Work

Tools for analyzing the intersection curve between a torus and a quadric through projection and lifting

Year: 2026

Type: article

Abstract: This article introduces several user-friendly tools for analyzing the intersection curve between a ringed torus and an irreducible quadric surface. Our main focus is the study of the projection of this curve onto the plane , known as the cutcurve, which plays a central role in ensuring correct lifting to the intersection curve. We also provide a detailed characterization of the singularities of both the projection and the intersection curve, as well as conditions for the existence of double tangents. A fundamental tool in our analysis is the theory of resultants and subresultants.

Source: Computer Aided Geometric Design

DOI: 10.1016/j.cagd.2026.102533

Authors: Jorge Caravantes, Gema M. Diaz-Toca, Mario Fioravanti, Laureano Gonzalez-Vega

Institutions: Universidad de Alcalá, Universidad de Murcia, Universidad de Cantabria, CUNEF Universidad

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: $2,930

Funders: Ministerio de Ciencia, Innovación y Universidades, Agencia Estatal de Investigación