CODEWITHSUNDEEP
c#unity-game-enginequaternions
Wojtek Wencel
Wojtek Wencel

Reputation: 2127

How to get a Vector3 rotation between two Quaternions

I'm writing a script which rotates a Rigidbody using a Configurable Joint. I've got the targetRotation figured out, but now I'm struggling with targetAngularVelocity, which should help me avoid wobbliness if set correctly.

targetAngularVelocity is defined like this in the documantation: "This is a Vector3. It defines the desired angular velocity that the joint should rotate into". The problem is that I don't know how to get this Vector3 based on two Quaternions - current rotation of the object and the target rotation.

Am I not understanding it correctly? Is there a function that returns a rotation vector based on two Quaternions?

Upvotes: 1

Views: 2010

Answers (1)

John Alexiou
John Alexiou

Reputation: 29264

So mathematically a Quaternion represents the orientation of a rigid body. Consider the forward problem first, and see how the orientation q_1 transforms to another orientation q_2 after a rotational velocity ω is applied for t time.

Mathematically the rotation vector has a magnitude ω and a direction k such that ω = ω* k

This is done with quaternion multiplication as

q_2 = q_ω * q_1

Where q_ω represents a rotation about the axis of k of an angle θ=ω*t.

In reverse, you need to find q_ω with

var q_ω = q_2 * Quaternion.Inverse(q_1);

and extract the rotation axis and angle

q_ω.ToAngleAxis(out float angle, out Vector3 axis);

and compose the rotational velocity vector, that corresponds to this transformation in time seconds.

var ω = (angle/time)*axis;

Upvotes: 7

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