# Searching for math expert! angle of vectors in a loop using law of cosines

3 views (last 30 days)
J.P. on 9 Nov 2016
Commented: Mostafa on 9 Nov 2016
Hello,
I created a loop to get each angle in between two vektors as you can see in the picture. My aim is to get the angle on each sixth point as shwon in the diagramm.
Using the follwing scipt, my resulting angle is always 90°! I can not see the mistake! Probably you do!?
alphaans=int16.empty(1,length(x1),0);
for i = 1:(length(x1)-2)
ax(i)=x1(1,i+1)-x1(1,i);
ay(i)=y1(1,i+1)-y1(1,i);
bx(i)=x1(1,i+2)-x1(1,i+1); %second (b) vector
by(i)=y1(1,i+2)-y1(1,i+1);
cx(i)=x1(1,i)+ax(i)+bx(i); %resulting, leading to third vector
cy(i)=y1(1,i)+ay(i)+by(i);
lcx(i)=x1(1,i+2)-x1(1,i); %third (c) vector
lcy(i)=x1(1,i+2)-x1(1,i);
Ba(i)=sqrt((ax(1,i)^2+ay(1,i)^2)); % norm (a)
Bb(i)=sqrt((bx(1,i)^2+by(1,i)^2)); % norm (b)
Bc(i)=sqrt((lcx(1,i)^2+lcy(1,i)^2)); % norm (c)
alpha(i)=acosd(((Bb(1,i))^2+(Ba(1,i))^2-(Bc(1,i))^2)/(2.*Ba(1,i).*Bb(1,i))); %law of cosines
alphaans(1,i,1)=alpha(i); %put each angle in the array alphaans
end
Thanks!
J.P. on 9 Nov 2016
I am sorry, but I preprocessed the data, so that every sixth point is calculated already as you can see in the picture. But thank you so much. I should take a closer look, after copy-pasting the rows. Thanks a lot again!
Mostafa on 9 Nov 2016
I think you only need to replace each instance of i+6 with i+1 and i+12 with i+2
Cheers.

Thorsten on 9 Nov 2016
Edited: Thorsten on 9 Nov 2016
% define sample values
x = [1234.77 936.40 681.39 516.59 355.26 82.90];
y = [241.90 155.16 118.73 193.32 408.43 458.74];
% plot values
y = 500 - y; % subtract to make y axis pointing upwards, just for display
% purposes
plot(x, y, 'ko-')
axis equal
grid on
box off
% get angle between successive line elements
vec = [diff(x)' diff(y)'];
for i = 1:size(vec, 1) - 1
u = vec(i,:);
v = vec(i+1,:);
theta(i) = acos( (u * v')/(norm(u)*norm(v)) );
% u * v' is the dot product between u and v
end

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