Figure 2.

Graphic illustration of (a) stereographic projection and (b) parallel transport. In panels (a) and (b), N and O denote the north pole (0, 0, 1) and the origin (0, 0, 0), respectively, and the red dash lines are the x, y, and z-axes. In panel (a), the red point (u, v, −1) is a selected point on the plane z = −1 and the green point $T_{\mathit{\text{st}};{(0,0,1)}^T}^{-1}((u,v,-1))$ is the inverse map of the stereographic projection mapping from (u, v, −1) back to S². In panel (b), the point A is on S², L_A(s) is in T_AS², and R_A,NL_A(s) ∈ T_NS² is the parallel transport of L_A(s) from A to the north pole N.