Conformal Mesh Parameterization Using Discrete Calabi Flow

TL;DR

This paper introduces a novel conformal mesh parameterization algorithm based on discrete Calabi flow, offering a new perspective and solid theoretical foundation, with performance comparable to existing flow-based methods.

Contribution

The paper presents the first application of discrete Calabi flow to mesh parameterization, providing a new mathematically grounded approach in graphics.

Findings

The method is theoretically sound with proven convergence under certain conditions.

Experimental results on various models show comparable performance to Ricci flow and CETM.

Provides a new perspective on conformal flow in mesh parameterization.

Abstract

In this paper, we introduce discrete Calabi flow to the graphics research community and present a novel conformal mesh parameterization algorithm. Calabi energy has a succinct and explicit format. Its corresponding flow is conformal and convergent under certain conditions. Our method is based on the Calabi energy and Calabi flow with solid theoretical and mathematical base. We demonstrate our approach on dozens of models and compare it with other related flow based methods, such as the well-known Ricci flow and CETM. Our experiments show that the performance of our algorithm is comparably the same with other methods. The discrete Calabi flow in our method provides another perspective on conformal flow and conformal parameterization.