To create a Bézier surface, We blend a mesh of Bézier curves using the blending function
where j and k are points in parametric space and represents the location of the knots in real space. The Bézier functions specify the weighting of a particular knot. They are the Bernstein coefficients. The definition of the Bézier functions is
where C(n,k) represents the binary coefficients. When u=0, the function is one for k=0 and zero for all other points. When we combine two orthogonal parameters, we find a Bézier curve along each edge of the surface, as defined by the points along that edge. Bézier surfaces are useful for interactive design and were first applied to car body design.
You can look at the Bezier surface from a 3x3 mesh, or the Bezier surface from a 4x4 mesh