NURBS curve is widely used in Computer Aided Design and Computer Aided Geometric Design. When a single weight approaches infinity, the limit of a NURBS curve tends to the corresponding control point. In this paper, a kind of control structure of a NURBS curve, called regular control curve, is defined. We prove that the limit of the NURBS curve is exactly its regular control curve when all of we...

Non-uniform complexity measures originated in automata and formal languages theory are characterized in terms of well-known uniform complexity classes. The initial index of languages is introduced by means of several computational models. It is shown to be closely related to context-free cost, boolean circuits, straight line programs, and Turing machines with sparse oracles and time or space bo...