On the Implicit Equation of Conics and Quadrics Offsets

Jorge Caravantes, Gema M. Diaz-Toca, Mario Fioravanti and Laureano Gonzalez-Vega
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Jorge Caravantes: Departamento de Física y Matemáticas, Universidad de Alcalá, 28805 Madrid, Spain
Gema M. Diaz-Toca: Departamento de Ingeniería y Tecnología de Computadores, Universidad de Murcia, 30100 Murcia, Spain
Mario Fioravanti: Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39005 Santander, Spain
Laureano Gonzalez-Vega: Departamento de Métodos Cuantitativos, CUNEF Universidad, 28040 Madrid, Spain

Mathematics, 2021, vol. 9, issue 15, 1-19

Abstract: A new determinantal representation for the implicit equation of offsets to conics and quadrics is derived. It is simple, free of extraneous components and provides a very compact expanded form, these representations being very useful when dealing with geometric queries about offsets such as point positioning or solving intersection purposes. It is based on several classical results in “A Treatise on the Analytic Geometry of Three Dimensions” by G. Salmon for offsets to non-degenerate conics and central quadrics.

Keywords: offsets; conics and quadrics; implicit equations; discriminant (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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