A Bézier (pronounced "bez-E-A") curve is a line or "path" used to create vector graphics. It consists of two or more control points, which define the size and shape of the line. The first and last points mark the beginning and end of the path, while the intermediate points define the path's curvature.
Bézier curves are used to create smooth curved lines, which are common in vector graphics. Since they are defined by control points, Bézier curves can be resized without losing their smooth appearance. Raster graphics, on the other hand, define each pixel within an image and appear blocky or pixleated when enlarged.
There are several types of Bézier curves, including linear, quadratic, and higher-order curves. A linear curve is a straight line defined by two points. A quadratic curve includes intermediate points that pull the control points, and therefore the path, in different directions. A higher-order curve may include additional intermediate points that fine tune how the path follows each control point.
The shape of a Bézier curve is calculated using interpolation, a method of approximating the path of the line between each control point. Since computer screens display graphics using pixels, Bézier curves are always approximated when displayed on a screen. If you zoom in on a Bézier curve using a drawing program or CAD software, you will see a more accurate representation of the path.
NOTE: Bézier curves are named after French engineer Pierre Bézier, which is why the "B" is always capitalized.