How to calculate a angle between two vectors in 3D

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Paulo Oliveira
Paulo Oliveira 2013-10-18
评论： Vivek Selvam 2013-10-21
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?

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Vivek Selvam
Vivek Selvam 2013-10-18
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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Paulo Oliveira
Paulo Oliveira 2013-10-21
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
Vivek Selvam 2013-10-21
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)));

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