Brandon T: These are _very_ hard to rotate as they are created in three point perspective, with the distortion it brings, in contrast to Echochrome which has levels displayed in parallel projection specifically to avoid that distortion.
(http://en.wikipedia.org/wiki/Perspective_projection_distortion)

Ben Eshbach: The perspective grid in the background actually differs for each piece. It is created after the figure is finished from the used perspective points and is not a premade graph paper used in the actual creation process. Dick Termes includes a number of perspective grids in his Book On Perspective Drawing, but you have to buy it for $10.
(http://www.termespheres.com/perspective.html)

Thank you Neatorama for posting my blog, and thanks for the comments!