# What is the difference between positive and negative rotation?

Say I have a wall piece, one is rotated 180° the other is rotated -180°. Another example is -90° and 270° and 630°. The two respective examples look the same in my scene, is there any difference? Should I go and make all of the rotation values positive? What is the purpose for rotation values above 360°?

• I guess it depends on the context. For animation it would make a big difference going in one direction or another. – cegaton Oct 16 '14 at 16:02

The Euler rotation is calculated by a rotation matrix which uses sine and cosine; These functions are periodical, which means it wouldn't make any difference whether you set the value for Φ to Φ+360° or Φ-360°. image by Udo Brechtel (Wikipedia); the label Einheitskreis means unit circle

Rotating a cube by 90 degrees (or a rectangle by 180°) wouldn't have any effect to the un-textured appearance of the mesh, but it would for materials (think of it like differently textured faces).

As @cegaton already commented, animations rely on the direction of your rotation. An arm could reach the same position by rotating 90° in one or 270° in the opposite direction.

When you increase the rotation by e.g. 720° between two keyframes the object would rotate twice around the keyframed axis. Note that Quaternions behave differently you can't express rotations > 360° with them.

When measuring angles in degrees, you have a range of 0.0 to 360.0 to work with. Anything outside of that is going to wrap back around to look just like some other value within that 0 to 360 range. Simply subtract 360 from the angle if it is over 360, or add 360 to the angle if it is under 0. For example, if you have a rotation of 540 degrees, that's really just a rotation of 180 degrees, because 540-360 = 180. Likewise, if you have a rotation of say... -810 degrees, that's really just 270 degrees because -810 + 360 = -450... +360 = -90... +360 = 270.

Now like cegaton says, context IS important. If you're just positioning an object, that's simple, but if you're animating an object, that can complicate things a bit. See if you Have the rotation animated from 0 to 720 degrees, that's two full rotations even though it will end up right where it started at the end.

• IMO the choice of 0, 360 is arbitrary. Take the concept of east and west for example, which uses what is effectively [-180, 180] as a range. +++ – batFINGER Oct 16 '18 at 13:41