Return quaternion as [x,y,z,w]

[pozdnyakov]

Even though a standard form of quaternion representation in math is starting from the real part (i.e. [w,x,y,z]) many of popular WebGL frameworks [1][2][3][4] use a different order of [x,y,z,w]. We probably should be compatible and should update the spec accordingly.

[1] https://doc.babylonjs.com/classes/2.4/quaternion
[2] https://threejs.org/docs/api/math/Quaternion.html
[3] https://www.blend4web.com/api_doc/module-quat.html#.fromValues
[4] http://developer.playcanvas.com/en/api/pc.Quat.html

[pozdnyakov]

@alexshalamov @anssiko @kenchris thoughts?

[alexshalamov]

sounds like a good idea.

[kenchris]

I think it makes a lot of sense. Also in math quaternions are normally represented using i, j and k components, so order doesn't matter, in mathematical sense. If we define just the values (ie no i, j and k), ie. x + yi +zj + wk, the order [x, y, z, w] makes a lot of sense.

The following are valid quaternions:

1
14
312 + 7i (a quaternion and a complex number!)
-1 + 4i - 8j + 8k

Like complex numbers they i^2 == -1 :-) and so it j^2 == -1 and k^== -1 and ijk == -1

[pozdnyakov]

in each of your examples the real component stays first and that's the standard representation :)

[kenchris]

Yes, I assume that x is used for representing the real component, right?

[pozdnyakov]

no, w is real, it's equal to cos(theta/2)

[kenchris]

Oh, not obvious :-) so is that also the case for the other implementations?

Maybe we should add a note explaining this

I guess it makes sense when you talk about scalar and vector part. But this definitely needs a note and we need to make sure that w is really the scalar part in the other APIs

[kenchris]

mrdoob/three.js#2250

http://answers.unity3d.com/questions/147712/what-is-affected-by-the-w-in-quaternionxyzw.html

https://books.google.dk/books?id=ID1tP9DfKgEC&pg=PA101&lpg=PA101&dq=quaternions+z+y+z+w&source=bl&ots=S6vsfPVF9f&sig=lscTZwRBT4EHr7Pflj5hZ25eLxg&hl=da&sa=X&ved=0ahUKEwjLgsu60pLTAhUKiCwKHfd_CKUQ6AEIXDAJ#v=onepage&q=quaternions%20z%20y%20z%20w&f=false

[pozdnyakov]

For both math and alphabetical reasons the current order [w,x,y,z] is correct, however for some reason JS frameworks prefer [x,y,z,w] , so this issue is more about API convenience..

[pozdnyakov]

Maybe we should add a note explaining this

Could you give more details, what such note should contain?

[kenchris]

Sure, say how quaternions are represented, ie w + xi + yj + zk, with a scalar w and a vector x, y, z. And then mention that we expose these as vector + scalar, [x, y, z, w] as that is the most prevalent way of doing that when exposed as an array, but that other libraries etc could impose a different order like [w, x, y, z]

[pozdnyakov]

Reopen to add an explaining note