f(z) =

Here you see how the stereographic projection of a sphere onto a plane is obtained. For each point on the surface, a ray from the north-pole through this point is constructed. The intersection of the ray with the plane is the projected point (use R to make this ray visible).

If you enter a complex function, it is pulled back through the stereographic projection. Each pixel with complex coordinate z gets the color of the pixel with coordinate f(z). You can select some example functions from the dropdown box.


I:Invert sphere.
R:Show Ray.
C/M:Change the input mode. By pressing C once, you can map a spherical image to the sphere. A further C maps a texture of the earth to the sphere. If you have a spherical camera (such as the Ricoh Theta), then you can use the spherical footage instead with pressing C multiple times. You can also drag and drop your spherical images to this applet and use them as texture.
L:Show (2 pi i)-periodic lines
A/B:Decrease or increase height of sphere.

You can also view, how the world looks like inside the sphere (spherical view)

Applet made with CindyJS. Author: Aaron Montag.