i am new to matlab and i am required to plot a circle in matlab and mark its center and generate a random coordinate inside the circle and the negative of this coordinate and measure the distance between these two points any idea ? thanks in advance

i am new to matlab and i am required to plot a circle in matlab and mark its center and generate a random coordinate inside the circle and the negative of this coordinate and measure the distance between these two points any idea ? thanks in advance

Answer 1

[Roger Stafford]

To place a single point randomly within a circle with a statistically uniform distribution area-wise, it is most convenient to use polar coordinates, but a square root operation is needed on the random radius to achieve true uniformity. Let the circle have its center at (xc,yc) and radius R.

 r = R*sqrt(rand);
 t = 2*pi*rand;
 x = xc + r*cos(t);
 y = yc + r*sin(t);
 plot(x,y,'yo')

In case you feel adventurous and want to place a large number of such random points within the circle just to test their uniformity, do this:

 % The random points
 n = 8192;
 r = R*sqrt(rand(n,1));
 t = 2*pi*rand(n,1);
 x = xc + r.*cos(t);
 y = yc + r.*sin(t);

 % The circle
 t2 = linspace(0,2*pi);
 X = xc + R*cos(t2);
 Y = yc + R*sin(t2);

 plot(xc,yc,'w*',X,Y,'r-',x,y,'y.')
 axis equal

The circle is in red, its center is at the white asterisk, and the random points are the yellow dots.

Answer 2

[Joseph Cheng]

to draw a circle you can use

R = 1;
rectangle('position',[0-R,0-R,R*2,R*2],...
    'curvature',[1,1],'linestyle','-','edgecolor','k');

Where you will get a circle with radius R centered around zero.

to get a random point within this circle perhaps use the rand() function to get x and y points and use some scheme to get +/- values( ex: 2*rand(1,2)-1). Mirror across the origin or single axis and use the pythagorean theorem. If the circle is larger than radius 1 just scale everything by the desired radius.