How to calculate a angle between two vectors in 3D

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 ~90º 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?

[sixwwwwww]

What is v1 and v2 here in your code?

[Paulo Oliveira]

v1 and v2 are vectors.

Answer 1

[Vivek Selvam]

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)

[Paulo Oliveira]

I saw your answer, but I guess that this is not a solution for my problem. Logically, the reference point for differents plans is the same, but that change is the "view". If you draw the coordinates for the selected segments the view xy the angle is 90º, for yz is 0º and for xz is 0º. and the reference point is the same. Do you understand my doubt?

[Vivek Selvam]

Paulo, how do you define v1, v2?

[Paulo Oliveira]

V1 is defined by P1 and P2 and V2 is defined by P1 and P7. As the point belong to a parallelepiped I know the angles, but I need a rotine to calculate the angles when I analyse a human motion. Do you understand me?

[Vivek Selvam]

This is an idea. Play around and modify it. Feel free to ask any questions.

function planar3d
% points
x = [ 1 1 1; 
      2 1 2
      9 7 3
      8 4 5]; 

% legend
xyz = 0;
yz  = 1;
xz  = 2;
xy  = 3;

% v1 = p1 & p3; v2 = p1 & p4 --> here xyz plane is same as xy plane
v1   = x(3,:)-x(1,:);
v2   = x(4,:)-x(1,:);
ang3 = planar2d(v1, v2, xyz);
ang2 = planar2d(v1, v2, xy);
disp(['ang3 = ' num2str(ang3) ', ang2 = ' num2str(ang2)]);

% v1 = p2 & p3; v2 = p2 & p4 -->  here xyz plane is not same as xz plane
v1   = x(3,:)-x(2,:);
v2   = x(4,:)-x(2,:);
ang3 = planar2d(v1, v2, xyz);
ang2 = planar2d(v1, v2, yz);
disp(['ang3 = ' num2str(ang3) ', ang2 = ' num2str(ang2)]);

function ang = planar2d(v1,v2,plane)
% % plane
% xyz = 0;
% yz  = 1;
% xz  = 2;
% xy  = 3;
if plane ~= 0 % reducing a plane is same as eliminating that coordinate
    v1(plane) = 0;
    v2(plane) = 0;
end
ang = rad2deg(atan2(norm(cross(v1,v2)),dot(v1,v2)));