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From my investigations of this idea, the modern algorithms for Guilloche patterns absolutely does comport well with embroidery. But, in this case we're talking about things like step-repeat patterns to fill a curve between a cycloid with period of turn/5 and another with a period of turn/7 following a sine wave between the two boundary conditions.
http://www.excourse.com/excentro/ is one of the best programs for this, and shows the typical UI this involves. It requires a series of shapes that are blended together in various ways with particular effects.
(Defunct Online Guilloche)
Basically you define a tree of different shapes descending from a base shape which is usually like a circle. Then you add to that circle an effect like a sine-wave, saw-tooth, or cycloid (dot rolling on a circle, rolling on the shape in question). You then calculate the position by figuring the location you would between 0,1 and shoe-horning that between the various other bases and effects, which form the envelope.
Copied from old to do list.
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