t  =  
      0;  b =  0; c = 3/4;
P1 = {0, 0}; P2 = {1, 1}; P3 = {2, 0}; 
    M  =  {{2, -2, 1, 1}, {-3, 3, -2, -1}, {0, 0, 1, 
          0}, {1, 0, 0, 0}};

TL = 
      0.5*(1 - t)*(1 - c)*(1 + b)*(P2 - P1)  + 
        0.5*(1 - t)*(1 + c)*(1 - b)*(P3 - 
              P2)
TR = 
      0.5*(1 - t)*(1 + c)*(1 + b)*(P2 - P1)  + 
        0.5*(1 - t)*(1 - c)*(1 - b)*(P3 - P2)

For[u = 0; plist = {}, u ≤ 1.0, u = u + 0.05, 
        U = {u*u*u, u*u, u, 1}; 
plist = 
          Append[plist, U . M . {P1, P2, {1, 0}, TL}]] ;For[
        u = 0; qlist = {}, u ≤ 1.0, u = u + 0.05, 
        U = {u*u*u, u*u, u, 1}; 
qlist = 
          Append[qlist, 
            U . M . {P2, P3, 
                TR, {1, 0}}]] ;

Show[
      Graphics[{PointSize[0.03], Point[P1], Point[P2], Point[P3], 
          Thickness[0.01], Line[plist], Line[qlist]}], 
      PlotRange -> {{-0.1,  2.1}, {-0.1, 1.1}}, 
      Axes -> Automatic]