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Originally Posted by deimos
Thomas, I'm not sure how you're trying to help.
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By asking the right questions and providing code. How can one answer the question whether a given precision is good enough without knowing what good enough means? If the peak error (l^infty) of the rotated vector is to be estimated, a hard error bound is given by the l^1 row norm of the errors of the rotation matrix.
Quote:
Originally Posted by deimos
Would you like me to explain the issues that "ordinary rotation matrices" bring
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It is the obvious approach, isn't it? I do not see any issues, I just wonder why this rather obvious approach is not used.
Quote:
Originally Posted by deimos
, and how the use of quaternions overcome them, while leading to more efficient code? Or are you confused about the supposedly "imaginary" nature of quaternions?
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No, I just wonder why one picks quaternions when rotation matrices do the job. Even more so as quaternions (aka SU(2)) are not fully equivalent to rotation matrices (SO(3)), but only up to a sign the former can pick up, see
https://en.wikipedia.org/wiki/3D_rot...SO(3)_and_SU(2)
Quote:
Originally Posted by deimos
And with regard to square root algorithms, I can point you to one from a trusted, published, source.
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Is an international standard good enough for you? The described algorithm is an integer implementation of it - actually, it is pretty much known and not novel. It is also the binary version of the manual "pen and paper" digit-by-digit square root.
If this makes you feel any better, mathieeedoubbas uses the same algorithm, for the IEEE mantissa of double precision numbers.