Far-field reflector problem and intersection of paraboloids

Machado Manhães De Castro, Pedro; Mérigot, Quentin; Thibert, Boris

hal.structure.identifier	Centro de Informatica UFPE [Recife] [CIn]
dc.contributor.author	Machado Manhães De Castro, Pedro
hal.structure.identifier	CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.author	Mérigot, Quentin HAL ID: 235
hal.structure.identifier	Laboratoire Jean Kuntzmann [LJK]
dc.contributor.author	Thibert, Boris HAL ID: 21388
dc.date.accessioned	2018-02-21T12:33:17Z
dc.date.available	2018-02-21T12:33:17Z
dc.date.issued	2016
dc.identifier.issn	0029-599X
dc.identifier.uri	https://basepub.dauphine.fr/handle/123456789/17452
dc.language.iso	en	en
dc.subject	Reflector problem	en
dc.subject	optimal transport	en
dc.subject	power diagram	en
dc.subject.ddc	516	en
dc.title	Far-field reflector problem and intersection of paraboloids	en
dc.type	Article accepté pour publication ou publié
dc.description.abstracten	In 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.isversionofjnlname	Numerische Mathematik
dc.relation.isversionofjnlvol	134	en
dc.relation.isversionofjnlissue	2	en
dc.relation.isversionofjnldate	2016-10
dc.relation.isversionofjnlpages	389–411	en
dc.relation.isversionofdoi	10.1007/s00211-015-0780-z	en
dc.relation.isversionofjnlpublisher	Springer	en
dc.subject.ddclabel	Géométrie	en
dc.relation.forthcoming	non	en
dc.relation.forthcomingprint	non	en
dc.description.ssrncandidate	non	en
dc.description.halcandidate	non	en
dc.description.readership	recherche	en
dc.description.audience	International	en
dc.relation.Isversionofjnlpeerreviewed	oui	en
dc.relation.Isversionofjnlpeerreviewed	oui	en
dc.date.updated	2018-02-21T12:25:59Z
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