On the implicit equation of conics and quadrics offsets

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URI: http://hdl.handle.net/10902/24540
ISSN: 2227-7390
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Autoría
Caravantes Tortajada, JorgeAutoridad Unican; Diaz-Toca, Gema M.; Fioravanti Villanueva, Mario AlfredoAutoridad Unican; González Vega, LaureanoAutoridad Unican
Fecha
2021-07
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© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).
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Mathematics, 2021, 9 (15) 1784
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MDPI
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Palabras clave
Offsets
Conics and quadrics
Implicit equations
Discriminant
Resumen/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.
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© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).Excepto si se señala otra cosa, la licencia del ítem se describe como © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).