Computing the points:

This result gives us a simple way for computing p(u, v) given (u, v). Here is why. As each q_i (v) is a point on the Bézier curve indicated by the i-th row of control points : p_i0, p_i1, . . . , p_in. Thus, for the i-th row and a given v, we may apply de Casteljau's algorithm for Bézier curve to calculate q_i (v). After m + 1 applications of de Casteljau's algorithm (that means one for each row), we will have q₀(v), q₁(v), ..., q_m(v) in hand. Then, applying de Casteljau's algorithm to these m + 1 control points again with u yields the final point p(u, v) onto the surface!

It illustrates this concept. The given surface is a degree (2, 2) Bézier surface described by a 3 × 3 control net. Imagine u = 2/3 and v = 1/3. To find out q₀ (1/3), we take the 0-th row of control points p₀₀, p₀₁ and p₀₂ and by apply de Casteljau's algorithm to this Bézier curve with v = 1/3. Repeat this for the first row & the second row with v = 1/3. This yields three intermediate control points q₀ (1/3), q₁ (1/3) and q₂ (1/3). At last, apply de Casteljau's algorithm to these three new control points with u = 2/3. The result is p(2/3,1/3).

At last , the following summarizes this algorithm :

Input : a m + 1 rows and n + 1 columns of control points & (u, v).

Output : point on surface p(u, v).

Algorithm : for i = 0 to m do

begin.

          By Apply de Casteljau's algorithm to the i-th row of control points along with v;

          Consider the point obtained be qi (v);

end

Apply de Casteljau's algorithm to q₀ (v), q₁ (v), . . . , q_m (v) with u;

The point obtained is p(u, v);