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I'm looking for a code/package which given a starting point $x_o$ and ending point $x_1$ to compute equally spaced points on the geodesic between $x_0$ and $x_1$ given a function which returns the Riemannian metric tensor at any point. This does not seem to be a trivial task since you need to solve some form of a differential equation. Is anyone aware of any such materials?

Alex Botev
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You can compute minimal geodesics by solving the Eikonal equation using the Fast Marching Method, which is implemented in Python in Jason Furtney's scikit-fmm. It may be ok for Riemannian metrics with weak anisotropy. If not, it's at least a place to start.

Update 2019/01: Jean-Marie Mirebeau has a rather more complex package of code implementing his fast-marching method for solving the eikonal equation with Riemannian metrics. The code includes tools for computing geodesics. It's non-trivial to install and run, but I've had some success after persevering.

Colin Stark
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