Improving shortest paths in the Delaunay triangulation

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/16981

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II
dc.contributor	Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
dc.contributor.author	Abellanas, Manuel
dc.contributor.author	Claverol Aguas, Mercè
dc.contributor.author	Hernández-Peñalver, Gregorio
dc.contributor.author	Hurtado Díaz, Fernando Alfredo
dc.contributor.author	Sacristán Adinolfi, Vera
dc.contributor.author	Saumell Mendiola, Maria
dc.contributor.author	Silveira, Rodrigo Ignacio
dc.date	2012
dc.identifier.citation	Abellanas, M. [et al.]. Improving shortest paths in the Delaunay triangulation. "International journal of computational geometry and applications", 2012.
dc.identifier.citation	0218-1959
dc.identifier.uri	http://hdl.handle.net/2117/16981
dc.language.iso	eng
dc.relation	info:eu-repo/grantAgreement/EC/FP7/251235/EU/Mathematical Foundations of High-Quality Terrain Models/MFHQTERRAINS
dc.rights	Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
dc.subject	Geometria integral
dc.subject	Triangulació
dc.subject	Trigonometria
dc.subject	Triangulation
dc.title	Improving shortest paths in the Delaunay triangulation
dc.type	info:eu-repo/semantics/publishedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	We study a problem about shortest paths in Delaunay triangulations. Given two nodes s, t in the Delaunay triangulation of a point set P, we look for a new point p that can be added, such that the shortest path from s to t, in the Delaunay triangulation of P ∪ {p}, improves as much as possible. We study several properties of the problem, and give efficient algorithms to find such point when the graph-distance used is Euclidean and for the link-distance. Several other variations of the problem are also discussed.

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