Rational Spline with Interval and Point Tension

Various curve designing methods have been developed, for the designing of distinct objects, for applications like font designing, Computer Aided Design (CAD), Computer Aided Engineering (CAE}, etc. Some methods are better suited for controlling the shape of the curve on an interval, while others are better suited for controlling the shape at the individual control points. In this paper, a rational cubic C spline curve is described which has interval and point tension weights for manipulating the shape of the curve. The spline is presented in both interpolatory and local support basis form, and the effect of the weights on these representations is analyzed.