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On the Implicit Equation of Conics and Quadrics Offsets

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jorge Caravantes & Gema M. Diaz-Toca & Mario Fioravanti & Laureano Gonzalez-Vega, 2021. "On the Implicit Equation of Conics and Quadrics Offsets," Mathematics, MDPI, vol. 9(15), pages 1-19, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1784-:d:603267
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