Drawing a direct analogy with the well-studied vibration or elastic modes, we introduce an object's fracture modes, which constitute its preferred or most natural ways of breaking. We formulate a sparsified eigenvalue problem, which we solve iteratively to obtain the n lowest-energy modes. These can be precomputed for a given shape to obtain a prefracture pattern that can substitute the state of the art for realtime applications at no runtime cost but significantly greater realism. Furthermore, any realtime impact can be projected onto our modes to obtain impact-dependent fracture patterns without the need for any online crack propagation simulation. We not only introduce this theoretically novel concept, but also show its fundamental and practical superiority in a diverse set of examples and contexts.

翻译：与研究周密的振动或弹性模式直接类比,我们引入了物体的断裂模式,这些模式是其首选或最自然的断裂方式。我们形成了一个被封闭的乙基值问题,我们通过迭代解决,以获得n最低的能量模式。这些可以预告给特定形状的形状,以获得一种可以取代艺术状态的裂缝模式,在不花费运行成本但大大更大的现实主义条件下实时应用。此外,任何实时影响都可以投射到我们的模式上,以获得依赖撞击的断裂模式,而不需要任何在线的裂缝传播模拟。我们不仅引入了这个理论上的新概念,而且还在多种例子和背景中展示了其基本和实际优势。