Equations of Parametric Curves and Surfaces via Syzygies

. In computer graphics, such a map is given by homogeneouspolynomials (a,b,c,d) with real coefficients, and knowing these polynomialsallows one to draw the real points of S on a computer screen. Most geometricmodelsin CAD(Computer Aided Design)use parametricsurfaces. This includescar bodies, airplanes, and animated figures in movies such as

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