Rapid Evaluation of Regular Quad-mesh Interpolatory Subdivision Surfaces Based on Parametric Decomposition

Two algorithms for evaluation of regular quad-mesh interpolatory subdivision surfaces are proposed. Algorithms are designed based on the parametric m-ary decomposition and construction of matrix sequence. The weights of the control points on the initial mesh can be obtained, through direct computation of the basic function values by multiplying the finite matrix sequence corresponding to the decomposition number sequence. Algorithm-I is based on 2D subdivision masks while the other is based on tensor-product. Numerical experiments show that algorithms are efficient with low storage cost.