Question Angle between rotations (ignoring longitudinal axis)

To make it simple, I need to check if a spaceship is moving approximately in the same direction as another spaceship, and get the angle between them.

Have tried Quaternion.Angle, but it also adds if the ship is rotated on its own longitudinal axis. For example, two ships facing the same direction in 3D space, but one is upside down relative to the other, will result in a 180° angle, and I needed 0°.

How to properly calculate this? Thanks!

 

Think you can just use some math after you turn their direction into a Vector



You can just get the Vector they're moving by doing

transform.forward

I believe, which you can just plug into this thing above. Technically, if you don't need the angle and just how much they're going in the same direction, you can just use the dot product which returns a value between 1 and -1 of how parallel they are.

 

This is a perfect case to use the dot product!

Code (CSharp):

1. Vector3 myShip = transform.forward;
2. Vector3 theirShip = target.transform.forward;
3.  
4. float product = Vector3.Dot(myShip, theirShip);

The dot product is 1 if they're aligned and -1 if they're going in opposite directions. It's 0 if they're perpendicular.

 

While digging around the Transform.forward page, I actually found this.

https://docs.unity3d.com/ScriptReference/Vector3.Angle.html

Which would probably be easier than the math, but pretty sure it does the exact same thing as the picture.

 

Thank you for all answers. This one worked perfectly for what I needed!

 

Dot-product is generally seen as an optimization, since it gives the cosin of the angle, while being faster than computing the angle. If you want to check for "facing away from me", than as you note, dotP<0 works great. Of if you want to check for "within 45 degrees" you can use dotP<0.707 (since most adults have the cosin of 45 memorized). But as you tinker with it you'll be mentally converting back and forth and it's often faster (for the coder) and less error-prone to just use Vector3.Angle(v1,v2)<45.

Don't get me wrong -- I can use dot-product just fine, the same way I can climb into my car through the window, and yet oddly, almost never do either.

 

Yeah, given that it's just as easy to call Angle, that's what you should generally be using. I think I just use it out of force-of-habit (and then wind up having to figure out what the cosine of the angle I want is...)