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Hypocycloid


hypocycloid.png

Hypocycloid is a parametric curve that is obtained by rolling a smaller circle (r) inside a larger one (R). It shows the trace of a point P, fixed on the circumference of the smaller circle.

General equation:

x(θ) = (k – 1)·cos(θ) + cos((k – 1)·θ)

y(θ) = (k – 1)·sin(θ) – sin((k – 1)·θ)

Outer radius: R =

Inner radius: r =

Ratio: k = R/r

 

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Substitute