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Constructing Anisotropic Geometric Metrics using Octrees and Skeletons

A three-dimensional anisotropic metric for geometry-based mesh adaptation is constructed from a triangulated domain definition. First, a Cartesian background octree is refined according to not only boundary curvature but also a local separation criterion from digital topology theory. This octree is then used to extract the domain skeleton through a medial axis transform. Finally, an efficient anisotropic metric is computed on the octree using the curvature tensor estimated from the boundary triangulation and the local domain thickness information embedded in the skeleton. Applications to geometric adaptation of overlay meshes used in grid-based methods for unstructured hexahedral mesh generation are also presented.