Designing multi-parameter curve subdivision schemes with high continuity

A class of binary convergent schemes with several parameters is proposed based on eigenvalues of their difference matrices and the relation between the subdivision schemes and the difference schemes. Then multi-parameter binary subdivision schemes with arbitrary order continuity can be devised according to the conditions for Ck continuity. Some existing subdivision schemes and new geometrically asymmetric ones can be obtained by setting values of parameters and a few illustrative application examples are presented. The method of designing binary multi-parameter subdivision schemes with high continuity can be generalized to design smooth a-ary subdivision schemes.