MATLAB: Negative angle between vectors / planes

anglegeometrynegativeplanevector

Hello,

I would like to ask a simple question: Is there a way to somehow compute and angle between two vectors / planes that is nor only positive??

I will be very thankful for a solution to this problem!!! Thank you.

Best Answer

In order to determine if the angle between two vectors is positive or not, there would have to be a reference normal plane vector (vn). If so, yes you can. There is a way to check if the angle between those two vectors should be negative. First take the cross product of the two vectors (v1 x v2) to get the normal of the plane (v3). Then, find the dot product of v3 and vn. If this dot product is negative, then the theta (angle between v1 and v2) should be negative

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MATLAB: How to get direction for 3d angles between 2 vectors

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

MATLAB: Angle between two vectors in 3d

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))

Best Answer

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