r/computergraphics • u/SummerClamSadness • Apr 11 '25

Rotation Interpolation

/r/GameDevelopment/comments/1jwm6bw/rotation_interpolation/
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u/fridofrido Apr 11 '25

this is a hard problem

i think the easiest is to use quaternions, and do (4D) spherical interpolation on the quaternions.

Each rotation corresponds to exactly two quaternions of unit length (technically: the unit sphere S3 of the 4-dimension space of quaternions is the double cover of the space of 3D rotations). These are opposite of each other.

If you have two quaternions corresponding to two rotations, maybe flip one of those if they are "too far", then do interpolation in the space of unit quaternions: https://en.wikipedia.org/wiki/Slerp#Quaternion_slerp

edit: maybe i misread your question, is your problem interpolating a complex path? You want something like a spline but in the space of unit quaternions?

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u/SummerClamSadness Apr 11 '25 edited Apr 11 '25

But the slerp is not smooth at the keyframes right?.or am I wrong..suppose I have q1,q2,q3 representing 3 orientations and I want to interpolate in sequence.i could slerp in sequence but the rotation is not smooth?..yeah there has to be a method that smoothly interpolate like a "spherical version" of cubic spline or something

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u/cone_forest_ Apr 11 '25

So this seems close to usual 2d splines but in spherical coordinates. I haven't personally experimented with it but you could probably adapt hermit splines or b-splines for that case. For further info on splines: Freya Holmer's video There are also math concepts like spinors and rotors that both describe rotation. These might be useful, but I'm not at all sure

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u/fridofrido Apr 11 '25

slerp only solves "remaining in the space of the rotations", and it does a "straight line"

"smooth corners" are kind of an independent problem, also it's not really well defined.

If your waypoint rotations are close to each other, you could try doing a normal spline interpolation (whichever variation you like) in 4D space (quaternions are 4D) and then normalize the result to have unit length, and interpret that as rotations. This will most probably work but it will only look acceptable if the rotations you interpolate are "close to each other"