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# What is affected by the W in Quaternion(x,y,z,w)?

I'm just wondering what is affected by the 'w' parameter in Quaternion...

**Answer** by keld-oelykke
·
Jul 28, 2011 at 10:02 PM

a quaternion is a complex number with

**w as the real part**and x, y, z as imaginary parts.If a quaternion represents a rotation then

**w = cos(theta / 2)**, where**theta**is the rotation angle around the axis of the quaternion.The axis

**v**(v1, v2, v3) of a rotation is encoded in a quaternion: **x = v1*sin (theta / 2), y = v2*sin (theta / 2), z = v3*sin (theta / 2)**.If w is 1 then the quaternion defines 0 rotation angle around an undefined axis v = (0,0,0).

If w is 0 the quaternion defines a half circle rotation since theta then could be +/- pi.

If w is -1 the quaternion defines +/-2pi rotation angle around an undefined axis v = (0,0,0).

A quater circle rotation around a single axis causes w to be +/- 0.5 and x/y/z to be +/- 0.5.

Kind Regards, Keld Ølykke

**Answer** by Eric5h5
·
Jul 24, 2011 at 05:14 AM

Quaternions are four-dimensional, so you need four properties. The x/y/z properties don't correspond to x/y/z in euler angles. With quaternions, each of the properties is a normalized float between 0 and 1, so for example a euler angle of 45/90/180 is represented by a quaternion as approximately .65/-.27/.65/.27.

**Answer** by testure
·
Jul 24, 2011 at 04:18 AM

If you don't already know, it's not something that's easily explained unfortunately.

$$anonymous$$ade my day ;) As one of the most useless comments out there. Why bother?

You may better watch the numberphile video on quaternions. Dr James Grime does a great job explaining the very basics.

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