This spline approximation method was developed by French Engineer Pierre Bezier for use in the design of Renault automobile bodies Bezier splines have a number of properties that make them highly useful and convenient for curves and surface design. They are easy to implement. Bezier splines are widely available in CAD systems.
Bezier Curves : A Bezier curve can be fitted to any number of control points. The number of control point to be approximated and their relative position determine the degree of Bezier polynomial. As with interpolation splines, a Bezier curve can be specified with boundary conditions, with characterizing matrix or with blending functions.
Suppose we have (n + 1) control point positions: Pk – (xk, yk, zk,) with K varying from 0 to n. These coordinate points can be blended to produce the following position vector P(u), which describes the path of an approximating Bezier Polynomial function between P0 & Pn.
A Bezier Curve is a polynomial of degree one less than the number of control points used.
Three points generates Parabola.
Four points generates Cubic Curve.
Bezier Curves generated from three or four control points. Dashed lines connect the control point positions.