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: $P_4=[-1,0,-1{]}^T,P_5=[0,1,0{]}^T,P_6=[1,0,-1{]}^T$