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In this paper we use Gröbner bases for the implicitization of rational parametric curves and surfaces in 3D-space. We prove that the implicit form of a curve or surface given by the rational parametrization x 1 := p 1 q 1 x 2 := p 2 q 2 x 3 := p 3 q 3 , where the p's and q's are univariate polynomials in y 1 or bivariate polynomials in y 1 , y 2 over a… (More)

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