Geometric Compression Based on Ricci Flow and Monge-Ampere Equation

Bella Gu International School of Boston

S.-T. Yau High School Science Awarded Papers mathscidoc:1702.35012

Geometric compression plays a fundamental rolein virtual reality and augmented reality (VR/AR) applications. Dense meshesare re-sampled and re-tessellatedtoreduce thecomplexity. This process is called remeshing. In this work,we propose a novel remeshing algorithm based on both angle-preservingparameterization, and measurecontrollable parameterization. The conformal parameterization iscarried out by discrete surface Ricci flow method, the measurecontrollable parameterization is obtaind by an optimal mass transportation map. The sampling is performed on the measurecontrollable parameterization domain, the triangulation is computed on the conformal parameterization domain using Delaunay refinement algorithm. This method gives the user full control of sampling distribution, and produces mesheswith curvature measure convergence. The meshing resultcan emphsizethe region of interests, is curvature sensitive. Experimental results demonstrate the efficiency and efficacy of the proposed method.
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  title={Geometric Compression Based on Ricci Flow and Monge-Ampere Equation},
  author={Bella Gu},
Bella Gu. Geometric Compression Based on Ricci Flow and Monge-Ampere Equation. 2016.
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