Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
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Modeling of the soap film for a given boundary curve, called Plateau's problem, is identical with constructing the surface of minimal area. Since mathematicians have dealt with this topic in 19th century, two methods have been widely used to solve the minimal surface problem. The first algorithm originated with solving the linear Dirichlet problem in [Pinkall and Polthier 1993], and another approach in [M. Desbrun 1999] was to evolve the surface via mean curvature flow. In order to describe the deformation of soap film based on dynamics, however, it is required to consider its physical properties as well as geometric properties. In this paper, we propose a physics-based model for the deformation of soap film through discrete differential geometry. It shows robust results for given boundaries as inputs.