Abstract: In an image synthesis system, a definer/editor (102) stores (1112) object definitions in the form of control points for spline curves. The system can generate "phantom control points" (A.sub.0 to A.sub.N+1) to define a spline object, such that the curve interpolates a desired set of points (P.sub.1 to P.sub.N) received from a user, for example via a mouse or graphics tablet. While the number N of received points, is variable, and may be large, the system operates quickly to generate coefficients (X.sub.ij) which can be used to derive the phantom control points (A), without the need for matrix inversion, and without storing a large number of pre-inverted matrices. This permits intuitive interaction with the user for the definition of spline objects. For large numbers N where interactivity may even so become difficult to achieve, the system is able to generate approximate phantom points, each derived from a relatively small sub-set of the received points.