The problem of nonobtuse triangulation has been studied in the 2D domains, however, guaranteed nonobtuse remeshing of curve surfaces is still an open problem. Nonobtuse meshes are desirable in certain situations such as geodesic computations and planar mesh embedding. In this paper, we propose a solution to nonobtuse remeshing and nonobtuse decimation. Our approach utilizes a “deform-to-fit &quot; strategy to solve the remeshing problem. We first construct an initial nonobtuse mesh, via a modified version of the Marching Cubes algorithm, that roughly approximates the input mesh. An iterative constrained optimization is then applied to obtain a high quality approximation of the input mesh. At each iteration, the constraints ensure the output mesh is guaranteed nonobtuse. By making use of quadric-based errors, we iteratively decimate the high-detail nonobtuse mesh in a similar constrained manner to obtain a hierarchy of nonobtuse meshes
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