Splines, Nurbs and Bézier curves?

Learning any new piece of software can be a daunting task. As a designer who has spent the best part of 20 years using Adobe’s Creative Suite, you find yourself using an ever-familiar layout of tools and menu items. Like muscle memory, these become second nature. Paths. Crop. Select. As designers, we all get to grips with these ever-familiar terms. So when I took on training for Cinema 4D, it came as some surprise to be faced with a whole new array of technical terms. Booleans. Splines. Nurbs. Hypernurbs. Bézier Curves. Bézier Nurbs. Bézier Splines even. These may sound like the kind of jargon you would expect to hear in a science fiction movie (“Activate the Hypernurb!”), but they are actually some the core elements to creating material in Cinema 4D. Bézier Splines, for example, is a method for creating soft, spatial curves. Hypernurbs, allow you to take geometric shapes and sculpt them into smooth, rounded objects. But why these strange names? Where did they come from?

Well, the development of NURBS (Non-uniform rational basis spline) began in the 1950s by engineers who were in need of a mathematically precise representation of freeform surfaces, like those used for ship hulls, aerospace exteriors and car bodies, which could be exactly reproduced whenever technically needed. Previously, this kind of surface only existed as a single physical 3D model created by a designer or sculptor.

The pioneers of this technical development were Pierre Bézier, who worked as an engineer at Renault, and Paul de Casteljau who worked at Citroën. Bézier worked in parallel to de Casteljau, neither knowing about the work of the other. But because Bézier published the results of his work, the average computer graphics user today at least recognizes the term splines — which are represented with control points lying off the curve itself — as Bézier splines. In the 1960s it became clear that non-uniform, rational B-splines are a generalization of Bézier splines, which can be regarded as uniform, non-rational B-splines.

At first NURBS were only used in the proprietary CAD packages of car companies. It was sometime later that they became part of standard computer graphics packages.

Real-time, interactive rendering of NURBS curves and surfaces was first made available on Silicon Graphics workstations in 1989. In 1993, the first interactive NURBS modeller for PCs, called NöRBS, was developed by CAS Berlin, a small start-up company cooperating with the Technical University of Berlin. Today, most professional computer graphics packages offer NURBS technology.

So there you have it. Thanks to Pierre Bézier I have a whole new digital vocabulary to get used to. And if that wasn’t enough, my Cinema 4D tutors name was Wolf Winter. His actual name. Unbelievable!

Dave B

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