CODEWITHSUNDEEP
mathquaternions
PolGraphic
PolGraphic

Reputation: 3364

Calculating rotation delta between two quaternions (as another quaterion)

I have some initial rotation r0 represented by quaternion and some actual rotation r (also an quaternion). I would like to get the quaternion that represents the delta of rotation.

E.g. if r0 stands for 30st OX rotation and r is 50st OX, the rDelta should contain quaternion that represents 20st OX rotation.

How to compute the rDelta?

My guess is either:

rDelta = r0.getConjugated() * r

or

rDelta = r.getConjugated() * r0

? But maybe none of those.

Upvotes: 2

Views: 3873

Answers (4)

eric frazer
eric frazer

Reputation: 1649

I might be wrong, but if I remember correctly, assuming you're in Unity and applying Q's in Right-to-Left order (because it's left-handed?), then in order to get "from" Q1 "to" Q2, you first inverse Q1, then apply Q2 to the result of that, and that gives you the delta. How much you need to rotate from Q1, to get to Q2..

    Quaternion r0 = Quaternion.Euler(10, 0, 0);
    Quaternion r = Quaternion.Euler(20, 0, 0);
    Quaternion rDelta = r * Quaternion.Inverse(r0);

Heck, I don't even know what a quaternion conjugate is! I think for homogenous matrices, they're the same as the inverse? Yep, just looked that up.

This is answered here too: https://gamedev.stackexchange.com/questions/143430/relative-quaternion-rotation-delta-rotation-produces-unstable-results

Upvotes: 1

minorlogic
minorlogic

Reputation: 1908

It depends , how your rDelta will be applied (from right or left)

1 )r = r0 * rDelta; r = r0 * conj(r0) * r; rDelta == conj(r0) * r;

2 )r = rDelta * r0; r = r * conj(r0) * r0; rDelta == r * conj(r0);

Upvotes: 1

BeyelerStudios
BeyelerStudios

Reputation: 4283

so you want to find rx where rx * r0 == r1?

rx * r0 * conj(r0) == r1 * conj(r0)
rx == r1 * conj(r0)

All you need to know is that a rotation around q = q2 * q1 is equivalent to a rotation first around q1 and then q2. If you want to go from an initial rotation r0 to the final rotation r1 you simply substitute: r1 = rx * r0 where rx is the missing step between r0 and r1.

Upvotes: 2

aka.nice
aka.nice

Reputation: 9382

Your quaternion q(R2/R1) represent the rotation of R2 w.r.t. R1

Your quaternion q(R3/R1) represent the rotation of R3 w.r.t. R1

You wish to have the rotation of R3 w.r.t. R2

That is q(R3/R2) = q(R3/R1) * q(R1/R2) = q(R3/R1) * conjugate(q(R2/R1)) where * is the product of quaternion

Upvotes: 0

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