We consider a uniformly parameterized planar rational cubic
interpolation. The necessary and sufficient conditions 
on inflection points and singularities for a convex data 
have been presented.
This paper uses the remaining two degrees of freedom. 
Shape preserving parameters are automatically generated 
and the degree of smoothness attained is $G^2$. Numerical 
examples with their curvature plots demonstrate high 
accuracy of our scheme for both $C$-type and $S$-type data.