how to find concave angle between three points

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

[Torsten]

May I ask what you mean by convex and concave angle ?

[Eliska Paulikova]

Sure, so the matlab gives me values 10, 30, 50 ... 180 degree and than (because it is circle it has 360 degrees) but matlab when it turns 180 it goes 170, 160 ... until 0

but I would like to go 180, 190 .. until 360

[Torsten]

Could you show reproducable code ?

[Eliska Paulikova]

for f=1:h
    t=(f-1)*k/20;
    m=f+1;
    P0=[70 70]; %střed [x,y]
    P1=[htabulka(1,1),htabulka(1,2)]; %XY1 [x,y]
    P2=[htabulka(f,1),htabulka(f,2)]; %XY2 [x,y]

    angstn = unwrap(atan2(norm(det([P2-P0;P1-P0])),dot(P2-P0,P1-P0)));
    ang=angstn*180/pi
    cosf=cos(ang);

[Torsten]

We cannot run this code since h, k, htabula are not known.

[Eliska Paulikova]

h is 219 and k is 500

But you can not run it because .. this code is connect with the another code where I use video ...

I send you the output

[Eliska Paulikova]

[Eliska Paulikova]

see it goes to 178 and than it suppose the be greater than 180 .. but it goes down

[Torsten]

We still don't know htabulka.

[Eliska Paulikova]

I give you the output ... I can not give you the whole code it is large and you need the video I use

[Torsten]

I cannot tell you more than using

P1(1) = 3;
P1(2) = 5;
P2(1) = 7;
P2(2) = -8;
P3(1) = 4;
P3(2) = 4;
angle = (atan2(P3(2) - P1(2), P3(1) - P1(1)) - atan2(P2(2) - P1(2), P2(1) - P1(1)))*180/pi

angle = 27.8973

if angle < 0 
  angle = angle + 360;
end

hold on
plot([P1(1);P2(1)],[P1(2);P2(2)])
plot([P1(1);P3(1)],[P1(2);P3(2)])
hold off

[DGM]

On behalf of OP, here is a MWE:

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
    P0=[0 0]; % some fixed point
    P1=[1 0]; % i'm going to fix this one too
    P2=[xx(f) yy(f)]; % this point moves in a circle about P0 [x,y]
    
    angstn = unwrap(atan2(norm(det([P2-P0;P1-P0])),dot(P2-P0,P1-P0)));
    ang(f) = angstn*180/pi;
end
cosf = cos(ang);

plot(thd,ang) % output is folded at 180

... but that kind of makes sense, if we're always looking for the interior angle.

[Torsten]

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]

Thank you so much

It means a lot for me

thank you

Answer 1

[David Goodmanson]

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)