Pointers: What does this line of code mean?

I'm new to programming, but have an internship this summer and I'm trying to get this code to run.

I'm going through someone else's c++ code ("Exact Geodesic for Triangular Meshes" open source) and one line is tripping me up. Anyway, the line is as follows:

geodesic::Mesh* mesh = algorithms[algorithm_id] - > mesh();

Correct me if I'm wrong, but first a pointer is being initialized. It looks like

class::pointerclass* thingpointedto = something[something] accessing member mesh();

I have no clue what the code on the right side of the equals operand means. Can anyone help me out?

Thanks for your interest,

Amanda