UWO ORCCA TR-02-01 Summary

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On the Support of the Implicit Equation of Rational Parametric Hypersurfaces, September 23, 2002, Ioannis Z. Emiris and Ilias S. Kotsireas, 10 pages

Abstract: We propose the use of various tools from algebraic geometry, with an emphasis on toric (or sparse) elimination theory, in order to predict the support of the implicit equation of a rational parametric hypersurface. The problem of implicitization lies at the heart of several algorithms in computer-aided design and geometric modeling. Two implicitization algorithms directly benefit from our work, and it is possible that other methods can also be improved. We use, on the one hand, degree bounds, formulated in terms of the mixed volume of Newton polytopes and, on the other, constraints on the support of the toric (or sparse) resultant. In many cases, we obtain the exact support of the implicit equation

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