Abstract: To increase the flexibility of a geometric modeling algorithm,parameters are introduced into the masks of the subdivision algorithm.The smoothness condition for the algorithm is discussed in terms of the generating function and a curve with a parameter is obtained.By applying the tensor product construction technique to subdivision masks,adjustable subdivision surfaces of arbitrary topology with one parameter are obtained.In addition,boundary conditions for open mesh are also derived naturally by making use of the masks of curves.The convergence property at an extraordinary vertex is studied by using the eigendecomposition techniques.Modeling examples show that the algorithm is able to meet the requirements of shape adjustment.