mechatronic mayhem

Tutorials, demos, and source code by Ken Johnson:

GraphDisplay: a Bezier based control for graphing functions and curves

Spirograph Shapes: WPF Bezier Shapes from Math Formulae

“In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point of a circle— called an epicycle — which rolls without slipping around a fixed circle. It is a particular kind of roulette.”

-http://en.wikipedia.org/wiki/Epicycloid

So, basically, a spirograph.

Here’s Henniny Koczy’s 3d epicloids:

The 3D Spirograph Project from Henning Koczy on Vimeo.

I found a few other attempts at 3d but most of them only translated one parameter along a 3d axis.  The result is tangled mess.

3D SpiroGraph Form from P&A LAB on Vimeo.

from p&a lab

I’d be more interested in a 3d interpretation that looks like it was grown instead of entangled.  It seems like one would be able to generate something akin to a rose with a 5 cusp equation.