
# The orthonormal basis in a tangent space

Since the dimension of $\mathbb S^1$ is 1, there is only one direction ($1$), and this direction is along the geodesic, hence the “curvature” is just zero.

### Matlab Documentation

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% [V,k] = TpMONB(p,q) an onb of the tangent space including log_pq
%   since on S1 there is only one direction, this is always
%   included and 1; the curvature coefficients are all zero, since
%   this is always along the geodesic
%
% INPUT
%   p,q : two point(sets) of cyclic data
%
% OUTPUT
%    Xi : basiscolumn matrice(s).
%    k : (optional) curvature coefficients, here all are 0.
% ---
% MVIRT 1.0, R. Bergmann ~ 2018-03-03