LayTracks: a new approach to automated geometry adaptive quadrilateral mesh generation using medial axis transform

Abstract

SUMMARYA new mesh generation algorithm called 'LayTracks', to automatically generate an all quad mesh that is adapted to the variation of geometric feature size in the domain is described. LayTracks combines the merits of two popular direct techniques for quadrilateral mesh generation-quad meshing by decomposition and advancing front quad meshing. While the MAT has been used for the domain decomposition before, this is the first attempt to use the MAT, for the robust subdivision of a complex domain into a well defined sub-domain called 'Tracks', for terminating the advancing front of the mesh elements without complex interference checks and to use radius function for providing sizing function for adaptive meshing. The process of subdivision of a domain is analogous to, formation of railway tracks by laying rails on the ground. Each rail starts from a node on the boundary and propagates towards the medial axis (MA) and then from the MA towards the boundary. Quadrilateral elements are then obtained by placing nodes on these rails and connecting them inside each track, formed by adjacent rails. The algorithm has been implemented and tested on some typical geometries and the quality of the output mesh obtained are presented. Extension of this technique to all hexahedral meshing is discussed.

Enhanced medial-axis-based block-structured meshing in 2-D

“…A method with some similarities to the presented method is LayTracks [23]. Its strategy for mesh generation is fundamentally different to decomposition based methods -it uses the medial axis to generate a mesh directly as opposed to of using it to infer mesh properties and with that information create a decomposition.…”

The receding front method applied to hexahedral mesh generation of exterior domains

“…A geometrical guide is provided by the medial axis, which is used to align and layer the elements according to the shape of the domain [27][28][29][30][31][32]. Instead of using the geometrical description of the medial axis as a guide, we propose to use the level sets of a scalar field.…”

Isotropic 2D Quadrangle Meshing with Size and Orientation Control

“…Including methods devised to generate quadrangle surface tilings, the rich literature on this topic contains approaches which proceed by quadrangulation [9,3], square packing [28], advancing front [22], conversion [8], decimation [18], Morse-Smale complexes [14,33,17], clustering [4,20], local and global operators [23,19], whisker weaving [32], medial axis [24], streamlining [1,21] and parameterization [25,29,7].…”