
# The logarithmic map on the sphere

The logarithmic map on the sphere $\mathbb S^n$ is defined for $x,y\in\mathbb S^n$, $x$ not antipodal to $y$, by

### Matlab Documentation

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% xi = log(x,y) logarithmic map at x of y.
%
% INPUT
%    x : point or set of (column) points indicating the
%    tangential base points
%    y : point(s) on S2 being put into the tangential plane at
%    their corresponding p
%
% OUTPUT
%    xi : points on the tangential plane at point(s) p
% ---
% Manifold-Valued Image Restoration Toolbox 1.0, R. Bergmann ~ 2014-10-19