Space globally deformed


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

  1. Conclusion of a letter from Pierre Bézier answering to the researcher Christophe Rabut, Paris, 5 November 1999, when he was collecting elements for "Mémoires d'un outilleur" (Translated from French) 

  2. Le Bulletin de la Section d’Histoire des Usines Renault, tome 5, juin 1985, n°30, 272-283. With the kind authorization of the Section d’Histoire des Usines Renault 

  3. MFtrace is a Python program that trace a TeX bitmap font into a PostScript Type1 font or TrueType font. 

  4. HP-GL (Hewlett-Packard Graphics Language) is a printer control language created by Hewlett-Packard. Primary printer control language used by HP plotters, it later became a standard for almost all plotters. 

  5. String art is characterized by an arrangement of colored thread strung between points to form geometric patterns or representational designs.