From Bézier to Bernstein

Bézier curves are ubiquitous in computer graphics. . . .

Introduction

Bézier curves are ubiquitous in computer graphics. They were introduced implicitly into theoretical mathematics long before computers, primarily by the French mathematician Charles Hermite and the Russian mathematician Sergei Bernstein. But it was only the work of Pierre Bézier, an employee of the automobile maker Renault, and of Paul de Casteljau, of Citroen, that made these curves familiar to graphics specialists. Recently, the polynomials defined by Bernstein have become again of interest to mathematicians.

A cubic Bézier curve.

Bill Casselman
University of British Columbia, Vancouver, Canada
cass at math.ubc.ca

From the editor's desk

Welcome!

These web essays are designed for those who have already discovered the joys of mathematics as well as for those who may be uncomfortable with mathematics. Mathematics is a fast growing and evolving subject. The domain of ways that mathematics is being applied is growing by leaps and bounds. Examples include CT scans, audio CD's, face recognition systems, and cell phone technology. Our goal is to share our excitement about these developments with you.
More . . .

Feature Columns at a Glance

October: Inside-out Frieze Symmetries in Ancient Peruvian Weavings
September: Gray Codes
August: Percolation: Slipping through the Cracks
June-July: The Mathematics of Surveying: Part II. The Planimeter
May: The Mathematics of Surveying: Part I
April: The Process of Electing a President
March: Random Numbers: Nothing Left to Chance
February: What Is the Length of a Year on Planet Sitnikov?
January: Urban Geometry
December: Pulling Digits out of Pi

View the full archive

Visit the rest of the site