Numerical Simulations of a Curve Flow Related to Centro-Affine Invariants

Abstract

In this paper, we propose a novel numerical implementation for visualizing the evolutionary process of a curve flow. This flow is an invariant second-order flow in centro-affine geometry. The key of the scheme proposed in this essay is to indirectly obtain the position vector by solving the evolution equation of the support function. Additionally, to improve efficiency, we choose a specific tangential velocity which can eliminate the necessity to update normal angles at each iteration. The reason is that the normal angles do not change over time under this tangential velocity. Finally, we conduct multiple experiments to demonstrate the feasibility and efficiency of our proposed method.