Computational models and tools for fluid animation

在过去的十年里，液体和气体物理的计算机模拟在真人电影和动画电影的视觉效果中发挥了至关重要的作用，从《阿凡达》到《料理鼠王》，通过自动创造虚拟的波浪、蜂蜜、爆炸、火、云等等。这个新的工具集为导演提供了讲述创造性故事的能力，否则这些故事将是昂贵的，危险的，或者完全不可能拍摄的。此外，现代电脑游戏开始将流体动力学融入游戏玩法中。人们也越来越关注分析和实验结果的匹配，这样，未来在培训、教育、建筑、设计和工程方面的交互式应用都可能从集成快速而准确的物理中受益。然而，这需要的不仅仅是简单地加速现有的工程方法。在计算机科学、物理和数学的交叉领域，还有许多基础研究问题有待解决，而计算机动画领域为追求全新的解决方案提供了理想的试验场。这些领域的创新也具有巨大的潜在积极经济影响：仅电影和游戏产业就各自为北美经济贡献了数百亿美元。安大略省的公司主导着世界3D动画软件市场（Houdini, Autodesk），安大略省快速增长的电脑游戏产业的年收入估计超过10亿美元。迄今为止所取得的成功也突显了我们当前的模拟工具在许多方面仍存在不足，因为专业视觉效果艺术家需要在更短的时间内模拟比以往更详细、更戏剧性和更复杂的场景。这项研究的重点是开发新的物理模型、数值技术以及几何和算法工具，使他们能够做到这一点。例如，水滴的详细模拟需要在强表面张力、重力和流体压力之间取得精确的平衡；目前的数值方法很难达到这种平衡，结果产生了不幸的可见误差。准确地表示快速变形液体表面的演变是一个持续的挑战，特别是对于泡沫，气泡和复杂的多相液体混合物（例如油/水/空气）。在飞溅过程中产生的非常薄的液体片和射流目前使用现有的方法消耗了大量的计算资源。本研究计划将利用我们在嵌入式边界方法、动态拓扑三角形网格和降维对象建模技术方面的专业知识来解决这些问题。这些进步将最直接地影响计算机动画和视觉效果，提高技术艺术家使用的软件工具的功能和生产力。与此同时，我们旨在开发的基本计算工具最终将在整个科学领域具有广泛的适用性，从研究泡沫和颗粒演变的材料科学家，到训练模拟虚拟人类的未来外科医生，这些虚拟人类的心脏泵出模拟血液。在计算机图形学领域，这项工作将从根本上有助于我们理解如何最好地表示和操纵流体和类流体材料的离散几何、拓扑和物理，这些材料经历了巨大而剧烈的变形。

Over the last decade, computer simulations of the physics of liquids and gases have come to play a critical role in the visual effects of both live-action and animated films, from Avatar to Ratatouille, by automating the creation of virtual waves, honey, explosions, fire, clouds, and more. This new toolset offers directors the ability to tell creative stories that would otherwise be prohibitively expensive, dangerous, or utterly impossible to film. Furthermore, modern computer games are beginning to incorporate fluid dynamics into their gameplay. There has also been an increasing focus on matching both analytical and experimental results, such that future interactive applications in training, education, architecture, design, and engineering are all likely to benefit from integrating fast yet accurate physics. However, this requires more than simply accelerating existing engineering methods. There remain to be solved many fundamental research questions which lie at the intersection of computer science, physics, and mathematics, and the field of computer animation offers an ideal testing ground for the pursuit of radically new solutions. Innovations in these areas also have tremendous potential for positive economic impact: the film and games industries each contribute tens of billions to the North American economy alone. Ontario-based companies dominate the world market for 3D animation software (Houdini, Autodesk), and the annual revenue of Ontario's rapidly growing computer gaming industry has been estimated to exceed $1 billion. The successes achieved to date have also served to highlight the many ways in which our current simulation tools remain inadequate, as professional visual effects artists demand the ability to simulate more detailed, more dramatic, and more complex scenarios than ever before, in less time. The focus of this research is to develop new physical models, numerical techniques, and geometric and algorithmic tools that will enable them to do so. For example, detailed simulation of water droplets requires a precise balance between strong surface tension, gravity, and fluid pressure; current numerical methods struggle to achieve this balance, yielding unfortunate visible errors as a result. Accurately representing the evolution of rapidly deforming liquid surfaces is an ongoing challenge, particularly for foams, bubbles, and complex multiphase liquid mixtures (e.g. oil/water/air). Very thin liquid sheets and jets which arise during splashing currently consume massive computational resources with existing methods. This research proposal will tackle these problems, leveraging our established expertise with embedded boundary methods, triangle meshes with dynamic topology, and modeling techniques for reduced dimensional objects. These advances will most immediately impact computer animation and visual effects, increasing the power and productivity of software tools used by technical artists. At the same time, the fundamental computational tools we aim to develop will ultimately have wide applicability across the sciences, from material scientists studying the evolution of foams and grains, to future surgeons training on simulated virtual humans whose hearts pump simulated blood. Within the field of computer graphics, this work will contribute fundamentally to our understanding of how best to represent and manipulate the discrete geometry, topology, and physics of both fluids and fluid-like materials which undergo large and dramatic deformations.