
# The exponential map on cyclic data

The exponential map on the sphere $\mathbb S^n$ is given by the formula

where $(\cdot)_{2\pi}$ denotes the symmetric modulo operation.

### Matlab Documentation

1
2
3
4
5
6
7
8
9
10
11
12
13
% exp(x,xi) - Exponential map at x with respect to xi in TxS1
%
% INPUT
%   x : a point or set of points on the manifold S1
%   xi : a point or set of point in the tangential spaces TpM
%
% OUTPUT
%   y : resulting point(s) on S1
%
% OPTIONAL
%   t : shorten xi by a factor.
% ---
% Manifold-Valued Image Restoration Toolbox 1.0, R. Bergmann ~ 2014-10-19