{"id":64979,"date":"2008-05-06T00:00:00","date_gmt":"2008-05-06T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/visibility-and-proximity-on-triangulated-surfaces\/"},"modified":"2008-05-06T00:00:00","modified_gmt":"2008-05-06T00:00:00","slug":"visibility-and-proximity-on-triangulated-surfaces","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/ciencia-de-los-ordenadores\/visibility-and-proximity-on-triangulated-surfaces\/","title":{"rendered":"Visibility and proximity on triangulated surfaces"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Marta Fort Masdevall <\/strong><\/h2>\n<p>In this thesis, we solve visibility and proximity problems on triangulated surfaces concerning generalized elements. As generalized elements, we consider: points, segments, polygonal chains and polygonal regions. The proposed strategies use algorithms of computational geometry and graphics hardware. We start by studying multi-visibility problems on triangulated terrain models concerning a set of generalized view elements. We present two methods to obtain approximate multi-visibility maps. A multi-visibility map is a subdivision of the terrain domain encoding visibility according to different criteria. The first method, of complex implementation, uses exactly computed visibility information to approximately reconstruct the unknown multi-visibility map. The second, from which implementation results are provided, uses approximate visibility information to compute and visualize discrete multi-visibility maps by exploiting graphics hardware capabilities. As applications, we compute multi-visibility maps, solve inter-region multi-visibility problems and approximately answer point and polygonal region multi-visibility queries. Next, we tackle proximity problems on triangulated polyhedral surfaces, where generalized obstacles are allowed, considering generalized sources. We present two methods, with implementation results, to compute distances on polyhedral surfaces from a generalized source. The first method computes exact shortest path distances from generalized sources. The second provides approximate weighted shortest path distances from generalized sites on weighted polyhedral surfaces. Both methods are posteriorly extended to handle the multiple-site problem where the corresponding distance field is obtained. As applications, we compute discrete order-k voronoi diagrams and approximately solve some facility location problems. We also provide a theoretical study on the order-k voronoi diagram complexity of a set of generalized sources for the non-weighted case.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Visibility and proximity on triangulated surfaces<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Visibility and proximity on triangulated surfaces <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Marta Fort Masdevall <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Girona<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 05\/06\/2008<\/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>Joan Antoni Sellar\u00e9s Chiva<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: ferran Hurtado d\u00edaz <\/li>\n<li>bel\u00e9n Palop del r\u00edo (vocal)<\/li>\n<li>Mar\u00eda  isabel Navazo alvaro (vocal)<\/li>\n<li>fran\u00ed\u00a7ois Anton castro (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Marta Fort Masdevall In this thesis, we solve visibility and proximity problems on triangulated surfaces concerning generalized 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