Conformal Surface Parameterization Using Euclidean Ricci Flow

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. Ricc i flow is a theoretic tool to compute such a conformal flat metric. This paper introduces an efficient and versatile parame terization algorithm based on Euclidean Ricci flow. The algorithm can parameterize surfaces with different topologi cal 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.

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