Quaternion Distance

[kevzettler]

I'd like to take two quaternions and get a distance value which is the delta between their separate orientations. Any methods to do this I'm overlooking?

[stefnotch]

You could use the dot product and convert it to an angle. You could also write a function that does this and create a PR.

[jWA86]

const invers = quat.invert(quat.create(), q1);
const diff = quat.multiply(quat.create(), invers, q2);
const radian = quat.getAxisAngle(vec3.create(), diff);

[kevzettler]

@stefnotch happy to write a PR but this a beyond my math skills.

How does jWA86's suggestion compare to the dot product idea?

[stefnotch]

@kevzettler

The quaternion dot product approach works as follows: https://www.3dgep.com/understanding-quaternions/#Quaternion_Dot_Product
It's really similar to the vector dot product.

jWA86's approach isn't that complicated either. A quaternion is a rotation, or an axis-angle. And, the multiplication of quaternions represents composing the two rotations: perform one rotation and then perform the other one (1).

So, to get the angle between q1 and q2 he

• takes the inverse of q1 and
• multiplies it by q2
• gets the angle of the result

Effectively, "this takes away the rotation q1 from q2", and then, getting the axis-angle from the result is trivial.

(1): Minor warning: It's not commutative, the order in which you do the multiplication matters.

[stefnotch]

Upon doing further research, you should probably implement jWA86's suggestion.