Is it possible to build a metal wire sphere whose shadow projects the 2d conformal maps of the Riemann Sphere on a flat wall?

Question

Is it possible to build a metal wire hollow sphere whose shadow from a nearby point light source projects the 2d conformal maps of the Riemann Sphere on a flat wall?

I believe that in theory it should be possible, but I was not sure if there would be any physical impracticabilities that would limit such a shadow project.

Answer 1

This can be done. For example, see

https://www.shapeways.com/model/1480313/grid-stereographic-projection.html

The technical name for this way of "casting shadows" is called stereographic projection. See

• https://www.youtube.com/watch?v=0z1fIsUNhO4
• https://www.youtube.com/watch?v=6JgGKViQzbc
• http://en.wikipedia.org/wiki/Stereographic_projection
• http://mathworld.wolfram.com/StereographicProjection.html
• http://www.ams.org/samplings/feature-column/fc-2014-02

and so on.