{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T22:13:24Z","timestamp":1780438404671,"version":"3.54.1"},"reference-count":17,"publisher":"Association for Computing Machinery (ACM)","issue":"6","license":[{"start":{"date-parts":[[2015,11,2]],"date-time":"2015-11-02T00:00:00Z","timestamp":1446422400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["GRK 1773"],"award-info":[{"award-number":["GRK 1773"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2015,11,4]]},"abstract":"<jats:p>\n            Spherical Fibonacci point sets yield nearly uniform point distributions on the unit sphere\n            <jats:italic>S<\/jats:italic>\n            <jats:sup>2<\/jats:sup>\n            \u2282 R\n            <jats:sup>3<\/jats:sup>\n            . The forward generation of these point sets has been widely researched and is easy to implement, such that they have been used in various applications.\n          <\/jats:p>\n          <jats:p>Unfortunately, the lack of an efficient mapping from points on the unit sphere to their closest spherical Fibonacci point set neighbors rendered them impractical for a wide range of applications, especially in computer graphics. Therefore, we introduce an inverse mapping from points on the unit sphere which yields the nearest neighbor in an arbitrarily sized spherical Fibonacci point set in constant time, without requiring any precomputations or table lookups.<\/jats:p>\n          <jats:p>We show how to implement this inverse mapping on GPUs while addressing arising floating point precision problems. Further, we demonstrate the use of this mapping and its variants, and show how to apply it to fast unit vector quantization. Finally, we illustrate the means by which to modify this inverse mapping for texture mapping with smooth filter kernels and showcase its use in the field of procedural modeling.<\/jats:p>","DOI":"10.1145\/2816795.2818131","type":"journal-article","created":{"date-parts":[[2015,10,27]],"date-time":"2015-10-27T12:36:39Z","timestamp":1445949399000},"page":"1-7","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":101,"title":["Spherical fibonacci mapping"],"prefix":"10.1145","volume":"34","author":[{"given":"Benjamin","family":"Keinert","sequence":"first","affiliation":[{"name":"University of Erlangen-Nuremberg"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matthias","family":"Innmann","sequence":"additional","affiliation":[{"name":"University of Erlangen-Nuremberg"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"S\u00e4nger","sequence":"additional","affiliation":[{"name":"hypnolords GbR"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marc","family":"Stamminger","sequence":"additional","affiliation":[{"name":"University of Erlangen-Nuremberg"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2015,11,2]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2501988.2502027"},{"key":"e_1_2_2_2_1","first-page":"2","article-title":"A survey of efficient representations for independent unit vectors","volume":"3","author":"Cigolle Z. H.","year":"2014","journal-title":"Journal of Computer Graphics Techniques (JCGT)"},{"key":"e_1_2_2_3_1","doi-asserted-by":"crossref","unstructured":"Dammertz S. and Keller A. 2008. Image synthesis by rank-1 lattices. In Monte Carlo and Quasi-Monte Carlo Methods 2006. Springer 217--236.  Dammertz S. and Keller A. 2008. Image synthesis by rank-1 lattices. In Monte Carlo and Quasi-Monte Carlo Methods 2006. Springer 217--236.","DOI":"10.1007\/978-3-540-74496-2_12"},{"key":"e_1_2_2_4_1","volume-title":"Proceedings of the Vision, Modeling, and Visualization Conference 2008, VMV 2008","author":"Engelhardt T.","year":"2008"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/133994.134093"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11004-009-9257-x"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/MCG.1986.276658"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/37\/48\/005"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/s003710050084"},{"key":"e_1_2_2_10_1","volume-title":"Smart Tools and Apps for Graphics - Eurographics Italian Chapter Conference, Eurographics Association","author":"Keinert B."},{"key":"e_1_2_2_11_1","doi-asserted-by":"crossref","unstructured":"Larkins R. L. Cree M. J. and Dorrington A. A. 2012. Analysis of binning of normals for spherical harmonic cross-correlation. In IS&T\/SPIE Electronic Imaging International Society for Optics and Photonics.  Larkins R. L. Cree M. J. and Dorrington A. A. 2012. Analysis of binning of normals for spherical harmonic cross-correlation. In IS&T\/SPIE Electronic Imaging International Society for Optics and Photonics.","DOI":"10.1117\/12.909466"},{"key":"e_1_2_2_12_1","volume-title":"Spherical Fibonacci Point Sets for Illumination Integrals. 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