Angle betwen two 3d vectors in the range 0-360 degree

I have set of two 3d vectors lying on the same plane. I would like to calculate

angles betwen each of these pairs, but in the "full" angle range: from 0 to 360 degree.

Using formula:

Angle = atan2d(norm(cross(v1,v2)),dot(v1,v2));

give me always angle in the rang from 0 to 180 degree, even if the second vector lies

on the right side of the first one.

How could this be improved?

[darova]

Where did you get that formula?

[James Tursa]

@darova:

https://www.mathworks.com/matlabcentral/answers/101590-how-can-i-determine-the-angle-between-two-vectors-in-matlab

[James Tursa]

@UWM: You will need to define the method for calculating this full range angle. I.e., you need to pick a normal vector on one side of the plane and use that to determine this full range angle, along with a method for choosing which vector is "first". Have you done that?

[UWM]

Thanks for clarification. I will try to do this according your tips.

Answer 1

[James Tursa]

E.g., here is one method:

function a = vecangle360(v1,v2,n)
x = cross(v1,v2);
c = sign(dot(x,n)) * norm(x);
a = atan2d(c,dot(v1,v2));
end

This is a simple (non-vectorized) function that takes two input vectors v1 and v2, and a vector n that is not in the plane of v1 & v2. Here n is used to determine the "direction" of the angle between v1 and v2 in a right-hand-rule sense. I.e., cross(n,v1) would point in the "positive" direction of the angle starting from v1. A sample run:

>> v1 = [2; 0; 0];
>> v2 = [1; 1; 0];
>> p = [0; 0; 1]; % The v1 & v2 plane normal vector
>> vecangle360(v1,v2,p)
ans =
    45
>> vecangle360(v1,v2,-p)
ans =
   -45
>> vecangle360(v2,v1,p)
ans =
   -45
>> vecangle360(v2,v1,-p)
ans =
    45

So you can see that the method returns an angle "from" the first vector "to" the second vector using a right-hand-rule with the n vector. It will be in the range -180 to 180, so if you really need 0 - 360 you will need to modify the result.

[UWM]

Many thanks!

[Erik]

I have found several examples of this solution online through searching but they never explain how you get the plane normal vector.

>> p = [0; 0; 1]; % The v1 & v2 plane normal vector

Where does this come from? How do I calculate it?

[Jan]

The vector cross(x,y) is perpendicular to the vectors x and y. If you normalize it, it is the orthonormal vector to the plane built by the vectors x and y.