Yes, I know how to code bezier curves, but why do they work so well? I mean, what''s the math behind them? b(u)= (k=0->N) Sigma pk*N!/(k!*(N-k)!)*u^k*(1-u)^(N-k) I just don''t get it. The N!/(k!*(N-k)!) looks like ( N ) ( k ) -Hans

First some notation BEZ(k,n)(u) is the kth Bezier polynomial for n points evaluated over u (also called Bernstein polynomials).

For points p(0) to p(n) the bezier curve that fits it is:
P(u) = Sum(k=0, n) p(k)BEZ(k,n)(u)

The Bernstein polynomials were chosen because

1. they fit the following relation:
BEZ(k,n)(u) = (1 - u)BEZ(k, n-1)(u) + u BEZ(k - 1, n)(u)
2. have the property that the sum of all the bezier polynomials BEZ(0,n)(u) to BEZ(n,n)(u) equals one.
3. each Bezier polynomial is greater than or equal to 0 between u = 0 to u = 1.

The first property make bezier matrices easy to calculate. The second and third property ensures that the bezier curve fit inside the convex hull of the points.
The second and third property also ensure that the curve blends well.