Bézier surface

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Bézier surface A surface swept out by a moving Bézier curve of constant degree. Each control point of the original Bézier curve also moves through space on a Bézier curve and the curves on which the control points move all have the same degree.

Suppose the initial curve is a Bézier curve of degree m, rm(u) = ∑;i=0m riBim(u),

and let each ri traverse a Bézier curve of degree n, ri = ri(v) = ∑j=0m rijBjn(v),

then the point rm,n(u,v) on the surface is given by rm,n(u,v) = ∑;i=0mj=0m rijBim(u)Bjn(v)