Are there any resources about finding the shortest path with straight lines instead of using tiles? I am still using a tile based system for my game but i want the player and mobs "detached" from the tiles. The image might illustrate things better.

The path will never get too long since the player can only click as far as the screen goes and it should not calculate past a wall if, let's say a door through it, is outside the screen. Mobs however should chase the player like this for let's say 2 or 3 screens away.
I am thinking of drawing a line between location and destination and where it crosses collidable object insert a waypoint there and move it around until. But since i can come up with many problems with this technique i honestly have no clear idea where i should start.
So if anyone has a good resource about this subject i'd love to dig into it.


















