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

Answer 1

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

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

Answer 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;

Answer 3

You can compute VdotB much faster and for vectors of arbitrary length using the dot operator, namely:

VdotB = sum(V(:).*B(:));

Additionally, as mentioned in the comments, matlab has the dot function to compute inner products directly.

Besides that, the formula is what it is so what you are doing is correct.

Answer 4

This function should return the angle in radians.

function [ alpharad ] = anglevec( veca, vecb )
% Calculate angle between two vectors
alpharad = acos(dot(veca, vecb) / sqrt( dot(veca, veca) * dot(vecb, vecb)));
end

anglevec([1 1 0],[0 1 0])/(2 * pi/360) 
>> 45.00

Answer 5

The solution of Dennis Jaheruddin is excellent for 3D vectors, for higher dimensional vectors I would suggest to use:

acos(min(max(dot(a,b)/sqrt(dot(a,a)*dot(b,b)),-1),1))

This fixes numerical issues which could bring the argument of acos just above 1 or below -1. It is, however, still problematic when one of the vectors is a null-vector. This method also only requires 3*N+1 multiplications and 1 sqrt. It, however also requires 2 comparisons which the atan method does not need.