A Class of Detailed Features Preserving Combined m-ary Subdivision Schemes with Two Parameters

Based on the smoothness of B-splines, a Laurent polynomial which can generate a class of m-ary combined subdivision schemes is constructed by the relationship between Laurent polynomials and generated polynomials. The new Laurent polynomial can not only contain some classical subdivision schemes but also generalize C^3-continuous new-type schemes with detailed features. Specifically, the support and continuities of the combined four-point ternary scheme has been analyzed;the necessary and sufficient condition for its C^3 continuity are also given and proved. Plenty of numerical examples are given to illustrate the influence of parameters on the limit curves. The comparisons show that the limit curves generated by the scheme can keep the detail features well.