Bezier Curves are built using Bernstein Polynomials.

The following examples show how to use four control points, and the four Bernstein polynomials above to create a parametric Bezier curve. In each example, verify that the two control points at the beginning and end of the curve do indeed lie on the curve, and that the slope of the tangent line to the curve at these two control points is the same as the slope of the corresponding line segments shown in the plots. It turns out that, as shown in the plots, the middle two control points generally don't lie on the curve.

Example 1.

Example 2.

Example 3.

Example 4.