We present a novel algorithm for efficiently splitting deformable solids along arbitrary piecewise linear crack surfaces in cutting and fracture simulations. The algorithm combines a meshless discretization of the deformation field with explicit surface tracking using a triangle mesh. We decompose the splitting operation into a first step where we synthesize crack surfaces, and a second step where we use the newly synthesized surfaces to update the meshless discretization of the deformation field. We present a novel visibility graph for facilitating fast update of shape functions in the meshless discretization. The separation of the splitting operation into two steps, along with our novel visibility graph, enables high flexibility and control over the splitting trajectories, provides fast dynamic update of the meshless discretization, and allows for an easy implementation. As a result, our algorithm is scalable, versatile, and suitable for a large range of applications, from computer animation to interactive medical simulation.

@Article\{SOG09,
  author       = "Steinemann, Denis and Otaduy, Miguel A. and Gross, Markus",
  title        = "Splitting Meshless Deforming Objects with Explicit Surface Tracking",
  journal      = "Graphical Models",
  volume       = "71",
  year         = "2009",
  url          = "http://gmrv.es/Publications/2009/SOG09"
}