A conformal flattening maps a curved surface to the plane without distorting angles—such
maps have become a fundamental building block for problems in geometry processing …

This paper describes a numerical method for surface parameterization, yielding maps that
are locally injective and discretely conformal in an exact sense. Unlike previous methods for …

A notion of discrete conformality for hyperbolic polyhedral surfaces is introduced in this
paper. This discrete conformality is shown to be computable. It is proved that each …

A discrete conformality for polyhedral metrics on surfaces is introduced in this paper. It is
shown that each polyhedral metric on a compact surface is discrete conformal to a constant …

This excellent introduction to topology eases first-year math students and general readers
into the subject by surveying its concepts in a descriptive and intuitive way, attempting to …

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 …

We prove a result on the convergence of discrete conformal maps to the Riemann mappings
for Jordan domains. It is a counterpart of Rodin and Sullivan's theorem on convergence of …

Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the
curvature evolves according to a heat diffusion process and eventually becomes constant …

Let S be the 2-sphere and V⊂ S be a finite set of at least three points. We show that for each
function κ: V→(0, 2 π) satisfying elementary necessary conditions, in each discrete …

In this paper, we present a computational framework for computational design and additive
manufacturing of free-form periodic metasurfaces. The proposed scheme rests on the level …