The Unified Surface Ricci Flow

摘要: Ricci flow deforms the Riemannian metric proportionally to curvature, such that curvature evolves according a heat diffusion process and eventually becomes constant everywhere. has demonstrated its great potential by solving various problems in many fields, which can be hardly handled alternative methods so far. This work introduces unified theoretic framework for discrete Surface Flow, including all common schemes: Thurston's Circle Packing, Tangential Inversive Distance Packing Discrete Yamabe. Furthermore, this also novel scheme, virtual radius circle packing, under framework. This gives explicit geometric interpretation energy schemes, Hessian of schemes with Euclidean back ground geometry. The frame deepen our understanding surface theory, inspired us discover new improved flexibility robustness algorithms, greatly simplified implementation debugging efficiency. Experimental results shows algorithms handle general surfaces different topologies, is robust meshes qualities, effective real problems.