I had fun with this one, for other examples of people doing Stereographic Projection, I highly recommend https://www.thingiverse.com/threonin/. His stuff is amazing and I love it.

This is a writeup of how to use this OpenSCAD design using dxf files.

• I have only tested this on a square pattern, but there's no reason it has to be square, it could be rectangular or circular as well.

Instructions

1. Find a black and white* pattern that you want to vectorize. Its easier if there aren't many grays. This step is skippable if you already have a monochrome vector pattern.
   • I just googled "black and white pattern".
   • Save the pattern to your computer.
2. Inkscape Directions
   1. Open a new file in Inkscape (0.92) and *import* the imagefile. Don't 'Open', it can crash Inkscape. (png is good, jpeg is less good)
   2. Use the Menu -> Path -> Trace Bitmap tool.
      1. Make sure the image is selected or the tool wont work.
      2. I used the "Brightness Cutoff" option, Threshold: 0.45, You will want to play with these options to see what works best for your pattern.
      3. The new pattern is dropped ontop of, or underneath the original image, so you need to drag it off the imported bitmap image.
      4. You can tell which is which by typing F2 to select the edit pathnodes tool. The one with paths is the one you want. Delete the other one.
      5. Next we need to break up the paths into small pieces with the Menu -> Extensions -> Modify Path -> Flatten Beziers.
      6. This breaks the curved lines up into bite-sized pieces because OpenSCAD does not like dxf splines. If you have curves, this step is not optional.
      7. The smaller the "Flatness" variable, the more segments, so I used '0.1'. If you pick numbers greater than 1, you're likely to see chunky, rather than smooth shapes.
      8. Verify it by hitting F2 again, and then save the file to svg. (thats Inkscape's native format)
      9. Resize the Page by Menu -> File -> Document Properties
         1. Its important to have a page size that fully encompasses the pattern. Inkscape will cut off things that aren't on the page.
         2. I sized the page to exactly the size of the pattern, in px.
         3. Then I used the Menu -> Object -> Transform tool to (uncheck 'Relative') Move it exactly to (0,0)
      10. You can check the Layer name from Menu -> Layer -> Layers... For my scad-file you want it to be "Layer 1".
      11. Then SaveAs filetype .dxf
      12. Once you click OK, it will ask you about how you want to save it, Uncheck the ROBO-Master option, and Check the LWPOLYLINE option. I left it defaulted to base unit of pt, but using mm makes sense too.
3. OpenSCAD
   1. When importing, OpenSCAD reads from the same directory that the scad file is in, but you can also use a full filepath. I was impatient, so my example assumes the dxf is sitting in the same directory as it.
   2. Its very helpful to know the size of the original image.
   3. I left helpful comments in the code to show you which variables to modify with what information.

Feel free to take out the Support Legs, if they are a bad fit for your pattern.

Also, this took literally 35 minutes to compile the stl, so be prepared.