Paper Info
Title
Area-preserving mesh parameterization for poly-annulus surfaces based on optimal mass transportation.
Abstract
This work proposes a novel method for computing area-preserving parameterization for genus zero surfaces with multiple boundaries (poly-annuli), which is based on discrete optimal mass transportation and surface Ricci Flow. We first begin with a conformal mapping (which may greatly distort area) by Ricci Flow and then correct the area distortion using the mass transport procedure via a convex optimization. The method is intrinsic and stable, and the resulting parameterization preserves area element and minimizes angle distortion. Comparing with existing algorithms, our method is more general and flexible. It can handle surfaces with more complicated topology, and gives users full control of the target measure, such as the areas of the holes. We have tested the method for applications in various fields. Our experimental results demonstrate the efficiency and efficacy of the proposed method. Area-preserving parameterization handles genus 0 surfaces with multiple boundaries.The mapping is diffeomorphic and unique under normalization.The mapping is invariant under conformal transformations.The number of unknown variables is reduced from O ( n 2 ) to O ( n ) .
Year
DOI
Venue
2016
10.1016/j.cagd.2016.05.005
Computer Aided Geometric Design
Keywords
Field
DocType
Area-preservation mapping,Multi-holed surface,Surface flattening,Optimal transport mapping,Ricci flow
Ricci flow,Topology,Mathematical optimization,Parametrization,Mesh parameterization,Conformal map,Invariant (mathematics),Convex optimization,Distortion,Mathematics,Diffeomorphism
Journal
Volume
Issue
ISSN
46
C
0167-8396
Citations 
PageRank 
References 
8
0.48
31
Authors
7
Name
Order
Citations
PageRank
Kehua Su1151.04
Li Cui2252.92
Kun Qian380.48
Na Lei45115.99
Junwei Zhang5469.28
Min Zhang6100.84
Xianfeng Gu72997189.71