Extrusion invariance of a ternary triangular scheme ($b_j={\sum }_{i\equiv 0(\mathrm{mod}3)}{a}_{i,j}={\sum }_{i\equiv 1}{a}_{i,j}={\sum }_{i\equiv 2}{a}_{i,j}$)

If a triangular-lattice subdivision mask has the displayed residue-sum equality, refining data $p_{i,j}=q_j$ gives $p_{I,J}^{\prime }={\sum }_k{b}_{J-3k}{q}_k$, independent of $I$. If affine coordinates reproduce their parameter positions, a geometrically straight extrusion is preserved. Rotationally symmetric masks give the corresponding property in all three lattice-edge directions. A boundary curve compatible with this extrusion uses the collapsed mask $b$, not just the central row of the two-dimensional mask.