
# 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

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% 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