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

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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.