Abstract：To improve modeling ability of subdivision surfaces

interactive shape modification algorithms for C-C subdivision surfaces are discussed. The constraints of points

normal vectors and local isoparametric curves on C-C surfaces

which can be converted into those on control vertices

are specified via setting up local coordinate systems in real-time operation. A global linear system is obtained and the shape of C-C subdivision surfaces can be modified with the various geometric constraints. Two methods based on least-square and energy optimization are presented. The former minimizes the total variation of control vertices. It is fast and suits for local

precise modification. The latter gives the optimal solution to the energy equation with penalty function method and it is a global modification with good fairness. Both methods can be solved explicitly by a pseudo-inverse matrix and are of invertible

commutative

and associative properties

which enhance the efficiency and controllability of the manipulation.