420 citations · 1.3k across the 61 of their papers we have counts for
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Decorated discrete conformal equivalence in non-Euclidean geometries
Alexander I. Bobenko, Carl O. R. Lutz
We introduce decorated piecewise hyperbolic and spherical surfaces and discuss their discrete conformal equivalence. A decoration is a choice of circle about each vertex of the sur…
Decorated discrete conformal maps and convex polyhedral cusps
Alexander I. Bobenko, Carl O. R. Lutz
We discuss a notion of discrete conformal equivalence for decorated piecewise euclidean surfaces (PE-surface), that is, PE-surfaces with a choice of circle about each vertex. It is…
Discrete conformal maps and ideal hyperbolic polyhedra
Alexander Bobenko, Ulrich Pinkall, Boris Springborn
We establish a connection between two previously unrelated topics: a particular discrete version of conformal geometry for triangulated surfaces, and the geometry of ideal polyhedr…
Variational principles for circle patterns and Koebe's theorem
Alexander I. Bobenko, Boris A. Springborn
We prove existence and uniqueness results for patterns of circles with prescribed intersection angles in constant curvature surfaces. Our method is based on two new functionals--on…