### Conformal Surface Parameterization Using Euclidean Ricci Flow

Miao Jin, Juhno Kim, Feng Luo, Seungyong Lee, Xianfeng Gu

Technical Report

Surface parameterization is a fundamental problem in
graphics. Conformal surface parameterization is equivalent
to finding a Riemannian metric on the surface, such
that the metric is conformal to the original metric and induces
zero Gaussian curvature for all interior points. Ricci
flow is a theoretic tool to compute such a conformal flat metric.
This paper introduces an efficient and versatile parameterization
algorithm based on Euclidean Ricci flow. The algorithm
can parameterize surfaces with different topological
structures in an unified way. In addition, we can obtain
a novel class of parameterization, which provides a conformal
invariant of a surface that can be used as a surface signature.