
# The exponential map on the sphere

The exponential map on the sphere $\mathbb S^n$ is given for $x\in\mathbb S^n$ and $\xi\in T_x{\mathbb S^n}$ by the formula

### Matlab Documentation

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 % y = exp(x,xi) exponential map at x with direction xi in TxM % % INPUT % x : a point or set of points on the manifold S2 % xi : a point or set of point in the tangential spaces TxM % % OPTIONAL: % t : [] following the geodesics for one time step % a scalar following the geodesics for time t % a set of t following each geodesic_i for time t_i % % OUTPUT % y : resulting point(s) on S2 % --- % Manifold-Valued Image Restoration Toolbox 1.0, R. Bergmann ~ 2014-10-19