Angle between two vectors matlab

Question

I want to calculate the angle between 2 vectors V = [Vx Vy Vz] and B = [Bx By Bz]. is this formula correct?

VdotB = (Vx*Bx + Vy*By + Vz*Bz)

 Angle = acosd (VdotB / norm(V)*norm(B))

and is there any other way to calculate it?

My question is not for normalizing the vectors or make it easier. I am asking about how to get the angle between this two vectors

Solution 1

Based on this link, this seems to be the most stable solution:

atan2(norm(cross(a,b)), dot(a,b))

Solution 2

There are a lot of options:

a1 = atan2(norm(cross(v1,v2)), dot(v1,v2))
a2 = acos(dot(v1, v2) / (norm(v1) * norm(v2)))
a3 = acos(dot(v1 / norm(v1), v2 / norm(v2)))
a4 = subspace(v1,v2)

All formulas from this mathworks thread. It is said that a3 is the most stable, but I don't know why.

For multiple vectors stored on the columns of a matrix, one can calculate the angles using this code:

% Calculate the angle between V (d,N) and v1 (d,1)
% d = dimensions. N = number of vectors
% atan2(norm(cross(V,v2)), dot(V,v2))
c = bsxfun(@cross,V,v2);
d = sum(bsxfun(@times,V,v2),1);%dot
angles = atan2(sqrt(sum(c.^2,1)),d)*180/pi;

Comments

[Dennis Jaheruddin]

If you want to be concise at least recommend V*B'

[High Performance Mark]

Is there some reason you have avoided the intrinsic dot function ?

[Marc Claesen]

@HighPerformanceMark Not apart from forgetting its existence.

[Jack_111]

no there is no reason and the dot function works very well but just I wrote the question like this.

[Jack_111]

That's why I am confused and I don't know which one is the correct one and why

[Dennis Jaheruddin]

Just read more via the link I provided. They are both correct in theory, but in practice this one is mentioned to provide more stable results (whilst the alternative with acos computes a bit faster).