Rolling curve / 05

Dual-fold hypotrochoid

Geometry

A circle of radius r rolls inside a fixed circle of radius R, and the rolling term is multiplied by sin(2·t).

x(t) = (R − r)·cos t · sin(2·t) + d·cos((R − r)/r · t)
y(t) = (R − r)·sin t · sin(2·t) − d·sin((R − r)/r · t)

Shape & appearance

Outer radius R Inner radius r Pen distance d Line width Base colour Auto-sweep first slider

Saved PNGs

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