Control points in nurbs surfaces -

so i've read lot nurbs , understand nurbs curves ( wrote small library ). i'm having problem surfaces. can see need 2 sets of control points. problem difference between points in these 2 sets is? can briefly explain or give me link does?

i think favorite way of understanding nurbs surfaces (if understand nurbs curves) beads on wire.

so, let's @ simpler example of bezier surface (i assume if understand nurbs curves understand bezier curves).

a cubic bezier curve has 4 control points. imagine bezier curve smooth horizontal curve. can compute point on curve given parameter value (usually called t).. plug t parametric equation of curve, , point produced.

now imagine have 4 horizontal bezier curves, each 1 above other. if plug same parameter value 4 curves, 4 points, 1 each curve. beads on wires. let's call parameter value horizontal curves 's'.

take 4 "bead" points , treat them control points of vertical curve. evaluate curve @ parameter value (this 1 we'll call 't', usual) , give point. point on surface. specifically, that's point p(s,t).

so, given 4x4 grid of control points, can use beads on wire compute points on surface. s changes, beads sweep out different curves along wire.. set of curves surface.

you can exact same thing nurbs curves.. need knot vector s, knot vector t, , grid of control points.