Question

Formula stereographic projection vector form

Answer 1

We can choose coordinates (x,y,z) so that the plane has equation z = 0; the sphere E is the sphere with radius 1 and center (0,0,0); and N = (0,0,1). Given Q = (u, v, 0) in the plane, the inverse stereographic projection is the point P that is the intersection (different from N) of line NQ with the sphere.