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How to derive control pts for cubic spline interpolation of quaternions

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Hi, I know there is equation to derive the ''An'' and ''Bn+1'' quaternions for the cubic spline interpolation, but it requires the quaternions ''Qn-1'' and ''Qn+2''. The problem is that the ''Qn-1'' is not exist if ''Qn'' is the initial point of the sequence, and also, ''Qn+2'' is not exist if ''Qn+1'' is the end point of the sequence. Can anyone tell me how should i handle these cases? Thx in advance.

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Depending on how you set them, your interpolation will look different. The extra quaternions are there to set an initial and a final ''velocity''. If you are supposed to start and stop with a zero velocity, try duplicating your first and last quaternions.

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Thx for answering.
I m currently trying to do vertex animation, actually i m not sure when should the "squad" be used. It seems that the animation is already very smooth even i only try to apply "slerp" to those quaternions pairwisely.
Can u suggest a kind of sequence in which "squad" is more preferred? Thx again.

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With squad you only need 2 control points to produce the same fluidity as a slerp with, say, 5 control points.

With squad you only need the start and end orientation (so long as the rotation is uniform) - even if they are 179o apart.

Or at least that''s the advantage as I understand it.

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Guest Anonymous Poster
hermite splines are better cheaper to calculate too

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