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B-spline curves - clipping and 3d primitives
B-spline curves are piecewise polynomial cubes with one or more polynomial pieces with a minimum smoothness requirement. For example, a C2 cubic B-spline curve has one or more cubic pieces which are joined in such a way that the resulting composite curve is twice continuously differentiable. B-spline curves have a very elegant expression similar to the Bezier representation with basis function as B-spline functions in place of Bernstein basis polynomials. B-spline basis functions can be computed iteratively using de Boor algorithm.
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Important point about the De casteljeau algorithm 1) Bezier Curve: P (u) = ................ (1) Here B n,i (u) = n c i u i (1 - u) n-i ..
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