Nonobtuse Meshes with Guaranteed Angle Bounds

High-quality mesh representations of 3D objects are useful in many applications ranging from computer graphics to mathematical simulation. We present a novel method to generate triangular meshes with a guaranteed face angle bound of [30, 90]. The strategy is to first remesh a 2-manifold, open or closed, mesh into a rough approximate mesh that respects the proposed angle bounds. This is achieved by a novel extension to the Marching Cubes algorithm. Next, we perform an iterative constrained optimization, along with constrained Laplacian smoothing, to arrive at a close approximation of the input mesh. A constrained mesh decimation algorithm is then carried out to produce a hierarchy of coarse meshes where the angle bounds are maintained. We demonstrate the quality of our work through several examples.