A RATIONAL PARAMETRIZATION OF BÉZIER LIKE CURVES

In this paper, we construct a family of Bernstein functions using class rational parametrization. The new basis on an index $\alpha \in {\left(-\infty \, , 0 \right)}\cup {\left(1 +\infty\right)}$, and for given degree $k\in \mathbb{N}^*$, these are with numerator denominator polynomials k. All the classical properties as positivity, partition unity hold they constitute approximation continuous spaces. B\'ezier curves obtained verify have computational algorithms like deCasteljau Algorithm algorithm subdivision similar accuracy. Given k control polygon points all converge to same curve case. That means is independent $\alpha$. polynomial seems asymptotic case our basis.