I asked a question a while back that was about finding the yaw and pitch
rotations for the equivelant of a direction (normalized) vector. That’s
no longer a problem (thanks again Reed), but now I am doing a
billboarded light beam and I need the z rotation (aka roll)
So I already have the x and y rotations, how do I compute roll with the
direction vector from my camera to the light.
Thanks in advance.
Please log in or register to post a reply.
One vector isn’t enough to pin down the roll. You can see that rolling
the vector would just rotate it around its own axis and wouldn’t change
it at all. Roll only matters when you have a full coordinate system with
That being said, you can calculate roll by looking at the left/right
axis of the coordinate system. If you use the convention of x = forward,
y = left, z = up, then the roll is atan2(left.z, sqrt(left.x\^2 +
left.y\^2)). Note that you can only roll up to +/- 90 degrees in this
scheme; then there will be a discontinuity in the Euler angles.
Thanks for the advice.
You’re making it sound a bit like I’m going about this wrong. My goal
here is (and I’m sure your familiar with it) I have a 2D light beam that
has a fixed X and Y orientation (those being the direction that the spot
light is pointed in). The only thing left to do is to keep the side of
the beam facing towards me (hence billboarding).
Is there a better or more elegant way to achieve this?
In that case, you can use the camera’s view direction. If your beam
texture is laid out with the direction of the light parallel to the U
axis, you can calculate the V axis for the texture in world space by
crossing the spotlight direction with the camera’s view direction. Those
U and V axes should be enough to construct the appropriate screen-facing
take the cross product of your view vector and beam vector, it will give
you the side vector.
and use an object space quad instead of a screen space billboard.