{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T09:11:32Z","timestamp":1767863492502,"version":"3.49.0"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2015,11,17]],"date-time":"2015-11-17T00:00:00Z","timestamp":1447718400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2016,10]]},"DOI":"10.1007\/s00211-015-0780-z","type":"journal-article","created":{"date-parts":[[2015,11,17]],"date-time":"2015-11-17T11:25:17Z","timestamp":1447759517000},"page":"389-411","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Far-field reflector problem and intersection of paraboloids"],"prefix":"10.1007","volume":"134","author":[{"given":"Pedro Machado Manh\u00e3es","family":"de Castro","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Quentin","family":"M\u00e9rigot","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Boris","family":"Thibert","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,11,17]]},"reference":[{"key":"780_CR1","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1137\/0216006","volume":"16","author":"F Aurenhammer","year":"1987","unstructured":"Aurenhammer, F.: Power diagrams: properties, algorithms and applications. SIAM J. Comput. 16, 78\u201396 (1987)","journal-title":"SIAM J. Comput."},{"issue":"1","key":"780_CR2","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/PL00009187","volume":"20","author":"F Aurenhammer","year":"1998","unstructured":"Aurenhammer, F., Hoffmann, F., Aronov, B.: Minkowski-type theorems and least-squares clustering. Algorithmica 20(1), 61\u201376 (1998)","journal-title":"Algorithmica"},{"issue":"1","key":"780_CR3","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/BF01589405","volume":"42","author":"DP Bertsekas","year":"1988","unstructured":"Bertsekas, D.P., Eckstein, J.: Dual coordinate step methods for linear network flow problems. Math. Program. 42(1), 203\u2013243 (1988)","journal-title":"Math. Program."},{"key":"780_CR4","unstructured":"Boissonnat, J.-D., Karavelas, M.I.: On the combinatorial complexity of Euclidean Voronoi cells and convex hulls of d-dimensional spheres. In: Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms (Philadelphia, PA, USA), SODA \u201903. Society for Industrial and Applied Mathematics, pp. 305\u2013312 (2003)"},{"key":"780_CR5","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/S0166-218X(00)00231-6","volume":"109","author":"H Br\u00f3nnimann","year":"2001","unstructured":"Br\u00f3nnimann, H., Burnikel, C., Pion, S.: Interval arithmetic yields efficient dynamic filters for computational geometry. Discret. Appl. Math. 109, 25\u201347 (2001)","journal-title":"Discret. Appl. Math."},{"issue":"1","key":"780_CR6","doi-asserted-by":"crossref","first-page":"299","DOI":"10.4007\/annals.2008.167.299","volume":"167","author":"LA Caffarelli","year":"2008","unstructured":"Caffarelli, L.A., Guti\u00e9rrez, C.E., Huang, Q.: On the regularity of reflector antennas. Ann. Math. Second Ser. 167(1), 299 (2008)","journal-title":"Ann. Math. Second Ser."},{"key":"780_CR7","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1090\/conm\/226\/03233","volume":"226","author":"LA Caffarelli","year":"1999","unstructured":"Caffarelli, L.A., Kochengin, S., Oliker, V.I.: On the numerical solution of the problem of reflector design with given far-field scattering data. Contemp. Math. 226, 13\u201332 (1999)","journal-title":"Contemp. Math."},{"issue":"1","key":"780_CR8","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/s10958-008-9152-x","volume":"154","author":"LA Caffarelli","year":"2008","unstructured":"Caffarelli, L.A., Oliker, V.I.: Weak solutions of one inverse problem in geometric optics. J. Math. Sci. 154(1), 39\u201349 (2008)","journal-title":"J. Math. Sci."},{"key":"780_CR9","unstructured":"Cgal, Computational Geometry Algorithms Library. http:\/\/www.cgal.org"},{"key":"780_CR10","unstructured":"Delage, C.: CGAL-based first prototype implementation of M\u00f6bius diagram in 2D. Technical Report ECG-TR-241208-01, INRIA Sophia-Antipolis, 2003"},{"issue":"3","key":"780_CR11","doi-asserted-by":"crossref","first-page":"4096","DOI":"10.1023\/A:1024856201493","volume":"117","author":"T Glimm","year":"2003","unstructured":"Glimm, T., Oliker, V.: Optical design of single reflector systems and the Monge\u2013Kantorovich mass transfer problem. J. Math. Sci. 117(3), 4096\u20134108 (2003)","journal-title":"J. Math. Sci."},{"issue":"2","key":"780_CR12","doi-asserted-by":"crossref","first-page":"205","DOI":"10.4310\/jdg\/1214460795","volume":"48","author":"P Guan","year":"1998","unstructured":"Guan, P., Wang, X.-J.: On a Monge\u2013Ampere equation arising in geometric optics. J. Differ. Geom. 48(2), 205\u2013223 (1998)","journal-title":"J. Differ. Geom."},{"key":"780_CR13","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.comgeo.2007.06.003","volume":"40","author":"L Kettner","year":"2008","unstructured":"Kettner, L., Mehlhorn, K., Schirra, S., Yap, C.K.: Classroom examples of robustness problems in geometric computations. Comput. Geom. Theory Appl. 40, 61\u201379 (2008)","journal-title":"Comput. Geom. Theory Appl."},{"key":"780_CR14","unstructured":"Kitagawa, J.: An iterative scheme for solving the optimal transportation problem (2012) (preprint). arXiv:1208.5172"},{"issue":"2","key":"780_CR15","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1088\/0266-5611\/13\/2\/011","volume":"13","author":"SA Kochengin","year":"1997","unstructured":"Kochengin, S.A., Oliker, V.I.: Determination of reflector surfaces from near-field scattering data. Inverse Probl. 13(2), 363 (1997)","journal-title":"Inverse Probl."},{"key":"780_CR16","doi-asserted-by":"crossref","unstructured":"M\u00e9rigot, Q.: A multiscale approach to optimal transport. In: Computer Graphics Forum, vol. 30, pp. 1583\u20131592. Wiley Online Library, New York (2011)","DOI":"10.1111\/j.1467-8659.2011.02032.x"},{"key":"780_CR17","volume-title":"Computational geometry\u2014an introduction through randomized algorithms","year":"1994","unstructured":"Mulmuley, K. (ed.): Computational geometry\u2014an introduction through randomized algorithms. Prentice Hall, Englewood Cliffs (1994)"},{"key":"780_CR18","doi-asserted-by":"crossref","unstructured":"Oliker, V.I.: Mathematical aspects of design of beam shaping surfaces in geometrical optics. In: Trends in Nonlinear Analysis, pp. 193\u2013224 (2003)","DOI":"10.1007\/978-3-662-05281-5_4"},{"issue":"1\u20132","key":"780_CR19","first-page":"1","volume":"2","author":"VI Oliker","year":"2006","unstructured":"Oliker, V.I.: A rigorous method for synthesis of offset shaped reflector antennas. Comput. Lett. 2(1\u20132), 1\u20132 (2006)","journal-title":"Comput. Lett."},{"issue":"11","key":"780_CR20","doi-asserted-by":"crossref","first-page":"4075","DOI":"10.1090\/S0002-9939-2010-10439-2","volume":"138","author":"VI Oliker","year":"2010","unstructured":"Oliker, V.I.: A characterization of revolution quadrics by a system of partial differential equations. Proc. Am. Math. Soc. 138(11), 4075\u20134080 (2010)","journal-title":"Proc. Am. Math. Soc."},{"key":"780_CR21","volume-title":"Handbook of Computational Geometry","year":"2000","unstructured":"Sack, J.-R., Urrutia, J. (eds.): Handbook of Computational Geometry. North-Holland Publishing Co., Amsterdam (2000)"},{"issue":"3","key":"780_CR22","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/s00526-003-0239-4","volume":"20","author":"XJ Wang","year":"2004","unstructured":"Wang, X.J.: On the design of a reflector antenna ii. Calc. Var. Partial Differ. Equ. 20(3), 329\u2013341 (2004)","journal-title":"Calc. Var. Partial Differ. Equ."},{"issue":"3","key":"780_CR23","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1088\/0266-5611\/12\/3\/013","volume":"12","author":"X-J Wang","year":"1996","unstructured":"Wang, X.-J.: On the design of a reflector antenna. Inverse Probl. 12(3), 351 (1996)","journal-title":"Inverse Probl."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-015-0780-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-015-0780-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-015-0780-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T16:27:18Z","timestamp":1558628838000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-015-0780-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,17]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,10]]}},"alternative-id":["780"],"URL":"https:\/\/doi.org\/10.1007\/s00211-015-0780-z","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,17]]}}}