The Bézier curve is used by Microsoft's Internet Explorer to draw curves on web pages via its own Vector Markup Language, VML. Other curves, lines or geometric shapes available through VML include line, rectangle, oval (hence circle), arc and polyline (continuous line comprised of straight line segments). For more information, see Microsoft's Shape Element documentation.

The Bézier curve was invented by Pierre Bézier in the late 1960's to help design the Renault car. He started his research with numerical methods for designing and manufacturing, then focused on drawing machines, computer control, interactive free-form curve, surface design and 3D milling.

The Bézier curve has since found use in aerodynamic design and the specification of fonts, especially Post Script fonts.

The Bézier curve is defined by the parametric equation:

where:

A straight line drawn from the start of the Bézier curve to the first control point is tangential to the curve at the start and a straight line drawn from the end of the Bézier curve to the second control point is tangential to the curve at the end.

For more information on the Bézier curve, see Bézier Curves and Piecewise Cubic Bézier Curves.