Line - Polygon Intersetion Detection

The problem:
I’m working on a method to do more accurate path finding for a special project. I haven’t yet found any sources on this so i have to write it myself.

The idea was to use a polygon mesh, draw waypoints between all points then discard ways intersecting with a polygon. After that use dijkstra’s algorithm to find the closest path.

Detecting whether a line intersects with a polygon mesh is the tricky part. I haven’t yet come up with any viable solution that is fast.

Any ideas of how i can determine whether a waypoint travels through a polygon?