A$.(10$ marks$)$

A designer selects the following control points to create parametric curves for the front and back of a new car hood. Compute the Bezier Surface equation, P$($u$,$v$),$ that generates the new car hood from the following control points:

Front of Hood: P$1=[-1,-1,3]$T$,$ P$2=[0,-2,4]$T$,$ P$3=[1,-1,3]$T

Back of Hood: P$4=[-1,0,-1]$T$,$ P$5=[0,1,0]$T$,$ P$6=[1,0,-1]$T