Browsing by Author "Gortler, Steven J."

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    Mesh Parameterization: a Viewpoint from Constant Mean Curvature Surfaces
    (The Eurographics Association, 2018) Zhao, Hui; Su, Kehua; Li, Chenchen; Zhang, Boyu; Liu, Shirao; Yang, Lei; Lei, Na; Gortler, Steven J.; Gu, Xianfeng; Fu, Hongbo and Ghosh, Abhijeet and Kopf, Johannes
    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.
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    Mesh Parametrization Driven by Unit Normal Flow
    (© 2020 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2020) Zhao, Hui; Su, Kehua; Li, Chenchen; Zhang, Boyu; Yang, Lei; Lei, Na; Wang, Xiaoling; Gortler, Steven J.; Gu, Xianfeng; Benes, Bedrich and Hauser, Helwig
    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.