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Implicitization of Parametric Hypersurfaces via Points

Ferruccio OrecchiaIsabella Ramella — 2018

Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche

Given a parametric polynomial representation of an algebraic hypersurface 𝐒 in the projective space we give a new algorithm for finding the implicit cartesian equation of 𝐒 .The algorithm is based on finding a suitable finite number of points on 𝐒 and computing, by linear algebra, the equation of the hypersurface of least degree that passes through the points. In particular the algorithm works for plane curves and surfaces in the ordinary three-dimensional space. Using C++ the algorithm has been...

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