An impossible object

digital sundial

Every day brings new wonders, and this one belonged to the special category of things that are marginally useful, prodigiously clever¹, totally novel and intensely nerdy: the Digital Sundial. I encountered it on LinkedIn, a website I am signed up to and detest (I call it HR porn). It is a version of the classical sundial where the gnomon is artfully hollowed out so that light passing through it casts a pattern of sunlit dots that gives the time in numbers. In order for it to work, the gnomon has to be internally carved in a very precise 3D pattern of small slats that select which dot will be lit up as the sun moves through the sky. It was invented by French engineer Julien Coyne and is a marvel of ingenuity and mathematics. It is also the first object I own that can only be made with a 3D printer, because no machining or casting could reproduce the intricate internal structure. The marvellousness of it all was compounded by the fact that I read about it while sipping much-maligned retsina wine at Athens airport, downloaded the 3D model and fed it remotely to my 3D printer in the UK, to find it ready to play with on arrival. We live in wonderful times.

1. From Claude: “Julien Coyne, the maker behind Mojoptix, built his digital sundial as a parametric CAD model rather than deriving it analytically: he quantized time into 20-minute steps from 10:00 to 16:00, defined the four-digit numeral that should appear at each step, and for every pixel that needed to be lit he computed the sun’s ray direction at that moment and bored a long, thin square channel through a solid block aligned to that ray, positioned so light entering along it exits at the correct spot in the cast shadow. Because a parametric CAD program could create the intricate 3D model of the gnomon with a few lines of code repeated for each desired sun angle and for each “pixel” defining the projected digits, the object was trivial to generate but hard to make any way other than 3D printing. Each channel is deep and narrow, so it transmits only when the sun is within a small angle of its axis; the block minus the union of all those angled channels therefore spells a different number as the sun moves, resolving into 16 slots that each form a column of up to six pixels. He released the printable files on Thingiverse, and the North American Sundial Society flagged the main limitation: the light tunnels are placed too close together, giving an entrance angle of only ±15°, while the sun annually moves ±23.5°, so the digits degrade away from the declination the tunnels were tuned for.”