Lay Tracks : New approach to automated quadrilateral mesh generation using MAT

Abstract

This thesis describes Lay Tracks, a new mesh generation algorithm to automatically generate an all quad mesh using the medial axis transform (MAT). LayTracks combines the merits of two popular direct techniques for quad mesh generation - Quad meshing by decomposition and Advancing front quad meshing. The algorithm uses the medial axis transform to both decompose the region using branch points and to lay rails across an arbitrary set of connected planar patches. Each rail starts from a node on the boundary and propagates towards the MA and then from the MA towards the boundary. This process of propagation of rails subdivides the set of planar patches into connected set of Corridors. Corridors are further subdivided into Tracks. Quadrilateral nodes are then placed on rails and connecting them inside each track results in quadrilateral elements. Spacing between the rails of tracks and between the quadrilateral nodes on the rails are fixed by the width of quadrilateral element. The medial axis serves as the natural termination for the propagation of both the rail and the mesh. Merging of non-quad elements at the medial axis and concave vertex results in all quad mesh. The algorithm has been implemented and used to generate an all quad mesh on a set of connected planar patches in 3-D space. Adaptive quadrilateral mesh on single patch is generated by varying the distance between the rails i.e. width of the track, based on the radius function. Extension of this technique to generate hexahedral meshing is discussed.