Given a rectangular image, tile it in an equilateral triangular lattice, when the underlying tiling infrastructure can only handle rectangular tiles laid orthogonally with the screen. That is, create a rectangular tile that looks like a triangular tile. This is not too difficult: pad the image to the right dimensions, then duplicate it in a second row (or column) split in half, swapping left and right.
Harder is if the input image is circular (so create a hexagonal close packing), or already a hexagon. These are probably specified as a region within a rectangular image. We probably need to use transparency to compose the tile.
Non-orthogonal angles are possible, but I think only rational slopes.
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