We introduce a method for efficiently computing the exact shortest path to the boundary of a mesh from a given internal point in the presence of self-intersections. We provide a formal definition of shortest boundary paths for self-intersecting objects and present a robust algorithm for computing the actual shortest boundary path. The resulting method offers an effective solution for collision and self-collision handling while simulating deformable volumetric objects, using fast simulation techniques that provide no guarantees on collision resolution. Our evaluation includes complex self-collision scenarios with a large number of active contacts, showing that our method can successfully handle them by introducing a relatively minor computational overhead.

翻译：我们提出了一种方法，用于高效计算在存在自交情况下从给定内部点到网格边界的确切最短路径。我们给出了自交对象最短边界路径的形式化定义，并提出了一种鲁棒算法，用于计算实际的最短边界路径。该方法为模拟可变形体积对象时的碰撞与自碰撞处理提供了有效解决方案，适用于使用无法保证碰撞解决结果的快速仿真技术。我们的评估涵盖了具有大量活跃接触的复杂自碰撞场景，结果表明，通过引入相对较小的计算开销，该方法能够成功处理这些场景。