For holiday gifts we decorated several travel mugs with illustrations of proteins such as Ξ±-hemolysin:

The task of placing this on the surface of a mug poses some tricky questions. Typically when projecting a 3d object onto a flat surface there's only one vantage point, so the transformation is intuitive. The surface of the mug, however, is looking at the 3d object from an omniscient, 360Β° inward-facing perspective. How do you represent what an object looks like from every direction?

I answered this by considering one vertical slice of the mug at a time. Just as a flatbed scanner constructs an image by scanning a sensor across a document, the mug's perspective can be constructed by scanning a vertical sliver of a rotating protein.

The result is peculiar, and easily misleading since the rear half, which appears to move the opposite direction from the front, is effectively scanned in reverse. To address that I first rendered only the front:

cylindrical projection of Ξ±-hemolysin (7AHL)

I like to imagine this as an β€œunwrapping” of the conveniently hollow protein.

To complete the effect I separately rendered the rear half in reverse, recomposed the two projections, and finally distorted the illustration to fit the actually truncated-conical mug:

truncated conical travel mug design