Geometry of equilibrium curves and surfaces for discrete anisotropic energy

Abstract

In this paper, we propose piecewise linear constant anisotropic mean curvature (CAMC) curves and surfaces based on a variational characterization. These curves (resp. surfaces) are equilibrium for the anisotropic energy amongst continuous piecewise linear variations which preserve the boundary conditions, the simplicial structures, and (in the non-minimal case) the area (resp. volume) to one side of the curves (resp. surfaces). Our discrete CAMC surfaces are a generalization of discrete CMC surfaces defined by the variational principle. We also show a stability result of discrete CAMC surfaces including the result for discrete CMC surfaces.