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)