Mesh Parameterization: a Viewpoint from Constant Mean Curvature Surfaces

Zhao, Hui; Su, Kehua; Li, Chenchen; Zhang, Boyu; Liu, Shirao; Yang, Lei; Lei, Na; Gortler, Steven J.; Gu, Xianfeng

Mesh Parameterization: a Viewpoint from Constant Mean Curvature Surfaces

Files

025-028.pdf (11.47 MB)

Date

2018

Authors

Zhao, Hui
Su, Kehua
Li, Chenchen
Zhang, Boyu
Liu, Shirao
Yang, Lei
Lei, Na
Gortler, Steven J.
Gu, Xianfeng

Publisher

The Eurographics Association

Abstract

We present a unified mesh paramterization algorithm for both planar and spheric domains based on mesh deformation. Unlike previous methods, our approach can produce intermediate frames from the original to target meshes. We derive and define a novel geometric flow: unit normal flow(UNF) and prove that if unit normal flow converges, it will deform a surface to a constant mean curvature(CMC) surface, such as plane and sphere. Our method works by deforming meshes of disk topology to planes, meshes of spheric topology to spheres. The unit normal flow we propose also suggests a potential direction for creating CMC surfaces.

        @inproceedings{10.2312:pg.20181272
,
booktitle = {Pacific Graphics Short Papers
},
editor = {Fu, Hongbo and Ghosh, Abhijeet and Kopf, Johannes
},
title = {{Mesh Parameterization: a Viewpoint from Constant Mean Curvature Surfaces
}},
author = {Zhao, Hui and 
Su, Kehua and 
Li, Chenchen and 
Zhang, Boyu and 
Liu, Shirao and 
Yang, Lei and 
Lei, Na and 
Gortler, Steven J. and 
Gu, Xianfeng
},
year = {2018
},
publisher = {The Eurographics Association
},
ISBN = {978-3-03868-073-4
},
DOI = {10.2312/pg.20181272
}
}