Spiro vectorial illustrations redrawn from Le Bulletin de la Section d’Histoire des Usines Renault^{1}
Pierre Bézier translated traditional projection techniques used for 'carrying over' physical 3D clay models to 2D planes, into new tools. His dreamy and fantastic drawings of coil springs and weights attached to anchors, drawing the ideal shapes of French cars, point at the way upright 'handles' seem appropriate ways to influence the flow of a curve.
There is something quite bizarre about the ‘cartbeforehorse’ order of process in these original Bézier curves. They follow the logic of placing a control point before actually shaping the line, and have a notion of 'live control' over the destination. When drawing, you must plan, make and review iteratively, in constant sequence. This also makes the apprenticeship of Bézier's curves complex, which has often been a point of friction for students and newcomers.
The original Bézier curves are appropriate within the context of translating threedimensional representations of curved surfaces, but the notation model of handles makes it awkward to draw curves in a twodimensional world.
The first vector drawing tool Illustrator (1987) implemented a 2D mode of what we now know as ‘Bézier curves’. When drawing in Illustrator or Inkscape, you just preform; the algorithm does the rest.

Le Bulletin de la Section d’Histoire des Usines Renault, tome 5, Juin 1985, N°30, 272283.  https://web.archive.org/web/20040703214430/http://www.gmm.insatlse.fr/~rabut/bezier ↩