How to determine the centroid of this fan(triangle) where the coordinates of one of the vertices is only known and the distance is also known?

I am not getting the centroid correctly. Please check the code.

x=[3];
y=[3];
r=[2];
    delta=pi/3;
    theta=2*pi*0.4;
    si=size(x);
for i=1:si(2)  
   theta2 = theta + delta; 
   t = linspace(theta,theta2);
   A = x(i) + r(i)*cos(t);
   B = y(i) + r(i)*sin(t);
   x_cen = mean(A)
y_cen = mean(B)
   plot([x(i),A,x(i)],[y(i),B,y(i)],'b-',x_cen,y_cen,'ro')
   axis([0 10 0 10]);
end

[Are Mjaavatten]

A and B contain points on the arc only, so you get the center of mass of the arc and not the sector. The centroid of a sector that is symmetric about the x axis is [2*r*sin(delta)/delta,0]. Rotate this point to the correct position.

See Wikipedia: List of centroids .

[Aida Jones]

I am still not getting it correctly. Please write the full code

[Aida Jones]

I have tried another one. Plz check this and correct this one to find the centroid of the sectored circle.: x=[3]; y=[3]; r=[2]; delta=pi/2; theta=2*pi; theta2 = theta + delta/2; t = linspace(theta,theta2); A = x + r*cos(t); B = y + r*sin(t); xV=x + ((2*r/3)*cos(theta2)*sin(delta/2)/(delta/2));%EDA II yV=y + ((2*r/3)*sin(theta2)*sin(delta/2)/(delta/2));%EDA II plot([x,A,x],[y,B,y],'b-',xV,yV,'ro') axis([0 10 0 10]);

[Aida Jones]

Thank you

Answer 1

[Are Mjaavatten]

In my comment there was a typo in the expression for the centroid. A factor of 1/3 was missing. Sorry about that.

Here is a script that should give you what you want:

clear;
% Circle:  
x_center= 3;
y_center= 3;
r = 2;
% Sector:
delta=pi/3;              % Sector width
theta=2*pi*0.4;          % Sector start angle 
alpha = theta+ delta/2;  % Sector center line angle
r_centroid = 4*r*sin(delta/2)/delta/3;
% Translate and rotate:
x_centroid = x_center + r_centroid*cos(alpha);
y_centroid = y_center + r_centroid*sin(alpha);
figure(1);
% Plot full circle:
t = linspace(0,2*pi);
x_circle = x_center + r*cos(t);
y_circle = y_center + r*sin(t);
plot(x_circle,y_circle,'--b',x_center,y_center,'*k');
hold on
% Plot sector:
t = linspace(theta,theta+delta);
A = x_center + r*cos(t);
B = y_center + r*sin(t);
plot([x_center,A,x_center],[y_center,B,y_center],'b-', ...
  x_centroid,y_centroid,'ro')
axis([0 6 0 6]);
axis equal
hold off

[Image Analyst]

Try again:

Undefined function or variable 'x'.
Error in test2 (line 18)
x_circle = x + r*cos(t);

[Are Mjaavatten]

At some point i changed the variable name from x to x_center, but forgot to change all occurrences. I should have learned by now to start a script with clear, to avoid goofs like this.

I have also corrected an error in the expression for r_centroid, where I had mixed up the full and the half sector angle. The script should be correct now.