Rational cubic curves as BR-curves Original Research Article

Rational curves are a useful class of curves for CAGD and CAM. For that purpose a rational cubic is determined via Bernstein polynomials by four massic vectors (BR-form). Showing that a BR-cubic is the projective transform of a cubic Bézier we emphasize some geometrical properties of a rational cubic. In the case of a plane cubic we study the degeneracy in a conic. Finally we determine some particular elements e.g., cusp, double point and inflection points relatively to the massic vectors.