## 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 **P**_{0} , **P**_{0}^{1} , **P**_{0}^{2}
, **P**(t) and **P**(t) , **P**_{1}^{2} ,
**P**_{2}^{1} , **P**_{3} are control points
of new small splines again.

To learn more..."Cubic
Bezier Patches Used to Draw Utah Teapot"