The work of the French engineer Pierre Bézier was at the intersection of physical and digital measures. He developed methods for modelling solid, geometric and physical structures and for representing curves. Just before passing away, he replied to a researcher enquiring about his work:

[...] My contribution could be summarized by this somewhat strange idea: instead of modifying a curve, or a family of curves, it is better to have the space into which we project these, receive a global deformation. The straight line is not... and so on. Best wishes, P. Bézier¹

Redrawn from a picture in Le Bulletin de la Section d’Histoire des Usines Renault²

Bézier tells us that he prefers the global space being considered as distorted, rather than just to focus on a twisting line. This helps humans to conceptualise how he developed his notation system, but computers often must chose a more economic, math based, form of notation, simply for the sake of calculation speed.

We would imagine that the continuous nature of curves could echo well with math based digital realms, and it does, but there is more often than not a need to render the curve out to a less fluid technology : grid, pixels, mosaic, dots, movements of x-y motors in HPGL⁴ plotters, lines or even strings⁵. These 'formats' need origins and dimensions, almost physical units, unlike abstraction friendly computer systems. Some continuous curves described using certain algorithms are even sometimes converted to discrete units (raster) to ease the conversion back to other continuous curves. The utilities to provide antique TeX fonts to recent laying-out platforms like MFTrace³ are examples of this hook.

String art, principle