  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.
