Guaranteed-quality all-quadrilateral mesh generation with feature preservation

Abstract

In this paper, a quadtree-based mesh generation method is described to create guaranteed-quality, geometry-adapted all-quadrilateral (all-quad) meshes with feature preservation for arbitrary planar domains. Given point cloud, our method generates all-quad meshes with these points as vertices and all the angles are within [45°, 135°]. For given planar curves, quadtree-based spatial decomposition is governed by the curvature of the boundaries and narrow regions. 2-refinement templates are chosen for local mesh refinement without creating any hanging nodes. A buffer zone is created by removing elements around the boundary. To guarantee the mesh quality, the angles facing the boundary are improved via template implementation, and two buffer layers are inserted in the buffer zone. It is proved that all the elements of the final mesh are quads with angles between 45° ± ε and 135° ± ε ( ε ≤ 5°) with the exception of badly shaped elements that may be required by the sharp angles in the input geometry. We also prove that the scaled Jacobians defined by two edge vectors are in the range of [ sin(45° − ε), sin90°], or [0.64, 1.0]. Furthermore, sharp features and narrow regions are detected and preserved automatically. Boundary layer meshes are generated by splitting elements of the second buffer layer. We have applied our algorithm to a set of complicated geometries, including the Lake Superior map and the air foil with multiple components.