Show simple item record

hal.structure.identifierCentro de Informatica UFPE [Recife] [CIn]
dc.contributor.authorMachado Manhães De Castro, Pedro
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorMérigot, Quentin
HAL ID: 235
hal.structure.identifierLaboratoire Jean Kuntzmann [LJK]
dc.contributor.authorThibert, Boris
HAL ID: 21388
dc.date.accessioned2018-02-21T12:33:17Z
dc.date.available2018-02-21T12:33:17Z
dc.date.issued2016
dc.identifier.issn0029-599X
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17452
dc.language.isoenen
dc.subjectReflector problemen
dc.subjectoptimal transporten
dc.subjectpower diagramen
dc.subject.ddc516en
dc.titleFar-field reflector problem and intersection of paraboloidsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this article, we study the intersection (or union) of the convex hull of N confocal paraboloids (or ellipsoids) of revolution. This study is motivated by a Minkowski-type problem arising in geometric optics. We show that in each of the four cases, the combinatorics is given by the intersection of a power diagram with the unit sphere. We prove the complexity is O(N) for the intersection of paraboloids and Omega(N^2) for the intersection and the union of ellipsoids. We provide an algorithm to compute these intersections using the exact geometric computation paradigm. This algorithm is optimal in the case of the intersection of ellipsoids and is used to solve numerically the far-field reflector problem.en
dc.relation.isversionofjnlnameNumerische Mathematik
dc.relation.isversionofjnlvol134en
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate2016-10
dc.relation.isversionofjnlpages389–411en
dc.relation.isversionofdoi10.1007/s00211-015-0780-zen
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelGéométrieen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2018-02-21T12:25:59Z
hal.author.functionaut
hal.author.functionaut
hal.author.functionaut


Files in this item

Thumbnail
Thumbnail

This item appears in the following Collection(s)

Show simple item record