F = BsplineFunction[model]; (* Model surface as B spline Function *)
(* Surface Sampling Function *)
SurfaceSampling[p_] := Flatten[Table[F[u, v], {u, 0, 1, p}, {v, 0, 1, p}], 1];


ModelSurface = SurfaceSampling[0.005]; (* Actual sampling *)
g = Drop[T1[[2]][[1]].Append[vec, 1], -1] (* T1 Geometric Transform of point "vec" *)

(* CtrlPts is the point could *)
T1 = FindGeometricTransform[Nearest[CtrlPts, ModelSurface], CtrlPts,
         "Transformation"- > "Rigid", Method -> "FindFit"];

(* Apply found transformation to the ModelSurface *)
ModelSurface = Map[g, ModelSurface]
(* After a couple of iterations, T will become the optimal transformation *)
T = T1[[2]][[1]].T;