Angle to vector?

This is pretty basic, and I think I've done it before, but I'm just drawing a blank today.

I have an angle. (And a speed.) I want to convert that into a vector so I can apply it to a rigidbody. (Across the X and Z axis.) How do I do this?

 

You need to decide what that angle is relative to. So basically get a vector that is your starting direction, as well as an axis of rotation. Then finally you can get the result vector with

Code (CSharp):

1. // plug your rotation and axis of rotation into here:
2. Quaternion myRotation = Quaternion.AngleAxis(myAngle, myRotationAxis);
3. Vector3 startingDirection = <some starting direction>;
4. Vector3 result = myRotation * startingDirection;

If your rotation axis is one of the three "world" x, y, or z axes, you can also use Quaternion.Euler.

 

This looks more complicated than I expected, and I don't understand why I need to multiply the rotation by another vector. What kind of vector would I need for a starting direction?

Just to be clear, I'm not trying to rotate my object, I want apply a velocity. I want to move it in a direction according to an angle (and speed) that I have.

 

You don't. I'm multiplying the starting direction by the rotation quaternion, which results in another vector that is the rotated version of the first vector.

Whatever direction you want a rotation relative to. For example maybe it's the

transform.forward

direction of your character or something.

but an angle relative to what, and rotated on what axis? For example, maybe it's 5 degrees rotated above the horizon. Or 20 degrees to the left of the direction your character is facing.

 

This is definitely more complicated than I thought it would be. I could have sworn it was some method in Vector3 that made a simple one line conversion.

Well, I managed to get it working. It took a bit of trial and error and some fixing of bugs I didn't know I had in my code to find that angle, but I got it working.
Thank you.

 

There's https://docs.unity3d.com/ScriptReference/Vector3.RotateTowards.html too but it requires the same information:

• a starting direction
• a target direction (which essentially defines a rotation axis)
• number of degrees

 

The most basic form is

Vector3 vecForAng = angle*Vector3.forward;

. angle is a quaternion representing a world-coords angle. Unity considers angle (0,0,0) as aimed along +z; that's why we use Vector3.forward. As an example, transform.forward is a shortcut for transform.rotation*Vector3.forward.

 

I usually use something like

return new Vector3(Mathf.Sin(Mathf.deg2rad * angle), 0, Mathf.Cos(Mathf.deg2rad * angle));

Naturally this only works in 2 dimensions, but it might give you a good idea about what you can do with the third dimension.

 

It is very simple as OP suggested.

https://matthew-brett.github.io/teaching/rotation_2d.html

 

x = sin(angle)
y = cos(angle)

"x" and "y" give the result between 0 to 1

hope this help

 

Please do not necro-post.
Also this is only valid in 2D. It is vastly different in 3D, which is the key point here.

Incorrect. "x" and "y" give the result between -1 and 1, because that's how sine and cosine work.

Edit:
That said, the solution to the problem

Assuming that the angle is in degrees, and speed is the magnitude:

In 2D

Code (csharp):

1. var rads = angle * Mathf.Deg2Rad;
2. Vector2 vec = speed * new Vector2(Mathf.Cos(rads), Mathf.Sin(rads));

In 3D more information is needed, for example a surface normal.

Code (csharp):

1. Vector3 vec = Quaternion.AngleAxis(angle, normal) * (speed * Vector3.right);

A surface normal for the XZ plane is Vector3.up.

Or, at least for the base planes, you can lock the computation in 2D, then rotate the result orthogonally.

Code (csharp):

1. Vector2 v2 = ... // 2D computation from above
2. Vector3 v3 = new Vector3(v2.x, 0f, v2.y);