2014/12/22 by Jian Sun, Tianqi Wu, Sun, Jian +5
Computer Science · Engineering · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences
paper · pdf · doi:10.48550/arxiv.1412.6892
openalex publication_date 2014/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce a definition of discrete conformality for triangulated surfaces with flat cone metrics and describe an algorithm for solving the problem of prescribing curvature, that is to deform the metric discrete conformally so that the curvature of the resulting metric coincides with the prescribed curvature. We explicitly construct a discrete conformal map between the input triangulated surface and the deformed triangulated surface. Our algorithm can handle the surface with any topology with or without boundary, and can find a deformed metric for any prescribed curvature satisfying the Gauss-Bonnet formula. In addition, we present the numerical examples to show the convergence of our discrete conformality and to demonstrate the efficiency and the robustness of our algorithm.