A generic rule-based formulation of knot-insertion across CAD applications

Abstract

In software design, a rule-based architecture is usually attempted as an alternative option when no sufficient information is available to devise a constructive algorithm. In this context, this paper starts by providing an account of rule-based systems and proceeds to provide a formulation of the knot insertion algorithm for B-spline curves in these terms. The benefits of that are clarity, flexibility and extendibility. In fact, the formulation not only admits knot insertion for B-spline and NURB surfaces as simple generalizations, but also extends to cover T-splines local refinement as well as similar notions in higher-dimensional structures.