Non-primal schemes

The interpolation degree can also be expressed in terms of the presentation of alternate terms of the product of the unit row eigenvector with the mask as a polynomial in S2. For non-primal schemes this approach has to be taken, since for such a scheme interpolation only means that the limit curve interpolates the data. Vertices of refined polygons do not coincide with original vertices. 

Because the unit row eigenvector is not a linear function of the mask, the quasi-interpolation degree is not necessarily a linear constraint in design space. 

The situation gets considerably more complex for higher arities. 

However, for primal schemes of any arity, any scheme with interpolation degree c will leave original vertices unchanged if they lie on a polynomial of degree less than or equal to c . A weighted mean of equal points is always the same point, and so this condition remains a linear one. 

---