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Hexagonal, equivalently, equilateral triangular tessellations indeed have many advantages over using squares. Your scheme reminded me of Delaunay triangulation and its dual, Voronoi tessellation.

I have a faint suspicion that your familiarity with finite element models had something to do with your choice of triangles.

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Triangles are used by game engines for good reason. Hexagonal cannot be mapped without discontinuities. Equilateral triangles are not necessary.

I've done finite element models, but they were pretty unsophisticated.

That's right, simplicial complexes of the right dimension would give one the most fidelity in terms of continuity. Triangles happen to be the one for 2D. For 3D one would get similar benefits using tetrahedra.

I was alluding the fact that barring boundary effects hexagonal tessellation and equilateral tessellation are essentially the same.

The method actually reminds me of a simple h-refinement scheme for FEM.

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