Error in finding the angle between three points using atan2

Hi everyone,

I was using the following formula to find the angle between three coordinate values (i.e., P1, P0, P2; finding angle at P0)

ang = (180/pi)*(atan2(abs(det([P2-P0;P1-P0])),dot(P2-P0,P1-P0)));

formula taken from: https://in.mathworks.com/matlabcentral/answers/57736-how-to-calculate-degree-between-3-points-in-matlab#answer_69886

So, it worked fine when I took the coordinate values as ;

P0 = [3,1];

P1 = [1,3];

P2 = [4,4];

figure;

plot(P0(1),P0(2),"*"); hold on;

plot(P1(1),P1(2),"*"); hold on;

plot(P2(1),P2(2),"*"); hold on;

ylim([0 7])

xlim([0 5])

legend("P0","P1","P2")

% P0 is the center where the angle would be

ang = (180/pi)*(atan2(abs(det([P2-P0;P1-P0])),dot(P2-P0,P1-P0))); % formula to get angle

% ang = 63.439 deg

But when I took three coordinate values as the following then it gave me a strange angle value, which is probably the supplmentary angle at P0.

P1 = [-16.49,-17.69];

P0 = [-25.83,-21.73];

P2 = [-40.77,-18.10]

figure;

plot(P0(1),P0(2),"*"); hold on;

plot(P1(1),P1(2),"*"); hold on;

plot(P2(1),P2(2),"*"); hold on;

legend("P0","P1","P2");

ang = (180/pi)*(atan2(abs(det([P2-P0;P1-P0])),dot(P2-P0,P1-P0)));

% ang = 142.9526 deg ; seems like the supplementary angle at P0.

Why is it happening? Any clues?

I need to apply this formula to calculate angle over 100s of coordinates and but if this kind of non-uniformity would happen then I wouldn't be able to use it.

Any help would be appreciated!

Thank you.

Answer 1

[Bruno Luong]

142.9 degree seem right to be. If you don't make the same aspect ratio of x and y with axis equal, angles are deformed on your screen monitor.

P1 = [-16.49,-17.69]; 
P0 = [-25.83,-21.73];
P2 = [-40.77,-18.10];
figure; 
plot(P0(1),P0(2),"*"); hold on; 
plot(P1(1),P1(2),"*"); hold on; 
plot(P2(1),P2(2),"*"); hold on;
P102 = [P1; P0; P2];
plot(P102(:,1),P102(:,2))
axis equal % This is important
legend("P0","P1","P2"); 

ang = (180/pi)*(atan2(abs(det([P2-P0;P1-P0])),dot(P2-P0,P1-P0))) % correct

ang = 142.9526

[Deepak Singh]

Thank you for your answer

Yes, you are right. Thanks a lot for the answer.