Physically-Based Animation of Cutting, Tearing and Fracturing in Computer Graphics

在计算机图形学中，基于物理的刚性和可变形固体的动画有许多应用，从游戏和电影中的特殊效果到交互式训练模拟器。在某些应用中，固体物体的破裂和切割起着重要的作用，例如在特效制作或医疗模拟器的破坏场景中。因此，本项目致力于开发基于物理的切割、撕裂和破裂动画的新方法。在现有的计算机图形学方法中，固体的几何形状与数值解运动方程所需的离散化密切相关。通常采用近似物体域的四面体或六面体网格进行离散化，并明确表示切割或断裂表面。因此，在切割或压裂过程中，必须永久适应离散化。大多数现有的方法都是基于网格重划分或体素化。基于网格划分的方法对离散化进行了持续的修正，以获得仿真对象和切割表面的良好逼近，从而得到准确的结果。然而，重新划分网格在计算上是昂贵的，形状不佳的元素可能导致不稳定，并且相应代码的并行化是非常重要的。基于体素化的方法使用正六面体网格离散几何。通过这种方式，元素保持良好的形状，自适应方法的应用很简单，代码并行化是可行的。然而，离散化也必须永久适应，表面几何形状只能近似，并且需要许多元素来充分表示切割表面。在这个项目中，我们将采用不同的方法。仿真对象和断裂面的几何形状应与离散网格完全解耦。这将通过使用扩展有限元法（XFEM）将实体几何的隐式表示嵌入到正六面体网格中来实现。这确保了形状良好的元素，并简化了自适应方法和并行化的使用。与以前的方法相比，在压裂或切割过程中不需要进行离散化，元件的数量保持不变。然而，由于该方法考虑了部分填充的元素，因此可以获得准确的结果。在该项目中，我们的目标是开发所描述的解耦方法，并随后将该方法扩展到具有分支的复杂渐进压裂。

In computer graphics the physically-based animation of rigid and deformable solids has many applications, ranging from special effects in games and movies to interactive training simulators. In some applications fracturing and cutting of solid objects plays an important role, e.g. in destruction scenarios in special effects production or medical simulators. Therefore this project is dedicated to the development of new methods for the physically-based animation of cutting, tearing and fracturing.In existing computer graphics approaches, the geometry of a solid is strongly coupled with the discretization that is required to numerically solve the equation of motion. Most often a tetrahedral or hexahedral mesh, which approximates the object domain, is used for discretization and cut or fracture surfaces are represented explicitly. Therefore, the discretization must be permanently adapted during a cutting or fracturing process. Most existing approaches are based on remeshing or voxelization. Remeshing based methods modify the discretization persistently to get a good approximation of the simulation objects and cut surfaces to produce accurate results. However, remeshing is computationally expensive, ill-shaped elements can lead to instabilities, and a parallelization of the corresponding code is non-trivial. Voxelization based approaches discretize the geometry using a regular hexahedral grid. In this way the elements stay well-shaped, the application of adaptive methods is simple, and code parallelization is feasible. However, the discretization must also be adapted permanently, the surface geometry can only be approximated, and many elements are required to represent a cut surface adequately. In this project we will follow a different approach. The geometry of simulation objects and fracture surfaces should be completely decoupled from the discretization mesh. This will be realized by embedding an implicit representation of the solid's geometry into a regular hexahedral mesh using an extended finite element method (XFEM). This ensures well-shaped elements and simplifies the usage of adaptive methods and parallelization. In contrast to previous approaches, the discretization does not have to be adapted during a fracturing or cutting process and the number of elements stays constant. However, accurate results can be achieved since the proposed method considers partially filled elements. In this project, we aim to develop the described decoupling approach and subsequently extend the method to support complex progressive fracturing with branches.