Interactive cutting and tearing in projective dynamics with progressive cholesky updates

We propose a new algorithm for updating a Cholesky factorization which speeds up Projective Dynamics simulations with topological changes. Our approach addresses an important limitation of the original Projective Dynamics, i.e., that topological changes such as cutting, fracturing, or tearing require full refactorization which compromises computation speed, especially in real-time applications. Our method progressively modifies the Cholesky factor of the system matrix in the global step instead of computing it from scratch. Only a small amount of overhead is added since most of the topological changes in typical simulations are continuous and gradual. Our method is based on the update and downdate routine in CHOLMOD, but unlike recent related work, supports dynamic sizes of the system matrix and the addition of new vertices. Our approach allows us to introduce clean cuts and perform interactive remeshing. Our experiments show that our method works particularly well in simulation scenarios involving cutting, tearing, and local remeshing operations.