mathematics - How to make the player slide smoothly against terrain

I'm making an isometric game. When the player tries to walk diagonally into a wall I want them to slide smoothly across it, so whatever portion of the movement would be legal is used, and anything in the direction of the normal is thrown away. Walls can be any angle, not just vertical or horizontal, and the player has 360 motion.

I feel like I'm almost there but I can't put the last piece into place.

Update: great news everyone! I have it working. But... I'm a bit confused what I should be normalising and what not. The normal just needs to be a unit vector, right? but then I'm mixing that with my input so I'm normalising that - am I wrong?

By the way, I have also found that I need to push the player 1 pixel in the direction of the normal, so that they don't get stuck on things - works well.

Answer

Just project your vector of motion onto the plane normal and then subtract the result from your vector of motion.

Vector undesiredMotion = normal * (dotProduct(input, normal));
Vector desiredMotion = input - undesiredMotion;

Something like that anyway. Although in your lovely diagram the input seems to be away from the wall so I'm slightly confused.