Quad-Dominant Mesh Adaptation Using Specialized Simplicial Optimization

The proposed quad-dominant mesh adaptation algorithm is based on simplicial optimization. It is driven by an anisotropic Riemannian metric and uses specialized local operators formulated in terms of an L∞ instead of the usual L2 distance. Furthermore, the physically-based vertex relocation operator includes an alignment force to explicitly minimize the angular deviation of selected edges from the local eigenvectors of the target metric. Sets of contiguous edges can then be effectively interpreted as active tensor lines. Those lines are not only packed but also simultaneous networked together to form a layered rectangular simplicial mesh that requires little postprocessing to form a cubical-dominant one. Almost all-cubical meshes are possible if the target metric is compatible with such a decomposition and, although presently only two-dimensional tests were performed, a three-dimensional extension is feasible.