Having this represetation of a NURBS curve:
where Bi is all the control points, t a parameter defining a point along the curve and Ni,k(t) is the Basis function defined as:
where k is the order of the curve and Xi is the conventional notation for the ith knot in the knot vector.
What formula can be used to extend the curve only by modifying position of existing control points while mantaining the existent shape (only extended)?