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a5 – Cycloids & Trochoids

Rolling circles & point tracers

Cycloids & Trochoids

Family Type

R outer radius, r rolling radius, d pen offset. Spiro blends multiple offsets.

Parameters R (outer) r (rolling) d (offset) Turns Points Stroke Speed

Colors Palette Blend Mode

Notes

Cycloid: x=t - sin t, y=1 - cos t (scaled).
(Epicycloid / Hypocycloid) classic rolling circle formulas.
Trochoids adjust offset d for loops / waves.
Spiro Blend draws multiple offsets for layered color.

Cycloidal harmonies – a-series. Export for vector spirograph art.

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