I read an article about Bezier surfaces and an algorithm about dynamic LOD of the Bezier surfaces. But for this algorithm I need the second derivate of the Bernstein basis, but I don''t know how to get it.
Bernstein: B (u) = (n!/(i!*(n-i)!)*u^i*(1-u)^(n-i)
If someone has a way, to get the second derive of that function, I''ll need it, no matter how slow it is.
Sorry, for my bad english...
With a Bezier surface each control point in the characteristic polyhedron affects the whole surface according to the Bernstein polynomes. With B-Spline surfaces each control point only affects the immediate surrounding area of the surface. How large this area is is determined by the grade of the B-Spline. A grade of three means that each point on the surface is affected by at most 9 control points.
A B-Spline surface of grade 3 can when rendered be divided into smaller patches, each controlled by 9 control points, and rendered just as the bi-quadratic Bezier surface. With slightly different weight functions of course.
Here is an article on NURB curves. It explains the NURB curve (Duh!). The Non-Uniform part can be a little tricky, but fortunately you'll most likely not need it, at least not anytime soon. The B-Spline is just a specialization of the NURB where the knot-vector is uniform, instead of non-uniform.