Tilting towards turn direction (for a motorbike)

Question

I have a motorbike which moves along based on a direction vector, I set its forward direction to the direction it's moving.

What I'd like to also do with it is have the motorcycle tilt in the direction it's turning, I haven't had much luck figuring this out though, any ideas?

Answer 1

Take the cross product of those two vectors (turning direction and current forward direction). Assuming your bike is riding on the XZ plane, if the vector points upward (y is positive) then the bike should tilt left, if it points downward (y is negative) then it should tilt right. The magnitude of the vector probably represents how "big" the tilt should be, but I haven't tried it.

For example, if the bike is currently facing down the negative z axis, the forward direction will be:

{0,0,-1}

If you want to turn 90 degrees right, the turning direction vector will be:

{1,0,0}

If you want to turn 90 degrees left, the turning direction vector will be:

{-1,0,0}

If you calculate the cross products for both left and right turns, they look like this:

Right turn: {0,0,-1} x {1,0,0} = {0,-1,0} 
Left turn: {0,0,-1} x {-1,0,0} = {0,1,0}