Magnetic Vector Movement

Hello people!

I’m working on a game with an interesting concept for player movement.

I’m trying to make a script that can lay out points on a 3D-space with vector lines between them.
I want to be able to choose what points are connected with vectors and I want to be able to curve the vectors.

But here is the deal! The player is able to run freely in 3D-space, but if the player comes within a short radius to the vector, the player will snap on to the vector and only be able to move forwards or backwards alongside the vectorline.

How can this be done?

http://forum.unity3d.com/threads/135510-Vectrosity-2.0