Restricted systems (Q1869354)

In this paper, so-called restricted systems are introduced and characterized. The definition of restricted systems is closely related to, but weaker than, local linear independence of univariate splines and serves as a generalization of splines in computer aided geometric design. This local ``consecutive'' control is important in CAGD because local modifications of the control points (the control polygon) should only result in local changes of the curve. In the spline case, this property is guaranteed due to the splines' inherent local linear independence, and here it is guaranteed by the new condition of restrictedness. Equivalent conditions for the \(p\)-restricted systems are given that are, again, similar to the properties of spline curves. For those, the concept of total positivity is highly relevant. Several examples are given.