Source : Free On-Line Dictionary of Computing

Bezier curve
     
         A type of curve defined by mathematical formulae,
        used in {computer graphics}.  A curve with coordinates P(u),
        where u varies from 0 at one end of the curve to 1 at the
        other, is defined by a set of n+1 "control points" (X(i),
        Y(i), Z(i)) for i = 0 to n.
     
        	P(u) = Sum i=0..n [(X(i), Y(i), Z(i)) * B(i, n, u)]
     
        	B(i, n, u) = C(n, i) * u^i * (1-u)^(n-i)
     
        	C(n, i) = n!/i!/(n-i)!
     
        A Bezier curve (or surface) is defined by its control points,
        which makes it invariant under any {affine mapping}
        (translation, rotation, parallel projection), and thus even
        under a change in the axis system.  You need only to transform
        the control points and then compute the new curve.  The
        control polygon defined by the points is itself affine
        invariant.
     
        Bezier curves also have the variation-diminishing property.
        This makes them easier to split compared to other types of
        curve such as {Hermite} or {B-spline}.
     
        Other important properties are multiple values, global and
        local control, versatility, and order of continuity.
     
        [What do these properties mean?]
     
        (1996-06-12)