Navigation grid and graph

Question

I am working on an SFML / C ++ project, and I need to use a navigation grid to move around the edge of a polygon. Like a little:

Here, the path uses both edge centers and vertices.

I tried to make navmesh with two-dimensional triangulations, but I had problems using the algorithm.

I need a library written in C ++ to handle this drawing. Is there a library that meets my requirements?

Thank you in advance