Greetings @prawnsushi et al.
With string art, you dance very close to the edge of a topic into which I have fallen many times — much to my delight. See, for example, Post #787 in Reptorian G’MIC Filters.
This “string art” formulation lies at the heart of De Castlejau’s Algorithm and its generalization, deBoor’s Algorithm. Through these absolutely simple straight-line strings, one recursively “boots up” to more complex curves, for the edge formed by these crisscrossing “first degree” linear curves (the lines) scribe a “second degree” curve. Keep an eye out for The Geometry Toolbox by Gerald Farin and Dianne Hansford. It’s been out for awhile and the 1st edition probably could be had from a second hand book store for $10-15 USD. I can’t think of a better introduction to drawing lines, curves and surfaces through parametric (u, v, w… and their ilk) equations. Have fun.