# how to find concave angle between three points

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Eliska Paulikova il 22 Nov 2022
Risposto: David Goodmanson il 23 Nov 2022
Hello how can I fing agle if I know three points, but I would like to reald also the concave one.
this function ang = atan2(norm(det([P2-P0;P1-P0])),dot(P2-P0,P1-P0)); , it gives me only convex one
thank you
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Torsten il 22 Nov 2022
Let the OP choose what better fits her needs:
thd = 0:10:360; % a sequence of angles from 0-360
xx = cosd(thd);
yy = sind(thd);
h = numel(thd);
ang = zeros(h,1);
for f = 1:h
P1=[0 0]; % some fixed point
P2=[1 0]; % i'm going to fix this one too
P3=[xx(f) yy(f)]; % this point moves in a circle about P0 [x,y]
angstn = atan2(P3(2) - P1(2), P3(1) - P1(1)) - atan2(P2(2) - P1(2), P2(1) - P1(1));
if angstn < 0
angstn = angstn + 2*pi;
end
ang(f) = angstn*180/pi;
end
cosf = cos(ang);
plot(thd,ang) % output is folded at 180
Eliska Paulikova il 22 Nov 2022
Thank you so much
It means a lot for me
thank you

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### Risposte (1)

David Goodmanson il 23 Nov 2022
Hi Eliska,
One thing that does not seem to be mentioned so far is your use of the norm function on the determinant. That makes all the sines positive, which puts you into the first or second quadrant and forces all the angles out of atan2d to be 0<=theta<180. Dropping the norm opens up the range of angles to 0<=theta<360. In the code below, (P2-P0) is a reference vector, and the angle is measured counterclockwise from (P2-P0) to (P1-P0) with 0<=theta<360.
P0 = [0 0];
P1 = [-1 2];
P2 = [1 1];
P20 = P2-P0; % reference vector
P10 = P1-P0;
theta = atan2d((det([P20;P10])),dot(P20,P10));
theta = mod(theta,360)
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