Fast Mean‐Curvature Flow via Finite‐Elements Tracking

In this paper, we present a novel approach for efficiently evolving meshes using mean‐curvature flow. We use a finite‐elements hierarchy that supports an efficient multigrid solver for performing the semi‐implicit time‐stepping. Although expensive to compute, we show that it is possible to track this hierarchy through the process of surface evolution. As a result, we provide a way to efficiently flow the surface through the evolution, without requiring a costly initialization at the beginning of each time‐step. Using our approach, we demonstrate a factor of nearly seven‐fold improvement over the non‐tracking implementation, supporting the evolution of surfaces consisting of 1M triangles at a rate of just a few seconds per update.