How a French car designer’s math trick became the foundation of modern digital design.

Art · Published 30 September 2026 Swipe more like this →

In short: Bézier curves are the invisible backbone of everything you see on a screen, from typography to animation. Developed in the 1960s to streamline the bodywork of Renault automobiles, these parametric curves allow computers to render smooth, scalable shapes that remain perfect at any size, forever changing visual communication.

The mathematical foundation for these curves, known as Bernstein polynomials, dates back to 1912. However, they remained theoretical until the late 1950s. In 1959, mathematician Paul de Casteljau, working for the French automaker Citroën, developed a numerically stable algorithm to evaluate these curves for computer-aided design. Simultaneously, and independently, French engineer Pierre Bézier began using the same principles at Renault in the 1960s to design car bodies. While de Casteljau’s work was patented in France, it was not publicly released until the 1980s, leaving Bézier to popularize the method during the 1960s.

At their core, Bézier curves are defined by a sequence of control points. The first and last points act as the curve's endpoints, while intermediate points dictate the shape's curvature without necessarily lying on the line itself. A linear curve connects two points, a quadratic curve uses three, and a cubic curve employs four. By adjusting these control points, designers can manipulate the 'physics' of a movement, such as how an icon accelerates across a screen or how a robotic welding arm moves to minimize mechanical wear.

Beyond static graphics, these curves are essential for vector-based design, where paths can be scaled indefinitely without losing quality. They are also used in the time domain to smooth out transitions in animation and user interfaces. Because they rely on affine combinations—where coefficients sum to one—they provide a robust, predictable way to model complex, real-world shapes that lack simple mathematical definitions. Today, they are the standard for everything from font rendering to sophisticated motion graphics.

General information, not professional advice. Spotted an error? Flag the card or see corrections and complaints.

Intellect Plus is a visual educational discovery platform for exploring fascinating facts and ideas. Brain Food, Not Brain Rot. What is Intellect Plus?

Related

• The engineer who turned automobile design into the language of modern digital graphics
• The mathematical engine behind the smooth curves of modern computer graphics
• Modern curves are continuous images of intervals—sometimes wild ones
• Why mathematicians use flexible wooden rulers to model complex digital curves
• The math that makes digital curves feel smooth and natural
• From manor managers to debt enforcers: the long, complex history of the bailiff
• Why the most important tool in modern car design is a lump of clay.
• How a giant catfish and a gold crisis ended Japan's feudal era
• A rare photographic record of the Holocaust, discovered by a survivor in a cupboard.
• Did Renoir paint two versions of his masterpiece, and which one is real?
• When Valerie Solanas shot Andy Warhol, she sought fame through a violent act of erasure.
• Why Barbara Hepworth painted the hollows of her sculptures with vivid blues and yellows

More in Visual arts · More in Art · Latest · A–Z · All topics