Meshfree physically-based animation of natural phenomena in computer graphics

职务名称：计算机图形学中基于物理的无网格自然现象动画我未来五年的研究计划将集中在基于物理的自然现象动画的无网格方法上。我们最近开发了一种新的和简单的基于核的方法来解决偏微分方程。我的计划是进一步扩展该方案，以便将其应用于模拟计算机图形中的自然现象动力学，如流体，固体和织物。光滑粒子流体动力学（SPH）由于其在考虑流体的模拟和可视化时的简单性而被广泛用于模拟液体。SPH也被认为是非常适合处理不规则域和拓扑变化。但是，使用SPH处理尖锐的域边缘时，并没有得到准确的结果，因为它与基于网格的变分方法。因此，用于模拟流体的基于粒子的方法通过网格来增强，以更准确地处理尖锐的边界。我们的无网格基于核的方法比SPH近似更准确，但它的使用提供了类似的简单性。在提案中，我强调简单性和易用性，认为这是产生真正影响的关键因素，特别是在交互式应用程序领域。在短期内，我们将在边界附近进行更精确的计算，而不必求助于网格。这是可能的方法，由于该方法的一个有前途的功能：它的灵活性，特别是考虑的内核的上旋的可能性。最后，我将把这个方法推广到流体以外的其他物质。基于粒子的方法已被用于模拟统一模型，这有助于不同类型的物质（流体-固体，流体-布料等）之间的相互作用。同样重要的是要提到，对于交互式应用程序，这种方法可以用于开发动画算法，并将充分映射到图形处理单元（GPU）。

Title: Meshfree physically-based animation of natural phenomena in computer graphics My research program for the next five years will focus on a mesh-free method for physically-based animations of natural phenomena. We recently developed a new and simple kernel-based method for solving partial differential equations. My plan is to further extend the scheme in order to apply it to simulating natural phenomena dynamics in computer graphics such as fluids, solids and cloths. Smoothed Particle Hydrodynamics (SPH) is popular for simulating liquids due to its simplicity when considering the simulation and the visualization of the fluid. SPH is also considered as being well suited when dealing with irregular domains and topological changes. But using SPH when dealing with sharp domain edges does not give as accurate results as it does with mesh-based variational methods. Hence particle-based methods for simulating fluids were enhanced with meshes to deal more accurately with sharp boundaries. Our Mesh-free Kernel-based method is more accurate than the SPH approximation, yet its use offers a similar simplicity. In the proposal, I emphasize simplicity and ease of use, believing that it is a key ingredient in having a true impact especially in the field of interactive applications. In the short term, we will work on more accurate computation near the boundaries, without having to resort to a mesh. This is possible with the method due to a promising feature of the method: its flexibility and in particular, the possibility to consider an upwinding of the kernels. Finally, I will generalize the method to encompass other matter than fluid. Particle-based methods have been used for simulating unified models, which facilitates the interactions between different types of matter (Fluid-Solid, Fluid-Cloths, etc.). It is also important to mention that, regarding interactive applications, this method can be used to develop animation algorithms, and will adequately map to the Graphics Processing Unit (GPU).