Clear["Global`*"]

Afin[a_]:={a[[1]]/a[[3]], a[[2]]/a[[3]]};
Homog[a_]:=Join[a,{1}];

domek={{-0.5,-0.5}, { 0.5,-0.5}, {0.5,0.5}, {0, 1}, {-0.5,0.5}};

A[t_, p_]:={{Cos[t], -Sin[t], p[[1]]},{Sin[t], Cos[t], p[[2]]},{0,0,1}};

MatrixForm[A[t, {p1, p2}]]

A1=A[0, {0,0}]

A2=A[Pi/2, {5,3}]

MatrixForm[A2]

start=Graphics[{Green, Polygon[Map[Afin, Transpose[A1.Transpose[Map[Homog, domek]]]]]}];
cil=Graphics[{Green, Polygon[Map[Afin, Transpose[A2.Transpose[Map[Homog, domek]]]]]}];

Show[{start,cil}, PlotRange->{{-1, 7},{-1, 7}} , Axes->True]

B[t_]=(1-t)*A1+t*A2

casB[t_]=Graphics[Polygon[Map[Afin, Transpose[B[t].Transpose[Map[Homog, domek]]]]]];

Manipulate[Show[  {start, cil, casB[t]}, PlotRange->{{-1, 7},{-1, 7}} , Axes->True], {t, 0, 1}]

B1[t_]=A[Pi*t/2, (1-t)*{0,0}+t*{5,3}]

MatrixForm[B1[t]]

cas1B[t_]=Graphics[Polygon[Map[Afin, Transpose[B1[t].Transpose[Map[Homog, domek]]]]]];

Manipulate[Show[  {start, cil, cas1B[t]}, PlotRange->{{-1, 7},{-1, 7}} , Axes->True], {t, 0, 1}]

c[t_]=(1-t)^3*{0,0}+3*(1-t)^2*t*{6,0}+3*(1-t)*t^2*{5,1}+t^3*{5,3}

c1[t_] = D[c[t],t];(* prvni derivace = c' *)

normc1[t_] = Norm[c1[t]] ;(* norma prvni derivace = ||c'||*)

T[t_]=c1[t]/normc1[t];

draha=ParametricPlot[c[t],{t, 0, 1}];

CC[t_]={{T[t][[1]], -T[t][[2]],c[t][[1]]}, {T[t][[2]], T[t][[1]], c[t][[2]]}, {0,0,1}};

casCC[t_]=Graphics[{Orange,Polygon[Map[Afin, Transpose[CC[t].Transpose[Map[Homog, domek]]]]]}];
Manipulate[Show[  {start, cil, draha, casCC[t]}, PlotRange->{{-1, 7},{-1, 7}} , Axes->True], {t, 0, 1}]

B2[t_]=A[0, {1,4}].A[Pi*t/2, {0, 0}].A[0, {-1,-4}];

MatrixForm[B2[t]]

cas2B[t_]=Graphics[{Blue,Polygon[Map[Afin, Transpose[B2[t].Transpose[Map[Homog, domek]]]]]}];

Manipulate[Show[  {start, cil, cas2B[t]}, PlotRange->{{-1, 7},{-1, 7}} , Axes->True], {t, 0, 1}]

Manipulate[Show[  {start, cil, casB[t],cas1B[t],cas2B[t],draha, casCC[t]}, PlotRange->{{-1, 7},{-1, 7}} , Axes->True], {t, 0, 1}]