In 2000, Wu presented two new types of generalized Ball curves, one of which is called an NB1 curve located between the Wang--Ball curve and the Said--Ball curve. In this article, the authors aim to discuss properties of NB1 curves and surfaces, including the recursive algorithms, conversion algorithms between NB1 and Bezier curves and surfaces, etc. In addition the authors compare the computation efficiency of recursive algorithms for the NB1 and above mentioned two generalized Ball curves and surfaces.