應用於虛擬實境電腦動畫的剛體與流體之物理動態模擬

Physically-Based Dynamics Simulation of Rigid Body and Fluid for Computer Animation in Virtual Reality

李佳達(Chia-Da Lee)

指導教授 ： 傅立成

國立臺灣大學/電機資訊學院/電機工程學研究所/碩士(2006年)

https://doi.org/10.6342/NTU.2006.00348

摘要

本論文著重於建構剛體與流體的物理動態模擬。我們引入了以衝量為基礎（impulse-based）的架構來實現物體與物體間的碰撞、接觸以及關節等互相影響的行為，同時也實現了剛體與流體的雙向固流耦合（two-way solid-fluid coupling）行為。我們提出以物理為基礎的剛體氣動力（aerodynamics）效果，根據剛體的狀態與形狀來計算並產生包括馬格納斯（Magnus）效應及升阻（lift-and-drag）效果的氣動力行為。我們引入平滑粒子流體力學（smoothed particle hydrodynamics），使用粒子系統來模擬流體的行為。我們提出了一個藉由流體粒子與剛體間的碰撞以達成雙向的固體與流體的耦合方法，實現了浮體與沉體的模擬。我們亦提出一個完整的模擬流程，將剛體模擬與流體模擬成功地整合，藉此模擬系統，我們能夠產生各式各樣逼真的剛體與流體的動態。此系統除了可應用於電腦動畫，商業影片或電腦遊戲，還可與六自由度動感平台整合，因此使得此虛擬實境動感駕駛模擬器能夠提供多樣化的乘駕場景。

關鍵字

物理建模 ； 衝量法則剛體模擬 ； 關節 ； 氣體動力學 ； 計算流體力學 ； 平滑粒子流體力學 ； 粒子系統 ； 雙向耦合 ； 固流互動

並列摘要

This thesis focuses on the construction of the physically-based dynamic simulation of rigid bodies and fluids. We introduce the impulse-based scheme to accomplish collision, contact, and articulation of body-body interactions, as well as the two-way coupling of solid-fluid (rigid body and fluid) interactions. We propose a physically-based aerodynamic effect including Magnus effect and lift-and-drag effect for the rigid body simulation. The computations of aerodynamic forces are dependant on the shapes and the states of rigid bodies. The particle-based fluid simulation using SPH (Smoothed Particle Hydrodynamics) is introduced in this thesis. We propose a two-way coupling method from the collisions between fluid particles and rigid bodies to accomplish the floating and sinking of bodies. We propose a simulation loop to integrate the impulse-based rigid body solver and particle-based fluid solver successfully. With the simulation system, we can generate many realistic dynamics of rigid bodies and fluid. Besides application in computer animations, commercial films, and computer games, such a system can also be integrated with the 6-dof motion platform to generate realistic motion cues for the platform. Therefore, the VR-based motion/pilot simulator is able to provide various motion scenarios.

並列關鍵字

physically-based modeling (PBM) ； impulse-based rigid body simulation ； articulation ； aerodynamics ； computational fluid mechanics (CFD) ； smoothed particle hydrodynamics (SPH) ； particle system ； two-way coupling ； solid-fluid interaction

參考文獻

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