Another Way to build a Bézier curve...
Bernstein-Bezier Formulation of Bezier Curve (Spline)
The Bernstein-Bezier formulation is based on the subdivision
property of Bezier curves.
The subdivision property completes the
definition of the spacing of the control points.
The subdivision construction is:
Draw lines connecting the control points, and then recursively
draw lines between the midpoints of those lines for a total of n-2 iterations,
where n is the degree of the Bezier curve (Figure 3.1.). For a cubic Bezier
curve, n=3, so there is just one subdivision.
Points P0 , P01 , P02
, P(t) and P(t) , P12 ,
P21 , P3 are control points
of new small splines again.
To learn more..."Cubic
Bezier Patches Used to Draw Utah Teapot"