Bernstein blending function
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In mathematics, the Bernstein blending function is a function for geometrically blending a number of points.
Consider applying the De Casteljau algorithm to the degenerate case of a Bezier Curve with only two knots. This gives the parametric line equation:
- P = (1 − μ)P0 + μP1
We are blending two position vectors to give a third. The parameter μ may be thought of as the distance along the line from P0 to P1. For more than two knots, more complex blending is required. This leads to the iterative formulation of a Bezier curve:
where i is an iterator over the number of knots N and W(N,i,μ) is the Bernstein blending function which is formally defined by
where 
