Hi,
I have read from 2 sources Orientation cannot be updated directly using Angular Velocity, see attached equation 1
This seems incorrect to me
Surely I can do attached equation 2?
I.e. put the angular velocity into a quaternion with the angle scaled by delta time & concatenate with the orientation?
1 hour ago, Cacks said:I have read from 2 sources Orientation cannot be updated directly using Angular Velocity, see attached equation 1
I don't understand what you are saying. That equation is a way to update the orientation using angular velocity...
I am not sure what "q_rot" does, so I can't comment on your second equation.
the 1st equation is from a book to update orientation using angular velocity, it says:
new orientation = old orientation + time delta * (0.5 * angular vel quaternion * old orientation)
The 2nd equation is mine to update orientation, it says:
new orientation = old orientation * Quaternion(angularVel.normalise(), angularVel.length() * time delta)
I think my equation should work?
I believe the first equation is a linearization of the second one. Notice how the first one doesn't involve any trigonometric functions, but the second one does.
Remember to re-normalize the orientation after you use the first formula.
ok I understand, the 1st equation is used because it gives better performance, that makes sense, cheers
on second look they both use trig functions because in the first equation 'w' is a Quaternion made from a vector
The 2nd equation seems to give more rotation as well, wondering which 1 is correct?
No, no. `w' is just the angular velocity, with a 0 as real part. No trigonometric functions involved.
Notice the equations could be re-written like this:
(1) q' = (1 + 0.5 * w * dt) * q
(2) q' = exp(0.5 * w * dt) * q
Since exp(z) = 1 + z + z^2/2 + z^3/6 + ..., you can think of the first equation as using a linear approximation to the exponential function.
in my implementation of Quaternion I use the trig functions in the constructor to scale the axis & angle so I used them in both forms of the equation
I may as well use the 2nd equation, cheers
You should probably provide a mechanism to create a quaternion from a vector by making the real part 0. For instance, when you use the quaternion to apply a rotation, you normally do something like
q' = q * v * conj(q)
That `v' means the vector used as a quaternion in the manner I described.
