Work

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

Year: 2025

Type: article

Abstract: 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.

Source: Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas

DOI: 10.1007/s13398-025-01806-0

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

Institutions: Universitat de València, Universidad de Alcalá

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

OpenAlex ID: W4416675652