Vertices of regular n-gon.

I want to find the perimeter of a regular inscribed polygon given N sides. I have a function that will calculate the distance from a set of coordinates. I have the following code to find the coordinates of the vertices for a regular n-gon;

    x = cos(n.*(2*pi)./N);
    y = sin(n.*(2*pi)./N);

I just don't know to store individual coordinates to pass through my function to find the distance between each vertex.

Answer 1

[John D'Errico]

Do it vectorized. Learn to use vectors.

t = linspace(0,1,N);

You can view t as the ratio n/N here, stored as a vector.

x = cos(t.*2*pi);
y = sin(t.*2*pi);

d = sum(sqrt(diff(x).^2 + diff(y).^2));

So, for N = 10, this yields

d =
        6.15636257986204

Not too far from 2*pi. Increase N to 1000,

d =
          6.28317495105715

2*pi
ans =
          6.28318530717959

You can see it does well enough. It should approach 2*pi asymptotically from below as N goes to infinity.

[nanying]

Just want to mention that d = sum(sqrt(diff(x).^2 + diff(y).^2)) only sum N-1*terms which is 9 in your case.

[John D'Errico]

@nanying - what is your point? The first and last vertices in the polygon as created are the same. So if you wanted to point out that to create a true N-gon, thus a regular polygon with N sides, you actually needed to use N+1 in the code above, that would have been a valid comment. The perimeter length of the polygon is correct though.

Answer 2

[Steven Lord]

If you're using release R2017b or later, you can use the nsidedpoly function.