English Amiga Board - View Single Post - Fixed point maths, quaternions, rounding errors and normalisation.

deimos · 09 November 2019, 17:20

I’ve just updated the 3D game thing I’m writing to use quaternions to hold the orientation / attitude of the camera and the objects I’m rendering.

It all seems to work and was not difficult to code. I’m reasonably happy with it.

But, I know there are rounding errors accumulating each time I pre-multiply the current quaternion with one that represents the change in orientation. All the literature says to expect this in the form of the quaternion drifting away from unit length, and to rectify it, once it has reached a certain point, by dividing the quaternion by its length, thus returning it to a unit length.

I’m using fixed point maths for everything. Currently 16 bits, 2 before the point, 14 after.

My rounding errors so far are small, but they do exist. They don’t become a problem in the small demo / play about code that I have at the moment, but I do suspect that they’ll cause issues over the time it takes to play the game for real.

I have questions about the use of quaternions in this way.

Is 2:14 fixed point format enough precision for this? Should I keep my precision when creating the rotation matrix that results from them? If so, how high? 2:30? And should I embiggen my sine table to match?
How far should I let the quaternions drift before I normalise them? Inversely, how do I calculate when it’s possible for the normalisation to be beneficial given the limitations of the fixed point maths, including the calculation of the length which involves a square root.

09 November 2019, 17:20	#1
deimos It's coming back! Join Date: Jul 2018 Location: comp.sys.amiga Posts: 762	Fixed point maths, quaternions, rounding errors and normalisation. I’ve just updated the 3D game thing I’m writing to use quaternions to hold the orientation / attitude of the camera and the objects I’m rendering. It all seems to work and was not difficult to code. I’m reasonably happy with it. But, I know there are rounding errors accumulating each time I pre-multiply the current quaternion with one that represents the change in orientation. All the literature says to expect this in the form of the quaternion drifting away from unit length, and to rectify it, once it has reached a certain point, by dividing the quaternion by its length, thus returning it to a unit length. I’m using fixed point maths for everything. Currently 16 bits, 2 before the point, 14 after. My rounding errors so far are small, but they do exist. They don’t become a problem in the small demo / play about code that I have at the moment, but I do suspect that they’ll cause issues over the time it takes to play the game for real. I have questions about the use of quaternions in this way. Is 2:14 fixed point format enough precision for this? Should I keep my precision when creating the rotation matrix that results from them? If so, how high? 2:30? And should I embiggen my sine table to match? How far should I let the quaternions drift before I normalise them? Inversely, how do I calculate when it’s possible for the normalisation to be beneficial given the limitations of the fixed point maths, including the calculation of the length which involves a square root.