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In this paper, a new method to compute a B\'ezier curve of degree n = 2m-1 isintroduced, here formulated as a set of points whose coordinates are calculatedfrom two Hankel forms in $\C^m$. From Vandermonde factorizations of the twoassociated Hankel matrices $H_x$ and $H_y$, the Hankel forms can be easilycalculated, thus yielding points on the B\'ezier curve. Here, a new proof ofthe existence of a Vandermonde factorization of regular Hankel matrix is givenfrom Pascal matrices techniques. But, even when the Hankel matrix associated tothe form is singular, the method can still be used by shifting itsskew-diagonal and counteracting it after, which is pratically done withoutcosts.. By comparing this new method with a Pascal matrix method andCasteljau's, we see that the results suggest that this new method is veryeffective with regard to accuracy and time of computation for various values ofn.

Vandermonde factorizations of a regular Hankel matrix and their application on the computation of B\'ezier curves