MATLAB: Angle between two vectors in 3d

3danglevectors

Hello,

I have two vectors in 3d and i want to find the angle between those two vectors.

Thanks in advance

Best Answer

Or:

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

See this compact discussion about this topic: CSSM: Angle between two vectors . Only 71 replies (Google finds 89 replies, so I assume 18 spam messages?) and 68300 views currently...

[EDITED]: W. Kahan suggested in his paper "Mindeless.pdf":

2 * atan(norm(x*norm(y) - norm(x)*y) / norm(x * norm(y) + norm(x) * y))

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MATLAB: Calculate the angle between multiple points

The ACOS and the corresponding ASIN approchs are numerically instable near to multiples of pi (half). Better use the more accurate ATAN2 method:

angle = atan2(norm(cross(v1,v2)), dot(v1,v2));

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You will need to define in your code which direction is the clockwise and which is counterclockwise. You can do that by defining up front a normal vector to your 3D plane that can be used to distinguish this. E.g., something like

PlaneNorm = a 3-element vector defining the normal to the 3D plane for counterclockwise direction
ang = atan2d(norm(cross(v1,v2)), dot(v1,v2)); % angle without regard to "direction"
if( dot(cross(v1,v2),PlaneNorm) < 0 ) % if v1 X v2 is on the other side of the plane
    ang = 360 - ang; % modify based on desired "direction"
end

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