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

在计算机图形学中，刚性和可变形实体的基于物理的动画有许多应用，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扮演着重要的角色，例如在特效制作或医学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，实体的几何形状与数值求解运动方程所需的离散化强烈耦合。大多数情况下，近似于对象域的四面体或六面体网格用于离散化，并显式地表示切割或断裂曲面。因此，离散化必须在切割或压裂过程中永久适应。现有的大多数方法都是基于重新网格化或体素化。基于重排的方法不断地修改离散化，以获得对仿真对象和切割曲面的良好逼近，从而产生准确的结果。然而，重新划分网格的计算代价很高，形状不好的元素可能会导致不稳定，并且相应代码的并行化也不是微不足道的。基于体素化的方法使用规则六面体网格离散几何体。这样，元素保持良好的形状，自适应方法的应用简单，代码并行化是可行的。然而，离散化还必须永久地适应，曲面几何图形只能近似，并且需要许多元素来充分表示剖切曲面。在这个项目中，我们将采用一种不同的方法。模拟对象和断裂面的几何形状应该与离散化网格完全解耦。这将通过使用扩展有限元方法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。与以前的方法不同，在压裂或切割过程中不需要调整离散化，单元的数量保持不变。然而，由于所提出的方法考虑了部分填充的单元，因此可以获得准确的结果。在这个项目中，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支持带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.