Implicitization of Parametric Hypersurfaces via Points

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, bylinear 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 implemented on an intel Pentium running Linux. Since our algorithm is based only on computations of linear algebra it reveals very efficient if compared with others that do not use linear algebra for the computations.