# 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…

• 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

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.

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