A system for creating a rectangular-cuboid periodic matrix for rendering a variable density 3D print is described. This is important for applications where the interior of manufactured objects require less material or weight while still maintaining strength. The matrix elements are grown from a line-based skeleton lattice using a "Line Dilation Algorithm". The method is computationally efficient allowing the design of large matrices to match the resolution and aspect ratio of the 3D printer. A voxel-based halftone model uses the resulting threshold arrays, allowing continuously varying densities. While the method is quite general, the very strong tetrahedral-octahedral lattice is detailed; rendering this triangular structure is made possible by reducing it to a simple rectangular period. Also, rendering constraints preserve structural integrity for multiscale lattices by guaranteeing strut-to-strut connectivity.