Study of Spline-Curves with Shape Parameters

To modify the curve shapes by means of adjusting the shape parameter is a topic of great significance in computer-aided geometric design. In order to adjust effectively the shape of a curve by using shape parameters and boost up its flexibility, the representations and properties of five types of B-spline curves with shape parameters are studied. For these curves, the approaching degree to their control polygon can be adjusted through the change of the value of shape parameters, and the curves with different continuity can be gained. The effects of the shape parameters on the curve shapes are analyzed, the range of shape parameters is presented, and the characteristics of each modeling means are compared. Through formula evolvements, experiments and illustrations with examples, some new approaches to present free-curves by means of different shape parameter values are also worked out. Experiments show that C-B spline curve, uniform B-spline with shape parameter, hyperbolic polynomial uniform B-spline with shape parameter and trigonometric polynomial uniform B-spline with shape parameter can be used to produce some frequently used free form curves in the industrial field when the shape parameter is assigned with some specific values. This process is simpler than producing these free form curves by using controlling vertex.