[droddktk] Square tilings

There exist some discrete angles and de-magnifications for which rotating and scaling a raster image is easy (not requiring bilinear or bicubic), for example, a tiling of 5 pixels in the shape of a cross, which corresponds to a rotation of a knight's move: arctan(2).

Obviously, all the NxN square tiles with rotation in 90 degree increments.

A brick-pattern domino tiling can achieve 45 degrees, but seems anisotropically weird.  Overlapping 2x2 blocks or overlapping 5-square pixels seem better.

Arctan 3 wants to average over a region of area 10. The area goes by Pythagoras's theorem.

Once we allow weighted averages, any angle and scale are possible; however, all pixels are treated the same only with rational rotations (but any translation). There is the somewhat messy problem of the area of intersection between overlapping squares, though perhaps it can be solved more elegantly than the rectangle case. Free translation suggests an interesting experiment of subpixel jittering of an image. What does it look like?

Maybe related to Laplacian kernels, the sinc function.

Carina