Bezier surface
bezier surface
graphics
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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