{"id":21399,"date":"2018-03-09T09:11:09","date_gmt":"2018-03-09T09:11:09","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/geometria-computacional-en-superficies-de-orbitas\/"},"modified":"2018-03-09T09:11:09","modified_gmt":"2018-03-09T09:11:09","slug":"geometria-computacional-en-superficies-de-orbitas","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/sevilla\/geometria-computacional-en-superficies-de-orbitas\/","title":{"rendered":"Geometr\u00eda computacional en superficies de \u00f3rbitas"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Jes\u00fas Valenzuela Mu\u00f1oz <\/strong><\/h2>\n<p>En los casi treinta a\u00f1os de historia de la geometr\u00eda computacional, s\u00f3lo recientemente se han comenzado a estudiar problemas en superficies distintas del plano, estudio que es necesario desde el momento en que surgen problemas para cuya modelizaci\u00f3n se requiere el uso de otros espacios. En esta memoria se aborda la extensi\u00f3n de las estructuras cl\u00e1sicas de la geometr\u00eda computacional a las superficies de \u00f3rbitas eucl\u00eddeas (euclidean 2-orbifolds) o caleidoscopios.  para ello es necesario en primer lugar distinguir cu\u00e1ndo un conjunto sobre una superficie est\u00e1 lo suficientemente agrupado como para presentar un comportamiento plano. Se dice que un conjunto est\u00e1 en posici\u00f3n eucl\u00eddea cuando sobre \u00e9l pueden aplicarse algoritmos planos para construir estructuras t\u00edpicas de la geometr\u00eda computacional. En esta memoria se presenta una definici\u00f3n del t\u00e9rmino para las superficies de \u00f3rbitas eucl\u00eddeas que generaliza la existente para el cilindro, el cono y el toro, junto con algoritmos que permiten su determinaci\u00f3n.  se estudia tambi\u00e9n la construcci\u00f3n de la envolvente m\u00e9tricamente convexa sobre estas superficies, comprob\u00e1ndose que, si el conjunto est\u00e1 en posici\u00f3n eucl\u00eddea, la forma de su envolvente es la que tendr\u00eda de estar sobre el plano. En caso contrario la envolvente convexa es demasiado grande, perdiendo gran parte de su utilidad.  en el caso de que un conjunto no est\u00e9 en posici\u00f3n eucl\u00eddea, se presentan m\u00e9todos para la b\u00fasqueda de sus subconjuntos con mayor cardinal que s\u00ed cumplan la propiedad, llamados subconjuntos m\u00e1ximos para la posici\u00f3n eucl\u00eddea o smpe.  tambi\u00e9n se establece la relaci\u00f3n entre la conexi\u00f3n del grafo de triangulaciones de un pol\u00edgono o una nube de puntos en una superficie cerrada y conexa y la m\u00e9trica de la superficie, prob\u00e1ndose que siempre puede construirse una m\u00e9trica para la que aparecen grafos de triangulaciones no conexos. para su m\u00e9trica habitual se estudia la conexi\u00f3n del<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Geometr\u00eda computacional en superficies de \u00f3rbitas<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Geometr\u00eda computacional en superficies de \u00f3rbitas <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Jes\u00fas Valenzuela Mu\u00f1oz <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Sevilla<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 29\/01\/2003<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Carmen Cort\u00e9s Parejo<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: ferran Hurtado d\u00edaz <\/li>\n<li>gregorio Hern\u00e1ndez pe\u00f1alver (vocal)<\/li>\n<li>Manuel Abellanas oar (vocal)<\/li>\n<li> D\u00edaz b\u00e1\u00f1ez Jos\u00e9 Miguel (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Jes\u00fas Valenzuela Mu\u00f1oz En los casi treinta a\u00f1os de historia de la geometr\u00eda computacional, s\u00f3lo recientemente se [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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