This is a mechanical spline [1]: a thin strip of wood constrained at one or more points, or "knots". They were used by ship builders and draftsmen before mathematicians and programmers invented cubic curves for computer aided design. IIRC, bending a beam with a single point force and no bending moments at the ends gives you a quadratic curve shape, and other, and adding bending moments gives you cubic curves.

1: https://en.m.wikipedia.org/wiki/Flat_spline