Characterization of Planar Cubic Alternative curve

In this paper, we analyze the planar cubic Alternative curve to determine the conditions for convex, loops, cusps and inflection points. Thus cubic curve is represented by linear combination of three control points and basis function that consist of two shape parameters. By using algebraic manipulation, we can determine the constraint of shape parameters and sufficient conditions are derived which ensure that the curve is a strictly convex, loops, cusps and inflection point. We conclude the result in a shape diagram of parameters. The simplicity of this form makes characterization more intuitive and efficient to compute.