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This paper describes a novel method of generating hex-dominant meshes usingpre-computed optimal subdivisions of the unit cube in a grid-based approach.Our method addresses geometries that are standard in mechanical engineering andoften must comply with the restrictions of subtractive manufacturability. Acentral component of our method is the set of subdivisions we pre-compute withAnswer Set Programming. Despite being computationally expensive, we obtainoptimal meshes of up to 35 nodes available to our method in a template fashion.The first step in our grid-based method generates a coarse Precursor Mesh formeshing complete parts representing the bar stock. Then, the resulting mesh isgenerated in a subtractive manner by inserting and fitting the pre-generatedsubdivisions into the Precursor Mesh. This step guarantees that the elementsare of good quality. In the final stage, the mesh nodes are mapped to geometricentities of the target geometry to get an exact match. We demonstrate ourmethod with multiple examples showing the strength of this approach.

Combinatorial Methods in Grid based Meshing