wishlist: Spirograph LPE

[Jerry W. Segers, Jr.]

The current spirograph plugin [1] only makes shapes based on two circles, and only creates line segments not curves. It is also not a live effect. I believe all these limitations are undesirable. To make a tool useful for making certificates, I would like a live path effect that takes two shapes and a point as input, and rolls the second shape around the first in a non-sliding manner, while preserving the relative position of the point to the rolling shape. It should then create a curve from the pen point. The plugin should not require closed shapes, and should include disguised scaling factors for the rolling shape such that you can approximately specify the number of revolutions per orbit, and exactly specify the number of orbits before the result closes.

I have tried to do this myself, the math is beyond me. You will need to understand a significant amount of calculus to pull this off because the formula to make the curve requires derivatives, and produces a result that is not in itself usable directly. For example, two lines and a point produce a series of second order curves, and a pair of second order curves produces a fourth order curve and so on additively, I don't know how to add points to remove orders from curves, but I have found a paper that describes the creation process of the curves from two shapes and a point. I will attach the paper.

If I can help (research is all I can think of but you may ask for anything and I'll try) just let me know.

[1] http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Extensions-Render.html#Extensions-Spirograph

[Jerry W. Segers, Jr. (segers-j)]

here is the best explanation of how to demote the order of a bezier curve I have been able to find.

http://fontforge.org/bezier.html

[Jerry W. Segers, Jr. (segers-j)]

Update: The current spirograph extension does now create proper curves instead of line segment approximations, but it's still not really useful for certificate borders.