Autor según el artículo: Herrera B; Samper A

Departamento: Escola Tècnica Superior d'Arquitectura

Autor/es de la URV: Herrera Gómez, Blas / Samper Sosa, Albert

Palabras clave: Quasi-equivalent oval Quadrarc Geometría Ellipse Eight-centered oval

Resumen: Let ?b be an ellipse (b=minor axis/major axis). In this paper we consider different approximations by ovals, which are composed from circular arcs and have also two axes of symmetry. We study a) three four-centered ovals (quadrarcs) Oa4,bOc4,b, and Ol4,b, which share the vertices with the ellipse ?b. In addition, Oa4,b has the same surface area, Oc4,b has the minimum error of curvature at the vertices, and Ol4,b has the same perimeter length. b) Further, we investigate three eight-centered ovals Oc8,b, Oc-a8,b and Oc-l8,b which also share the vertices with ?b. The ovals Oc8,b have the same curvature at the vertices, and in addition, Oc-a8,b has the same surface area, and Oc-l8,b has the same perimeter length as ?b. As a conclusion, the eight-centered oval Oc-l8,b seems to be optimal and can therefore be called 'quasi-equivalent' to ?b. We show that the difference of surface areas Ab = A(Oc-l8,b)-A(?b) is rather small; the maximum value A0.1969 = 0.007085 is achieved at b = 0.1969. The deformation error Eb = E(?b, Oc-l8,b) has the maximum value 0.008970 which is achieved at b = 0.2379. © 2015 Heldermann Verlag.

Áreas temáticas: Mathematics Geometry and topology Ensino Engenharias i Ciencias sociales Ciência da computação Arquitetura e urbanismo Applied psychology Applied mathematics

Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/

Direcció de correo del autor: albert.samper@urv.cat blas.herrera@urv.cat

Identificador del autor: 0000-0002-4795-2127 0000-0003-2924-9195

Fecha de alta del registro: 2023-02-27

Versión del articulo depositado: info:eu-repo/semantics/publishedVersion

URL Documento de licencia: http://repositori.urv.cat/ca/proteccio-de-dades/

Referencia al articulo segun fuente origial: Journal For Geometry And Graphics. 19 (2): 257-268

Referencia de l'ítem segons les normes APA: Herrera B; Samper A (2015). Definition and calculation of an eight-centered oval which is quasi-equivalent to the ellipse. Journal For Geometry And Graphics, 19(2), 257-268

Entidad: Universitat Rovira i Virgili

Año de publicación de la revista: 2015

Tipo de publicación: Journal Publications