The sixteen control points of a bi-cubic Bezier patch are given as follows.

(0.0 0.0 0.5), (1.0 0.5 2.0), (2.0 0.7 0.5), (3.0 1.0 2.5)

(0.5 1.2 0.7), (1.5 1.5 1.0), (2.5 1.3 0.5), (3.0 1.9 2.0)

(0.2 2.5 2.0), (0. 7 2.7 0.7), (2.5 2.3 1.0), (3.0 3.0 2.5)

(0.5 3.5 2.0), (1.0 3.0 2.0), (2.0 3.7 0.5), (3.0 4.0 1.5)

Take part (0.2 u 0.8, 0.1 u 0.9) of the above Bezier patch to form a new bi-cubic Bezier patch, and regard the new patch as a regular bi-cubic Bezier patch. Derive and calculate the sixteen new control points of the new bi-cubic Bezier patch. Express the new Bezier patch using Matrix form. Plot the new Bezier patch in solid surface representation together with its control point network using MATLAB.

The sixteen control points of a bi-cubic Bezier patch are given as follows. (0.0 0.0 0.5), (0.5 1.2 0.7), (0.2 2.5 2.0), (0.5 3.5 2.0), (1.0 0.5 2.0), (1.5 1.5 1.0), (0.7 2.7 0.7), (1.0 3.0 2.0), (2.0 0.7 0.5), (2.5 1.3 0.5), (2.5 2.3 1.0), (2.0 3.7 0.5), (3.0 1.0 (3.0 1.9 (3.0 3.0 (3.0 4.0 2.5) 2.0) 2.5) 1.5) Take part (0.2