解決的問題也獲得改善。

Physically-based simulation such as cloth simulation is helpful to fertilize visual effect in many applications. Techniques have been proposed are mostly aiming at more stable numerical method, or less time-consuming framework. In this thesis which based on spring-mass system, we will introduce a fast and stable numerical integrator from merging verlet method and approximate implicit integrator. Both of them have the advantage of short computational time and high stability. Additionally, in order to decrease the whole simulation time for a cloth object, we first find flat segments before each simulation, then, interpolate positions and velocities of nodes within each segment, saving time spent by using integration method. Thus we can have efficient and stable real-time simulation system without sacrificing visual quality.