Customizable stereographic projection

prusaprinters

<p>I made a customizable version of henrysegs ingenious design that uses stereographic projection to project a grid from a sphere to a plane: <a href="https://www.thingiverse.com/thing:202774">http://www.thingiverse.com/thing:202774</a></p> <p>You can simply upload an image with the size of 75x75 and it will be projected on a sphere and back again when a light source is added to the north pole.</p> <p>There are some things to consider: You need to check if pixels are touching in just one point that lie diagonally to each other, this will result in failure to produce a manifold mesh, look at the illustration in the gallery. Black pixels indicate where material is added, so make sure all are connected, white pixels represent holes. I uploaded the input to generate the examples along the results rendered in blender, this should show how this works. (I uploaded zipped versions because Thingiverse resizes all images no matter what)</p> <p>The level of detail is limited by the thickness of the walls, the thinner they are, the more detail will show up. In the center more detail can be displayed than on the border.</p> <p>The examples may be a little to fragile to print, but they show the principle very nicely.</p> <p>The theory is described here: <a href="http://en.wikipedia.org/wiki/Stereographic_projection">http://en.wikipedia.org/wiki/Stereographic_projection</a></p> <p>Edit:</p> <p>Revised version which incorporates henrysegs tip and produces cleaner projections is here: <a href="https://www.thingiverse.com/thing:295281">http://www.thingiverse.com/thing:295281</a></p> <p>Edit2: Minor bug with the outer borders fixed. This version now also uses 75x75 pixels, as 150x150 doesn't work with the customizer.</p> <p>If you need bigger versions you can do it locally with OpenScad and this script: <a href="http://jsfiddle.net/threonin/3j2c2pwe/">http://jsfiddle.net/threonin/3j2c2pwe/</a></p> Category: Math Art