Li, J. Y. S.Zhang, H.Alla Sheffer and Konrad Polthier2014-01-292014-01-2920063-905673-24-X1727-8384https://doi.org/10.2312/SGP/SGP06/235-238Quality meshing in 2D and 3D domains is an important problem in geometric modeling and scientific computing. We are concerned with triangle meshes having only nonobtuse angles. Specifically, we propose a solution for guaranteed nonobtuse remeshing and nonobtuse mesh decimation. Our strategy for the remeshing problem is to first convert an input mesh, using a modified Marching Cubes algorithm, into a rough approximate mesh that is guaranteed to be nonobtuse. We then apply iterative "deform-to-fit" via constrained optimization to obtain a high-quality approximation, where the search space is restricted to be the set of nonobtuse meshes having a fixed connectivity. With a detailed nonobtuse mesh in hand, we apply constrained optimization again, driven by a quadric-based error, to obtain a hierarchy of nonobtuse meshes via mesh decimation.Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling