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Bezier surface
A surface defined by mathematical formulae, used in {computer graphics}. A surface P(u, v), where u and v vary orthogonally from 0 to 1 from one edge of the surface to the other, is defined by a set of (n+1)*(m+1) "control points" (X(i, j), Y(i, j), Z(i, j)) for i = 0 to n, j = 0 to m.
P(u, v) = Sum i=0..n {Sum j=0..m [
(X(i, j), Y(i, j), Z(i, j))
* B(i, n, u) * B(j, m, v)]}
B(i, n, u) = C(n, i) * u^i * (1-u)^(n-i)
C(n, i) = n!/i!/(n-i)!
Bezier surfaces are an extension of the idea of {Bezier curves}, and share many of their properties.
(1996-06-12)
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