发表机构
RWTH Aachen University（亚琛工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文介绍计算机图形学中多物理仿真方法的数学基础、关键算法及软硬件框架，涵盖刚体、流体、颗粒材料等及其相互作用，并展望机器学习驱动的动画新趋势。
AI 中文摘要
物理仿真是众多计算机图形学应用的基石，涵盖电子游戏、虚拟现实、视觉效果以及计算设计等领域。因此，在过去几十年中，基于物理的建模与动画技术数量激增，促进了各种材料和物理现象的仿真。本课程讲义深入介绍了面向计算机图形学的多物理仿真方法，涵盖了最广泛使用的方法背后的数学基础、关键算法和实际考量。我们重点关注计算机图形学界开发的各种物理现象和材料仿真方法，包括刚体、可变形体、流体和颗粒材料，以及它们之间的相互作用。对于每种方法，我们呈现其底层数学框架并给出详细推导，同时讨论不同材料和耦合策略如何融入该公式。此外，还介绍了一些提供开箱即用多物理建模能力的软件框架。最后，我们探讨了基于物理的动画领域的新兴趋势，包括近年来日益流行的基于机器学习的方法。
英文摘要
Physics simulation is a cornerstone of many computer graphics applications, ranging from video games and virtual reality to visual effects and computational design. The number of techniques for physically-based modeling and animation has thus skyrocketed over the past few decades, facilitating the simulation of a wide variety of materials and physical phenomena. These course notes provide an in-depth introduction to multiphysics simulation methods for computer graphics, covering the mathematical foundations, key algorithms, and practical considerations behind the most widely used approaches. We focus on methods developed by the computer graphics community for simulating various physical phenomena and materials -- including rigid and deformable bodies, fluids, and granular materials -- as well as the interactions between them. For each method, we present the underlying mathematical framework with detailed derivations and discuss how different materials and coupling strategies fit into the formulation. A selection of software frameworks that offer out-of-the-box multiphysics modeling capabilities is also presented. Finally, we touch on emerging trends in physics-based animation, including machine learning-based methods which have become increasingly popular in recent years.
