from a circle to polygon

Hello All,

If I have a circle (x-a)^2 +(x-b)^2 = r^2 , is the any matlab function that converts this circle to polygon?

Thanks

Mohamed

Answer 1

[Scott MacKenzie]

I know of no such formula, although no doubt one could be put together.

You can think of circle as a polygon with a large (infinite!) number of vertices. Reduce the number of vertices and the shape starts to look like a polygon. Using trig functions, here's one way to demonstrate this:

radius = 1;
tiledlayout(1,4);

nexttile;
n = 100; % number of vertices (+1)
theta = linspace(0,2*pi,n);
x = cos(theta) * radius;
y = sin(theta) * radius;
plot(x,y);
title(compose('Number of vertices = %d', n-1));
set(gca, 'xlim', [-1 1], 'ylim', [-1 1]);

nexttile;
n = 16; % number of vertices (+1)
theta = linspace(0,2*pi,n);
x = cos(theta) * radius;
y = sin(theta) * radius;
plot(x,y);
title(compose('Number of vertices = %d', n-1));
set(gca, 'xlim', [-1 1], 'ylim', [-1 1]);

nexttile;
n = 9; % number of vertices (+1)
theta = linspace(0,2*pi,n);
x = cos(theta) * radius;
y = sin(theta) * radius;
plot(x,y);
title(compose('Number of vertices = %d', n-1));
set(gca, 'xlim', [-1 1], 'ylim', [-1 1]);

nexttile;
n = 4; % number of vertices (+1)
theta = linspace(0,2*pi,n);
x = cos(theta) * radius;
y = sin(theta) * radius;
plot(x,y);
title(compose('Number of vertices = %d', n-1));
set(gca, 'xlim', [-1 1], 'ylim', [-1 1]);

[Mohamed soliman]

Hello @Scott MacKenzie

Thanks a lot for your help.

BR

Mohamed

[Scott MacKenzie]

You're welcome. Glad to help. Have fun.

Answer 2

[Steven Lord]

As @Scott MacKenzie stated, you can approximate a circle as a many-sided regular polygon. The nsidedpoly function will create such a many-sided polygon that you can plot or operate on.

for k = 1:6
    subplot(2, 3, k)
    P = nsidedpoly(3^k);
    plot(P);
    title(3^k + " sides")
end

[Mohamed soliman]

Thanks @Steven Lord for your help.

[Mohamed soliman]

I have a nother question, is there a function that , given a polygon: pgon2 = nsidedpoly(8,'Center',[5 0],'Radius',10); can automatically construct A and b matrices such that A.x<= b

i.e this polygon can be represented by a set of inequaltiy constraints

Best regards

Mohamed