Simulating the kinematics of completely faceted surfaces

We fully generalize a previously-developed computational geometry tool [1] to perform large-scale simulations of arbitrary 2 + 1D faceted surfaces z = h(x, y). The method is an explicit front-tracking scheme that uses a compact, three-component facet/edge/junction storage mode. Because it naturally mirrors the intrinsic surface structure, this scheme allows both rapid simulation of large ensembles, and easy extraction of geometrical statistics. To do so, it must overcome the barrier of detecting and resolving a wide variety of topological changes that occur during surface evolution. However, while the variety of topological events is larger than in the case of 2D cellular networks, it is still limited, and our main result is a comprehensive algorithm performing these changes in the code.