Mesh Parametrization Driven by Unit Normal Flow

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

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Based on mesh deformation, we present a unified mesh parametrization algorithm for both planar and spherical domains. Our approach can produce intermediate frames from the original meshes to the targets. We derive and define a novel geometric flow: ‘unit normal flow (UNF)’ and prove that if UNF converges, it will deform a surface to a constant mean curvature (CMC) surface, such as planes and spheres. Our method works by deforming meshes of disk topology to planes, and spherical meshes to spheres. Our algorithm is robust, efficient, simple to implement. To demonstrate the robustness and effectiveness of our method, we apply it to hundreds of models of varying complexities. Our experiments show that our algorithm can be a competing alternative approach to other state-of-the-art mesh parametrization methods. The unit normal flow also suggests a potential direction for creating CMC surfaces.

Original languageEnglish (US)
Pages (from-to)34-49
Number of pages16
JournalComputer Graphics Forum
Issue number1
StatePublished - Feb 1 2020

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design


  • constant mean curvature
  • deformation
  • mesh parametrization
  • rotation
  • unit normal flow


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