A novel approach to generating microstructurally-aware non-convex domains

We present a novel methodology for generating synthetic microstructures in non-convex domains. Simple techniques that include mapping, point identification, divide and map, clockwise and counter-clockwise ordering of vertices, approximate convex decomposition and stitching are proposed to realize tessellated non-convex geometries, both in two- and three-dimensions. A tessellated convex domain is used as a reference for mapping of either simply or multiply connected non-convex geometries that are difficult to generate through simple cut operations using geometric primitives. Subroutines are developed in MATLAB for mapping the tessellations. The developed routines are also capable of generating geometry files that allow in further discretization or meshing of the tessellated domain. We present several case studies in two- and three-dimensions to demonstrate the robustness of the tool developed and highlight the unique capabilities of the proposed methodology in handling non-convex internal and external boundaries of the domain to be mapped.