Dec 13, 2014 | By Kira

Everything old is new again—even when it comes to 3D printing. Mathematician Jason Cole was inspired by a classic technique that goes as far back ancient Greece in order to create beautiful, personalized stereographic light displays.

If you remember this post about stereographic projections, they are basically 2D maps projected from a 3D sphere. Light from a single source hits a three-dimensional shape (the spherical shell) and then produces a two-dimensional image, in this case, a playful shadow pattern on the wall. In the past, however, cartographers and astronomers have used this method to map out the Earth and sky.

The modernized version of this technique, in which light and shadow replace pencil and paper, was devised by mathematicians Henry Segerman, of Oklahoma State University, and Saul Schleimer, of the University of Warwick. Rather than starting with a pattern on a sphere to be mapped, they decided to work backwards, starting with the map and then working out the pattern on the sphere.

On his blog, Cole outlines the complex mathematical procedure that he followed in order to create a 3D printable lampshade. Rather than create a map, he simply wanted to use the same technique to project an arbitrary, decorative pattern onto a globe, which could then be used as a lampshade.

After mapping out the coordinates of his projection, Cole found a floral image on Google, and then used Matlab to binarise it, selecting which parts to keep and which ones to 'cut out' to form the holes in his lampshade, and then transform it from a bitmap image to a 3D-printable vector format.

Original floral patter from Google and the vectorized-version for 3D printing

Once he had a workable mesh, he imported it into Blender to see if it could be printed. Using Blender, he was able to solidify the mesh and add a light source to check the stereographic projection. The result is a superb light show that even the Ancient Greeks would have admired.

Cole also experimented with different geometric patterns and even a graffiti image of a panda. Although he notes that he can only make black and white images using this technique, it could be possible to project onto a sphere made of transparent printed plastic in order to create colour images.

Since he didn't have a 3D printer at the time, Cole uploaded his .blend file containing the models he created onto a Dropbox account, so that interested 3D designers can play around with it and print their own customized lampshades.

Ultimately, it goes to show that with a bit of inspiration, some in-depth mathematical knowledge, and a 3D printer, even ancient mapping techniques can come to life as beautiful stereographic projections.

Posted in 3D Design


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