On the Implicit Equation of Conics and Quadrics Offsets
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 po...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/9/15/1784 |
| _version_ | 1827686504706605056 |
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| author | Jorge Caravantes Gema M. Diaz-Toca Mario Fioravanti Laureano Gonzalez-Vega |
| author_facet | Jorge Caravantes Gema M. Diaz-Toca Mario Fioravanti Laureano Gonzalez-Vega |
| author_sort | Jorge Caravantes |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T09:12:00Z |
| format | Article |
| id | doaj.art-645c3b8044f34597acb95ba884045549 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T09:12:00Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-645c3b8044f34597acb95ba8840455492023-11-22T05:56:41ZengMDPI AGMathematics2227-73902021-07-01915178410.3390/math9151784On the Implicit Equation of Conics and Quadrics OffsetsJorge Caravantes0Gema M. Diaz-Toca1Mario Fioravanti2Laureano Gonzalez-Vega3Departamento de Física y Matemáticas, Universidad de Alcalá, 28805 Madrid, SpainDepartamento de Ingeniería y Tecnología de Computadores, Universidad de Murcia, 30100 Murcia, SpainDepartamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39005 Santander, SpainDepartamento de Métodos Cuantitativos, CUNEF Universidad, 28040 Madrid, SpainA 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.https://www.mdpi.com/2227-7390/9/15/1784offsetsconics and quadricsimplicit equationsdiscriminant |
| spellingShingle | Jorge Caravantes Gema M. Diaz-Toca Mario Fioravanti Laureano Gonzalez-Vega On the Implicit Equation of Conics and Quadrics Offsets Mathematics offsets conics and quadrics implicit equations discriminant |
| title | On the Implicit Equation of Conics and Quadrics Offsets |
| title_full | On the Implicit Equation of Conics and Quadrics Offsets |
| title_fullStr | On the Implicit Equation of Conics and Quadrics Offsets |
| title_full_unstemmed | On the Implicit Equation of Conics and Quadrics Offsets |
| title_short | On the Implicit Equation of Conics and Quadrics Offsets |
| title_sort | on the implicit equation of conics and quadrics offsets |
| topic | offsets conics and quadrics implicit equations discriminant |
| url | https://www.mdpi.com/2227-7390/9/15/1784 |
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