Computer Dictionary of Information Technology

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.