Browsing by Author "Gu, Xianfeng"

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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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    Polycube Shape Space
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Zhao, Hui; Li, Xuan; Wang, Wencheng; Wang, Xiaoling; Wang, Shaodong; Lei, Na; Gu, Xianfeng; Lee, Jehee and Theobalt, Christian and Wetzstein, Gordon
    There are many methods proposed for generating polycube polyhedrons, but it lacks the study about the possibility of generating polycube polyhedrons. In this paper, we prove a theorem for characterizing the necessary condition for the skeleton graph of a polycube polyhedron, by which Steinitz's theorem for convex polyhedra and Eppstein's theorem for simple orthogonal polyhedra are generalized to polycube polyhedra of any genus and with non-simply connected faces. Based on our theorem, we present a faster linear algorithm to determine the dimensions of the polycube shape space for a valid graph, for all its possible polycube polyhedrons. We also propose a quadratic optimization method to generate embedding polycube polyhedrons with interactive assistance. Finally, we provide a graph-based framework for polycube mesh generation, quadrangulation, and all-hex meshing to demonstrate the utility and applicability of our approach.