
# The distance on the sphere

The distance on the sphere $\mathbb S^1$ is defined for any $x,y\in\mathbb S^n$, $x$ as the length of a shorter arc connecting them.

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

### Matlab Documentation

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% dist(a,b) computes the length of the smaller arc of a,b on S1
%   also works for arbitrary sized array a and b componentwise
%    INPUT
%        x,y    : 2 point sets on the S1 = [-pi,pi)
%
%    OUTPUT
%        d      : lengths of the shorter arcs between a and b
% ---
% Manifold-Valued Image Restoration Toolbox 1.0, R. Bergmann ~ 2013-10-25 | 2014-10-22