Quote:
Originally Posted by deimos
Perhaps someone with experience could say, "well, game engine x renormalises its quaternions when they drift more than y% away from unit length". That would be a worthwhile contribution to the conversation.
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I doubt there is an answer like this. The answer is more likely: If your screen has a resolution of W, and you multiply a vector with a matrix to obtain a position on the screen, what is the resolution to ensure that the placement of such a vector is pixel-precise after N multiplications. That is an answer I can give, but for that, the screen dimension needs to be known, and the number of multiplications needs to be known.
If you have a f-fractional bit matrix, then clearly, the resulting relative error of a multiplication with a 4x4 matrix can not be higher than 4*2^-f. If you have a screen resolution of W pixel, then you get a maxmal absolute error of W*4*2^-f. Approximately, after N iterations, you get an error of N*W*4*2^-f pixels.
This is not really "high mathematics", just some basic estimates.
Concerning quaternions: After thinking about it, I believe you must be using homogeneous coordinates. In such a case, the sign collected from the SU(2) rotations (instead of SO(3) = rotation matrices) does not matter. But without seeing your formulae, it is hard to tell. I'm also not clear why this should be better than the typical 4x4 matrices you use for coordinate computation in projective space (aka "homogeneous coordinates).