If I start with a matrix of zeros, how can I easily create a Hypocycloid of ones in that matrix?

I want to make an Hypocycloid with a matrix of zeros, it is for make the Fourier Transformation of the image. Something like this https://la.mathworks.com/help/images/fourier-transform.html but instead the Rectangle I need a Hypocycloid like the examples of this page https://es.wikipedia.org/wiki/Hipocicloide when K=3,4 and 5

I need this in Matlab, but not like a plot because the fast fourier transformation doesn't let make the FT to plots

[Jan]

Please mention the details. How should the "hypocycloid" look like? What have you tried so far? What is "the TF"?

[Carlos Santiago Rodríguez Sarmiento]

I've just actuallized the question, TF is because I wrote thinking the concept in Spanish ( Transformada de Fourier) but is FT (Fourier Transformation)

Answer 1

[Jan]

A point to start from - it is not hard to expand this to fill elements of the zero matrix:

M  = zeros(512, 512);

a = linspace(0, 2*pi, 10000);

% Hypocycloid:
r1 = 1;
r2 = 0.2;  % 1/n
x = (r1 - r2) * cos(a) + r2 * cos(a * (1 - r1 / r2));
y = (r1 - r2) * sin(a) + r2 * sin(a * (1 - r1 / r2));

xx = 1 + round((x + 1) / 2 * 511);
yy = 1 + round((y + 1) / 2 * 511);
M(sub2ind(size(M), xx, yy)) = 1;

% Circle:
x = r1 * cos(a);
y = r1 * sin(a);
xx = 1 + round((x + 1) / 2 * 511);
yy = 1 + round((y + 1) / 2 * 511);
M(sub2ind(size(M), xx, yy)) = 1;

colormap([1,1,1; 0,0,0])  % Display the matrix:
image(M + 1)