2021/04/09 by Marcel Campen, Ryan Capouellez, Campen, Marcel +9 · 1 citation
Computer Science · Engineering · #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #Graphics (cs.GR) #Image Processing and 3D Reconstruction #Robotics and Sensor-Based Localization
paper · pdf · doi:10.48550/arxiv.2104.04614
openalex publication_date 2021/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe an efficient algorithm to compute a conformally equivalent metric for a discrete surface, possibly with boundary, exhibiting prescribed Gaussian curvature at all interior vertices and prescribed geodesic curvature along the boundary. Our construction is based on the theory developed in [Gu et al. 2018; Springborn 2020], and in particular relies on results on hyperbolic Delaunay triangulations. Generality is achieved by considering the surface's intrinsic triangulation as a degree of freedom, and particular attention is paid to the proper treatment of surface boundaries. While via a double cover approach the boundary case can be reduced to the closed case quite naturally, the implied symmetry of the setting causes additional challenges related to stable Delaunay-critical configurations that we address explicitly in this work.