Implicitization by Dixon A-Resultants

Authors:
Eng-Wee Chionh;Ming Zhang;Ronald N. Goldman
Affiliations:
-;-;-
Venue:
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Year:
2000

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Abstract

It is well known that the Dixon resultant implicitizes exactly a general tensor product surface. In this paper, we show that a minor of the Dixon resultant matrix can also implicitize exactly. This occurs when the monomial support of the surface parametrization is a rectangle missing at most one sub-rectangle at each of its corners. Unlike the Sylvester dialytic method, this way of finding the implicit equation in determinant form is automatic, in bracket form, and uses much smaller matrices.