NURBS curve blending using extension

Curve and surface blending is an important operation in CAD systems, in which a non-uniform rational B-spline (NURBS) has been used as the de facto standard. In local corner blending, two curves intersecting at that corner are first made disjoint, and then the third blending curve is added-in to smoothly join the two curves with G¹-or G²-continuity. In this paper we present a study to solve the joint problem based on curve extension. The following nice properties of this extension algorithm are exploited in depth: (1) The parameterization of the original shapes does not change; (2) No additional fragments are created. Various examples are presented to demonstrate that our solution is simple and efficient.