An algorithm for two-dimensional mesh generation based on the pinwheel tiling
Pritam Ganguly, Stephen A. Vavasis, Katerina D. Papoulia
TL;DR
The paper tackles the challenge of generating 2D meshes that force crack paths to align with mesh boundaries so that edge-path distances approximate true fracture paths. It introduces the PINW mesh generator, built on a generalized subdivision of the $1:2$ pinwheel tiling to arbitrary triangles, and defines a deviation ratio to quantify path accuracy. The authors prove that the generalized tiling preserves an isoperimetric property and present an algorithm to convert a tiling into a mesh with controlled element quality, establishing bounded aspect ratio. This approach enables more accurate cohesive interface finite element simulations by ensuring crack propagation paths converge to the true path under mesh refinement, with practical impact for fracture modeling.
Abstract
We propose a new two-dimensional meshing algorithm called PINW able to generate meshes that accurately approximate the distance between any two domain points by paths composed only of cell edges. This technique is based on an extension of pinwheel tilings proposed by Radin and Conway. We prove that the algorithm produces triangles of bounded aspect ratio. This kind of mesh would be useful in cohesive interface finite element modeling when the crack propagation pathis an outcome of a simulation process.