Computer Dictionary/Bezier surface

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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 [[Computer Dictionary/Sum j=0..m [ (X(i, j), Y(i, j), Z(i, j)) * B(i, n, u) * B(j, m, v)|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 [[Computer Dictionary/Bezier curves|Bezier curves]], and share many of their properties.


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