How to calculate a angle between two vectors in 3D

Question

Paulo Oliveira 2013-10-18

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/90668-how-to-calculate-a-angle-between-two-vectors-in-3d

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
0  0  0
70.5  0  0
141  0  0
141  0  141.5
70.5  0  141.5
0  0  141.5
0  137.5  0
70.5  137.5  0
141  140  0
141  141.5  141.5
70.5  139  141.5
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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sixwwwwww 2013-10-18

What is v1 and v2 here in your code?

Paulo Oliveira 2013-10-18

v1 and v2 are vectors.

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Answer 1

Vivek Selvam 2013-10-18

2
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/90668-how-to-calculate-a-angle-between-two-vectors-in-3d#answer_100171

在 MATLAB Online 中打开

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 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 2013-10-21

在 MATLAB Online 中打开

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)));