MATLAB: How to plot midpoints between the points of circle

circlecircle points

I draw a circle with s1=4 points.
I have this code
    t1 = 0:(pi/(5*s1)):2*pi; % s1 is the number of points I want to have on the  circle
    x1unit = r1 * cos(t1) + x1;  
    y1unit = r1 * sin(t1) + y1;
    a1=x1unit(1:10:s1*10); % is xi for my circle
    b1=y1unit(1:10:s1*10); %is yi
    plot(x1unit, y1unit, 'b', x1, y1, 'ok');%circle  with the center x1,y1
    plot(a1, b1, 'o'); % x,y for s1 times my points
if I want to add one point right in the middle, between to other points(a1,b1) I use this code:
    ae1=x1unit(6:10:s1*10);
    be1=y1unit(6:10:s1*10);
So, I have one midpoint [s1=4, (1-2,2-3,3-4,4-1) ] . I want more midpoints, for example three or n,if it is possible .
If I want 3 points i use this code
ae11=x1unit(3:10:s1*10);
be11=y1unit(3:10:s1*10);
ae12=x1unit(6:10:s1*10);
be12=y1unit(6:10:s1*10);
ae13=x1unit(9:10:s1*10);
be13=y1unit(9:10:s1*10);
but I don't like this way. Maybe there is more practical way with less code.
My plot is the following picture.Ignore the inner circle. I would like 9 green points,instead one.
like the 3 blue dots,like in the picture:
How I have 9 points which equidistant between the s1 points ???
Thanks in advance

Best Answer

Create the coordinates of the wanted points directly:
x1 = 0;
y1 = 0;
r1 = 1;
n   = 3;  % Points per quadrant
t2  = linspace(0, 2*pi, 4 *(n+1) + 1);
t2(end) = [];   % Do not draw last point twice
xx2 = r1 * cos(t2) + x1;  
yy2 = r1 * sin(t2) + y1;
plot(xx2, yy2, 'o');
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