Spirograph (Hypotrochoid)

The classic Spirograph curve: one circle rolling inside another, with a pen tracing a point offset from the rolling circle's centre. Generates beautifully intricate rosette patterns from three numbers.

A rosette Spirograph pattern on the Fabric Sculpt canvas

Parameters

Hypotrochoid parameters

Fixed Radius (R): Radius of the outer fixed circle in mm. Range 10–200, default 100. Roughly the overall pattern size.
Rolling Radius (r): Radius of the inner rolling circle in mm. Range 1–100, default 30. The ratio R / r determines the shape — integer ratios produce closed rosettes, irrational ratios spiral forever.
Pen Distance (d): Offset of the pen from the rolling circle's centre in mm. Range 1–200, default 50. At d = r the curve is a hypocycloid; larger d produces longer loops.
Revolutions: How many times the rolling circle orbits. Range 1–200, default 10. Integer multiples of R / gcd(R, r) close the curve perfectly; non-integer counts give partial traces.
Resolution (pts/rev): Number of sample points per revolution. Range 10–360, default 100. Increase for smooth circles; the curve is closed, so jaggy sampling shows up at the crossings.

Tuning tips

To close the curve set Revolutions = R / gcd(R, r). Example: R = 100, r = 30 → gcd = 10, so R / gcd = 10. Ten revolutions close the rosette.
Petal count equals R / gcd(R, r) — the example above produces a 10-petal rosette.
Thin filigree vs full loops — pick small d for delicate traces, large d for bold overlapping loops.

Typical use

Decorative coasters / tiles — one generator produces a complete design.
Jewellery pendants — scale down and print in TPU or PLA at thin nozzle widths.
Artistic prints — filters like ripple and twist layer beautifully on top.

Fabric Sculpt Overview
Concentric Curves — simpler nested rings.
Transform filter — rotate copies of the pattern for stacked rosettes.