應用顯隱性變分積分器於變形物體的高頻震動運動保持

Abstract

本論文提出了一個有效率的方法可維持變形物體之高頻振動運動。在電腦動畫中，變形物體之高頻振動運動的細節日益被重視，然而相關之研究鮮少被討論。在過去為了模擬高頻振動運動，通常使用隱性變分積分器以維持高頻能量。但變形物體同時具有高頻和低頻運動，而隱性變分積分器將無法有效率地模擬低頻運動。本論文使用顯隱性變分積分器模擬變形物體，該變分積分器以顯性法模擬低頻位能、隱性法模擬高頻位能，使之效能優於一般變分積分器。然而，顯隱性變分積分器無法直接使用在一般變形物體的模擬方法上，因此我們採取簡化有限元素法透過Courant-Friedrichs-Lewy(CFL)條件將系統位能分成高頻和低頻位能再將之運用至顯隱性變分積分器之上。實驗結果顯示我們的架構可加速模擬速度並有效的保持系統能量，應用在不同變形物體上。

In this thesis, we propose an efficient approach to preserve high frequency vibration of deformable objects. In computer animation, the motion details of deformable objects have become more and more important but rarely been discussed. In the past, simulating high-frequency vibration motion in implicit variational integrators are usually applied to preserve high-frequency energy. The motions of deformable objects could be decomposed into low-frequency and high-frequency modes; however, implicit variational integrators cannot simulate low-frequency modes efficiently. We use the implicit-explicit variational integrator to simulate deformable objects. The computational performance of implicit- explicit variational integrator is better than that of normal variational integrators as the low-frequency energy part is integrated explicitly and the high-frequency energy part is integrated implicitly; however, the implicit-explicit variational integrator cannot directly applied to deformation simulation. Therefore, we use the Courant-Friedrichs-Lewy (CFL) condition to decompose system potential energy into low-frequency and high-frequency potential energy, respectively. In our experiments, our framework can improve the simulation speed and preserve the system energy on different deformable objects.