Post #2480025

2026-05-08 04:45 UTC

I wonder if any math people can tell me why these two quaternion interpolation methods appear to be functionally equivalent (apart from tiny differences in precision) superficially there&#39;s a similar amount of sin/cos/acos calls so slerp is probably a simplification of the latter, but the surrounding multiplications make a huge mess of understanding that interestingly the second option doesn&#39;t seem to require quaternions to work (should also work with 3x3 matrices) #gamedev #math

Replies (2)

@archo@mastodon.gamedev.place 2026-05-08 07:45

the reason why I'm looking into this less efficient form of interpolation is that I want to combine it with angular velocity for my quadratic spline thing the problem with quaternions being that interpolating quaternions does not map to any kind of physical behavior at the numerical level whereas axis-angle is angular velocity vec3 dir=axis, length=angle encoding also allows componentwise separation such that each component can get a separate curve #gamedev #math

Open ##2671177
@sibaku@mas.to 2026-05-08 08:10

@archo@mastodon.gamedev.place From looking at it, it makes sense to me (there might be edge cases I am missing). Slerp computes a rotation with constant angular velocity around a fixed axis from q0 to q1. Now keep in mind that a rotation quat basically encodes axis angle (v* sin a/2, w*cos a/2) so it is already similar. The second method computes the relative rotation (q0 to q1), extracts axis + angle from that and interpolates the angle, so it is a constant angular velocity around a fixed angle, just like the first!

Open ##2671182