Discrete conformal maps and ideal hyperbolic polyhedra

DOI10.2140/gt.2015.19.2155zbMath1327.52040arXiv1005.2698OpenAlexW3103304244MaRDI QIDQ2517172

Boris A. Springborn, Alexander Ivanovich Bobenko, Ulrich Pinkall

Publication date: 17 August 2015

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.2698

zbMATH Keywords

polyhedron hyperbolic geometry discrete conformal geometry

Mathematics Subject Classification ID

Three-dimensional polytopes (52B10) General geometric structures on low-dimensional manifolds (57M50) Circle packings and discrete conformal geometry (52C26)

Related Items

Book Review: Ricci flow for shape analysis and surface registration: theories, algorithms and applications ⋮ Rigidity of inversive distance circle packings revisited ⋮ A new class of discrete conformal structures on surfaces with boundary ⋮ Discrete Riemann surfaces: linear discretization and its convergence ⋮ Discrete Conformal Deformation: Algorithm and Experiments ⋮ Discrete differential geometry. Abstracts from the workshop held March 1--7, 2015. ⋮ Isothermic triangulated surfaces ⋮ Comparing shapes of genus-zero surfaces ⋮ Discrete Riemann surfaces based on quadrilateral cellular decompositions ⋮ Combinatorial \(p\)-th Calabi flows for discrete conformal factors on surfaces ⋮ Duality structures and discrete conformal variations of piecewise constant curvature surfaces ⋮ Ideal polyhedral surfaces in Fuchsian manifolds ⋮ The boundary value problem for discrete analytic functions ⋮ Combinatorial Ricci flow on compact 3-manifolds with boundary ⋮ Discrete conformal geometry of polyhedral surfaces and its convergence ⋮ Combinatorial Ricci flows and the hyperbolization of a class of compact 3-manifolds ⋮ Rigidity of the hexagonal Delaunay triangulated plane ⋮ Computing Harmonic Maps and Conformal Maps on Point Clouds ⋮ A simple proof of an isoperimetric inequality for Euclidean and hyperbolic cone-surfaces ⋮ Rigidity of bordered polyhedral surfaces ⋮ Ideal hyperbolic polyhedra and discrete uniformization ⋮ Orthogonal ring patterns in the plane ⋮ Boundary metric of Epstein-Penner convex hull and discrete conformality ⋮ A generalized combinatorial Ricci flow on surfaces of finite topological type ⋮ Abelian Higgs vortices and discrete conformal maps ⋮ Discrete Yamabe problem for polyhedral surfaces ⋮ Prescribed curvature problem for discrete conformality on convex spherical cone-metrics ⋮ Deformation of discrete conformal structures on surfaces ⋮ 3-dimensional combinatorial Yamabe flow in hyperbolic background geometry ⋮ The convergence of discrete uniformizations for genus zero surfaces ⋮ The Riemann Mapping Theorem and Its Discrete Counterparts ⋮ Dihedral deformation and rigidity ⋮ Computing quasiconformal maps using an auxiliary metric and discrete curvature flow ⋮ Fundamentals of computational conformal geometry ⋮ Rigidity of polyhedral surfaces. III. ⋮ A discrete version of Liouville's theorem on conformal maps ⋮ Volume and rigidity of hyperbolic polyhedral 3‐manifolds ⋮ Convergence of discrete period matrices and discrete holomorphic integrals for ramified coverings of the Riemann sphere ⋮ On the deformation of discrete conformal factors on surfaces ⋮ Infinitesimal conformal deformations of triangulated surfaces in space ⋮ On the deformation of inversive distance circle packings. II ⋮ On the deformation of inversive distance circle packings. III ⋮ Quasiconformal dilatation of projective transformations and discrete conformal maps ⋮ Discrete uniformization of polyhedral surfaces with non-positive curvature and branched covers over the sphere via hyper-ideal circle patterns ⋮ On a combinatorial curvature for surfaces with inversive distance circle packing metrics ⋮ Conformally covariant operators and conformal invariants on weighted graphs ⋮ Weighted Triangulations for Geometry Processing ⋮ Combinatorial Calabi flow on 3-manifolds with toroidal boundary ⋮ Quadratic differentials and circle patterns on complex projective tori ⋮ \(C^\infty \)-convergence of conformal mappings for conformally equivalent triangular lattices ⋮ Three-dimensional right-angled polytopes of finite volume in the Lobachevsky space: combinatorics and constructions ⋮ Discrete Yamabe flows with \(R\)-curvature revisited ⋮ Minimal surfaces from infinitesimal deformations of circle packings ⋮ Computational design and additive manufacturing of periodic conformal metasurfaces by synthesizing topology optimization with conformal mapping ⋮ Variational principles and combinatorial \(p\)-th Yamabe flows on surfaces ⋮ Discrete Conformal Maps: Boundary Value Problems, Circle Domains, Fuchsian and Schottky Uniformization ⋮ Approximation of Conformal Mappings Using Conformally Equivalent Triangular Lattices ⋮ Holomorphic Vector Fields and Quadratic Differentials on Planar Triangular Meshes ⋮ On the deformation of inversive distance circle packings, I ⋮ On the deformation of ball packings ⋮ Combinatorial Calabi flow with surgery on surfaces ⋮ Parameterized discrete uniformization theorems and curvature flows for polyhedral surfaces, II ⋮ Rigidity of infinite hexagonal triangulation of the plane ⋮ Canonical tessellations of decorated hyperbolic surfaces ⋮ Prescribing discrete Gaussian curvature on polyhedral surfaces ⋮ Combinatorial Calabi flows on surfaces with boundary ⋮ Parameterized combinatorial curvatures and parameterized combinatorial curvature flows for discrete conformal structures on polyhedral surfaces

Uses Software

CirclePack

Cites Work