Abstract: Aming at the problems that Loop subdivision can’t satisfy the shape adjustment and interpolate
the given mesh, a progressive interpolation scheme for Loop subdivision surfaces with shape adjustment is
presented. Firstly, an equivalent Loop subdivision mask that can adjust the mesh vertices uniformly and
facilitate the introduction of weight to adjust the shape of subdivision surfaces is proposed. Secondly, the
new grid is generated by the iterative adjustment of the initial control grid, and using the two-phase Loop
subdivision scheme presented in this paper to subdivide the new mesh, the shape-adjustable Loop
subdivision surface that interpolate the initial control vertices is obtained. Finally, the convergence of the
scheme is proved and some typical examples are illustrated to verify its effectiveness.

Key words: Loop subdivision, shape adjustment, progressive interpolation, weight