Abstract:Discrete conformal structure on polyhedral surfaces is a discrete analogue of the smooth conformal structure on surfaces that assigns discrete metrics by scalar functions defined on vertices. It unifies and generalizes tangential circle packing, Thurston's circle packing, inversive distance circle packing and the vertex scaling on polyhedral surfaces. In this paper, we introduce combinatorial α-curvature for discrete conformal structures on polyhedral surfaces, which is a parameterized generalization of the cl… Show more
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