Hyperbolic polynomial uniform B-spline curves and surfaces with shape parameter

In this paper, we study in depth a new modeling method for parameter curves and surface-hyperbolic polynomial uniform B-spline surfaces with shape parameter. Based on this model, we give an example of free-form curve modeling, and analyze the effect that different shape parameters have on the curve shape. In light of computer graphics theories, we develop a space free-form surface modeling system on the Microsoft Windows operating system. By means of the prototype system, we perform free-form surface modeling, give examples for its application, and discuss how the adjustment of the shape parameter affects the shape of free-form surfaces.