Generate random coordinates around a circle

How can I generate 15 random 2-D coordinates around a circle of radius R with the center of the circle being a defined [x y] 2-D coordinate? Thanks

[Cedric]

What have you tried so far?

[John]

I can generate the random coordinates within R (below) but I don't know how to change them so that they are distributed around coordinate, say [20 30]

R.*rand(15,2)

[Richard Brown]

Hint: polar coordinates

[John]

Unfortunately, I rarely use Matlab, I have no clue how to do it even with the polar coordinates hint

Answer 1

[Azzi Abdelmalek]

x0=10; % x0 an y0 center coordinates
y0=20;  
radius=10;  % radius
angle=-pi:0.1:pi;
angl=angle(randperm(numel(angle),15));
r=rand(1,15)*radius;
x=r.*cos(angl)+x0;
y=r.*sin(angl)+y0;
xc=radius.*cos(angle)+x0;
yc=radius.*sin(angle)+y0;
scatter(xc,yc,'.r')
hold on
scatter(x,y)
xlim([-radius radius]+x0)
ylim([-radius radius]+y0)
axis square
hold off

[Richard Brown]

Again, you're choosing from an artificially finite set (63) of evenly spaced angles there. Also, this method will cluster points near the centre of the circle.

[John]

The link http://matlab.wikia.com/wiki/FAQ#How_do_I_create_a_set_of_random_locations_within_a_circle.3F provided by Richard Brown worked, Thanks you all for your help

Answer 2

[Azzi Abdelmalek]

x0=10; % x0 and y0 are center coordinates
y0=20;  
r=1;  % radius
angle=-pi:0.1:pi;
angl=angle(randi(numel(angle),15,1))
x=r*cos(angl)+x0
y=r*sin(angl)+y0
scatter(x,y)
xlim([-r r]+x0)
ylim([-r r]+y0)
axis square

[Richard Brown]

I presume you mean

angl = 2*pi*rand(1, 15)

[John]

This seems to work but the coordinates seem to be distributed along the circle circumference. Is there a way to distribute them all over the circle? Thanks

[Richard Brown]

I seem to recall Roger Stafford answering this very question maybe yesterday? Could be worth trawling through recent questions to have a look. edit Actually, it was a while ago, but it got updated yesterday:

http://matlab.wikia.com/wiki/FAQ#How_do_I_create_a_set_of_random_locations_within_a_circle.3F

[Azzi Abdelmalek]

Do you mean inside the circle?

[Azzi Abdelmalek]

Richard, I think it's better to use randperm, with rand or randi there is a risk to have repetition