$\DeclareMathOperator{\arccosh}{arccosh} \DeclareMathOperator*{\argmin}{arg\,min} \DeclareMathOperator{\Exp}{Exp} \newcommand{\geo}{\gamma_{\overset{\frown}{#1,#2}}} \newcommand{\geoS}{\gamma} \newcommand{\geoD}{\gamma_} \newcommand{\geoL}{\gamma(#2; #1)} \newcommand{\gradM}{\nabla_{\M}} \newcommand{\gradMComp}{\nabla_{\M,#1}} \newcommand{\Grid}{\mathcal G} \DeclareMathOperator{\Log}{Log} \newcommand{\M}{\mathcal M} \newcommand{\N}{\mathcal N} \newcommand{\mat}{\mathbf{#1}} \DeclareMathOperator{\prox}{prox} \newcommand{\PT}{\mathrm{PT}_{#1\to#2}#3} \newcommand{\R}{\mathbb R} \newcommand{\SPD}{\mathcal{P}(#1)} \DeclareMathOperator{\Tr}{Tr} \newcommand{\tT}{\mathrm{T}} \newcommand{\vect}{\mathbf{#1}}$

# The geodesic

Returns evaluations of the geodesic $\gamma_{x,y}\colon\mathbb R \to \M$, either equidistant at pts points (which is set to 100) by default. If t is given as a vector of evaluation poitns, this one dominates.

### Matlab Documentation

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% geo = geodesic(this,x,y)
% Compute the geodesic between x and y using pts-2 points to
% interpolate
%
% INPUT
%   x,y : two points of the manifold
% OPTIONAL
%   pts : (100) optional length of geodesic, or set to length t
%               if t is chosen
%     t : vector of points lead to geo = \gamma_{x,y}(t)
%
% OUTPUT
%   geo : the geodesic between x,y evaluated at several points.
%
% ---
% Manifold-valued Image Restoration Toolbox 1.0 ~ J. Persch ~2015-10-29