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<p>This paper presents an interpretation for the extraneous factors appearing in the computation of iterated resultants with respect to a variable for three multivariate polynomials defined from the rational parametrization of a surface. We introduce a method for deriving the implicit equation of a surface using only two univariate resultants, whose polynomials match the degree of the parametrization. Our results provide a new approach to extracting the implicit representation of rational surfaces.</p>

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Implicitization of 3D rational surfaces using iterated univariate resultants and avoiding extraneous factors

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月25日

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  • Rafael Magdalena Benedicto,
  • Sonia Pérez-Díaz,
  • Marian Fernández de Sevilla

摘要

This paper presents an interpretation for the extraneous factors appearing in the computation of iterated resultants with respect to a variable for three multivariate polynomials defined from the rational parametrization of a surface. We introduce a method for deriving the implicit equation of a surface using only two univariate resultants, whose polynomials match the degree of the parametrization. Our results provide a new approach to extracting the implicit representation of rational surfaces.