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

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Carlos Santiago Rodríguez Sarmiento 2022-3-9

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编辑： Jan 2022-3-11

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

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Jan 2022-3-9

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

Carlos Santiago Rodríguez Sarmiento 2022-3-9

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

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Answer 1

Jan 2022-3-10

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https://ww2.mathworks.cn/matlabcentral/answers/1667754-if-i-start-with-a-matrix-of-zeros-how-can-i-easily-create-a-hypocycloid-of-ones-in-that-matrix#answer_914419

编辑：Jan 2022-3-11

在 MATLAB Online 中打开

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)

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

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