MATLAB: How to calculate a angle between two vectors in 3D

3danglevector

Hi, I have a question, I have a table with 12 reference points
if true
% POINT  X  Y  Z
1  0  0  0
2  70.5  0  0
3  141  0  0
4  141  0  141.5
5  70.5  0  141.5
6  0  0  141.5
7  0  137.5  0
8  70.5  137.5  0
9  141  140  0
10  141  141.5  141.5
11  70.5  139  141.5
12  0  141.5  141.5
end
The segment 1 is defined by the point 1 and point 2 and the segment 2 is defined by the point 1 and point 7. I am able to calculate the angle with the following rotine,
if true
  % angle_x1_x13 = atan2(norm(cross(v1,v2)),dot(v1,v2));
    anglout = radtodeg(angle_x1_x13); 
end
The result is ~90ยบ and this result is correct if I think in xy plan, but I need to calculate the angle to yz plan and xz plan. Anyone help me?

Best Answer

This code uses your angle calculation and shows for different reference points (3d). 2d is the same for your formula.
% Origin is reference point
p1 = 1*ones(1,3); % directly v1 = p1 
p2 = 2*ones(1,3); % directly v2 = p2
% With origin as the reference point, the angle between vectors is 0
ang = rad2deg(atan2(norm(cross(p1,p2)),dot(p1,p2)));
disp(ang)
% Choosing reference point such that new v1, v2 are at 90 degrees
refpoint = [2 2 1];
v1 = p1 - refpoint;
v2 = p2 - refpoint;
angNew = rad2deg(atan2(norm(cross(v1,v2)),dot(v1,v2)));
disp(angNew)
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