Elkadi, Mohamed; Mourrain, Bernard Residue and implicitization problem for rational surfaces. (English) Zbl 1058.14073 Appl. Algebra Eng. Commun. Comput. 14, No. 5, 361-379 (2004). The implicitization problem for rational surfaces has been studied intensively in the last 10 years, because of its relevance for applications in computer-aided geometric design. The approach studied here is based on resultants: the implicit equation is obtained by computing determinants of Bezout-type matrices and analyzing their factors. Many theoretical problems in the resultant methods arise from the presence of base points. In this paper, the authors present a resultant-based implicitization method that works in the presence of arbitrary base points. The algorithm does not require factorisation of polynomials. The paper also contains a method for computing the equation of the offset of a rational surface. Reviewer: Josef Schicho (Linz) Cited in 7 Documents MSC: 14Q10 Computational aspects of algebraic surfaces 14J26 Rational and ruled surfaces 15A54 Matrices over function rings in one or more variables Keywords:resultant; Bezout-type matrices; algorithm PDFBibTeX XMLCite \textit{M. Elkadi} and \textit{B. Mourrain}, Appl. Algebra Eng. Commun. Comput. 14, No. 5, 361--379 (2004; Zbl 1058.14073) Full Text: DOI