To represent a complex surface, it is useful to describe it as a set of simple parametric primitives such as quadrics. But if one wants to use few primitives, these have to be smoothly blended. To define this blending, we propose to describe the initial global surface with charts. The blending surfaces result from a convex combination of primitives whose weights are defined on open sets of IR(sup 2) given by the charts. We have established the properties that the weight functions must satisfy to obtain a G(sup 1) representation of the global surface, and we have constructed such functions.