2012/03/30 by Michael Kazhdan, Jake P. Solomon, Kazhdan, Michael +5
Computer Science · Engineering · Mathematics · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Computer Graphics and Visualization Techniques #Differential Geometry (math.DG) #FOS: Mathematics #math.DG
paper · pdf · doi:10.48550/arxiv.1203.6819
openalex publication_date 2012/03/30 · arxiv created 2012/05/14 · arxiv updated 2012/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work considers the question of whether mean-curvature flow can be modified to avoid the formation of singularities. We analyze the finite-elements discretization and demonstrate why the original flow can result in numerical instability due to division by zero. We propose a variation on the flow that removes the numerical instability in the discretization and show that this modification results in a simpler formulation for both the discretized and continuous formulations. We discuss the properties of the modified flow and present empirical evidence that not only does it define a stable surface evolution for genus-zero surfaces, but that the evolution converges to a conformal parameterization of the surface onto the sphere.