Robust Methods for the Physically-Based Animation of Large Deformations in Computer Graphics

本研究项目的目标是为计算机图形学应用中基于物理的大变形动画开发健壮而有效的方法。该项目由德国研究基金会（DFG）资助，为期18个月。在此期间，我们课题组首先研究了退化和倒单元引起的有限元模拟稳定性问题。我们可以用一种基于解析极分解的方法来解决这些问题。此外，在项目的第一个阶段，我们开发了一种基于协同弹性模型的新颖、高效的模拟方法，比使用相同模型的先前方法快100多倍。这使我们能够实时执行包含数十万个元素的动画。在计算机图形学中，由于隐式欧拉法具有良好的稳定性，时间积分多采用隐式欧拉法进行。然而，这种方法受到数值阻尼的影响，导致重要细节和真实感的损失。因此，本课题组开发了一种稳定的高阶隐式时间积分方法，提供了更精确的结果，并显著降低了数值阻尼。在这个项目的继续，我们计划研究新材料模型的应用，以稳健地模拟大变形。更准确地说，我们想研究微极模型，它已经成功地用于计算机图形学来模拟弹性棒和流体。这些模型定义了额外的旋转自由度，可以更好地表示可变形体的弯曲和扭转。改进后的表示方法可以减少弹性杆模拟所需的单元数。此外，还表明，在使用微极模型模拟湍流时，数值阻尼可以显著减小。在这个研究项目的下一阶段，我们计划使用微极材料模型来制作二维和三维可变形体的动画。据我们所知，在计算机图形学中还没有这样做过。通过这种方式，我们希望从微极模型的优势中受益，特别是在模拟带有旋转的大变形时。首先，我们计划开发一种体积体的模拟方法。然后，我们想扩展这种方法来模拟二维壳。为了进行时间积分，我们在第一阶段开发的方法应该扩展到解决微极模型所需的附加方程。此外，我们计划研究考虑旋转自由度的塑性变形的动画。最后，我们希望使用额外的自由度来实现高分辨率表面网格的详细可视化。

The goal of this research project is the development of robust and efficient methods for the physically-based animation of large deformations in computer graphics applications. This project has been funded by the German Research Foundation (DFG) for 18 months. In this time period our research group first investigated the stability problems in finite element simulations caused by degenerate and inverted elements. We were able to solve these problems using a method based on an analytic polar decomposition. Further, in the first project phase we developed a novel, very efficient simulation method based on a corotated elasticity model, which is more than a hundred times faster than previous methods using the same model. This enabled us to perform animations with multiple hundred thousand elements in real-time. In computer graphics time integration is mostly performed using the implicit Euler method due to its good stability. However, this method suffers from numerical damping which leads to a loss of important details and realism. Therefore, our group developed a stable implicit time integration method of higher order, which provides more accurate results and which reduces the numerical damping significantly. In the continuation of this project we plan to investigate the application of new material models to robustly simulate large deformations. More precisely, we want to investigate micropolar models, which were already successfully used in computer graphics to simulate elastic rods and fluids. These models define additional rotational degrees of freedom which enable a better representation of the bending and torsion of a deformable body. The improved representation has the advantage that less elements are required in elastic rods simulations. Moreover, it was shown that the numerical damping could be significantly reduced in simulations of turbulent fluids using a micropolar model. In the next phase of this research project we plan to use micropolar material models for the animation of two- and three-dimensional deformable bodies. To the best of our knowledge this has not been done before in computer graphics. In this way we want to benefit from the advantages of micropolar models, especially when simulating large deformations with rotations. First, we plan to develop a simulation method for volumetric bodies. Then we want to extend this method to simulate two-dimensional shells. To perform the time integration, the method, which we developed in the first phase, should be extended to solve the additional equations required for the micropolar models. Further, we plan to investigate the animation of plastic deformations considering the rotational degrees of freedom. Finally, we want to use the additional degrees of freedom to realize a detailed visualization with high-resolution surface meshes.