{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T23:01:47Z","timestamp":1776812507162,"version":"3.51.2"},"reference-count":32,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03n04","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1661348"],"award-info":[{"award-number":["1661348"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1819229"],"award-info":[{"award-number":["1819229"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2020,9]]},"abstract":"<jats:p> We propose an Euler transformation that transforms a given [Formula: see text]-dimensional cell complex [Formula: see text] for [Formula: see text] into a new [Formula: see text]-complex [Formula: see text] in which every vertex is part of the same even number of edges. Hence every vertex in the graph [Formula: see text] that is the [Formula: see text]-skeleton of [Formula: see text] has an even degree, which makes [Formula: see text] Eulerian, i.e., it is guaranteed to contain an Eulerian tour. Meshes whose edges admit Eulerian tours are crucial in coverage problems arising in several applications including 3D printing and robotics. <\/jats:p><jats:p> For [Formula: see text]-complexes in [Formula: see text] ([Formula: see text]) under mild assumptions (that no two adjacent edges of a [Formula: see text]-cell in [Formula: see text] are boundary edges), we show that the Euler transformed [Formula: see text]-complex [Formula: see text] has a geometric realization in [Formula: see text], and that each vertex in its [Formula: see text]-skeleton has degree [Formula: see text]. We bound the numbers of vertices, edges, and [Formula: see text]-cells in [Formula: see text] as small scalar multiples of the corresponding numbers in [Formula: see text]. <\/jats:p><jats:p> We prove corresponding results for [Formula: see text]-complexes in [Formula: see text] under an additional assumption that the degree of a vertex in each [Formula: see text]-cell containing it is [Formula: see text]. In this setting, every vertex in [Formula: see text] is shown to have a degree of [Formula: see text]. <\/jats:p><jats:p> We also present bounds on parameters measuring geometric quality (aspect ratios, minimum edge length, and maximum angle of cells) of [Formula: see text] in terms of the corresponding parameters of [Formula: see text] for [Formula: see text]. Finally, we illustrate a direct application of the proposed Euler transformation in additive manufacturing. <\/jats:p>","DOI":"10.1142\/s0218195920500090","type":"journal-article","created":{"date-parts":[[2021,6,5]],"date-time":"2021-06-05T05:23:32Z","timestamp":1622870612000},"page":"183-211","source":"Crossref","is-referenced-by-count":2,"title":["Euler Transformation of Polyhedral Complexes"],"prefix":"10.1142","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3660-4415","authenticated-orcid":false,"given":"Prashant","family":"Gupta","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Washington State University, PO Box 643113, Pullman, WA, 99164, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2727-6547","authenticated-orcid":false,"given":"Bala","family":"Krishnamoorthy","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Washington State University, 14204 NE Salmon Creek Ave, Vancouver, WA, 98686, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,6,4]]},"reference":[{"key":"S0218195920500090BIB001","first-page":"128","volume":"8","author":"Euler L.","year":"1736","journal-title":"Commentarii Academiae Scientiarum Imperialis Petropolitanae"},{"key":"S0218195920500090BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/BF01442866"},{"key":"S0218195920500090BIB003","doi-asserted-by":"publisher","DOI":"10.1088\/1742-6596\/382\/1\/012042"},{"key":"S0218195920500090BIB004","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2017.2655523"},{"key":"S0218195920500090BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.robot.2013.09.004"},{"key":"S0218195920500090BIB007","doi-asserted-by":"publisher","DOI":"10.1002\/rob.4620050202"},{"key":"S0218195920500090BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2020.102880"},{"key":"S0218195920500090BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/0925-7721(93)90003-O"},{"key":"S0218195920500090BIB010","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480194265611"},{"key":"S0218195920500090BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-03367-4_2"},{"key":"S0218195920500090BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-012-1247-y"},{"key":"S0218195920500090BIB013","first-page":"103","volume-title":"Proceedings of the 22nd Annual Canadian Conference on Computational Geometry, CCCG 2010","author":"Pel\u00e1ez C.","year":"2010"},{"key":"S0218195920500090BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-77028-4_87"},{"key":"S0218195920500090BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-013-1389-6"},{"key":"S0218195920500090BIB016","doi-asserted-by":"publisher","DOI":"10.1137\/130925712"},{"key":"S0218195920500090BIB017","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-011-9218-z"},{"key":"S0218195920500090BIB018","doi-asserted-by":"publisher","DOI":"10.1002\/num.21905"},{"key":"S0218195920500090BIB019","doi-asserted-by":"publisher","DOI":"10.1109\/IROS.2006.282649"},{"key":"S0218195920500090BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4485(78)90110-0"},{"key":"S0218195920500090BIB021","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4485(78)90111-2"},{"key":"S0218195920500090BIB022","doi-asserted-by":"publisher","DOI":"10.1007\/PL00009412"},{"key":"S0218195920500090BIB023","volume-title":"Algebraic Topology","author":"Hatcher A.","year":"2002"},{"key":"S0218195920500090BIB024","volume-title":"Elements of Algebraic Topology","author":"Munkres J. R.","year":"1984"},{"issue":"12","key":"S0218195920500090BIB025","first-page":"752","volume":"1","author":"Aichholzer O.","year":"1995","journal-title":"Journal of Universal Computer Science"},{"key":"S0218195920500090BIB026","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-87744-8_13"},{"key":"S0218195920500090BIB027","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.02031.x"},{"key":"S0218195920500090BIB028","first-page":"15","volume-title":"Proceedings of 5th International Conference Analytical Number Theory and Spatial Tessellations","author":"Aurenhammer F.","year":"2013"},{"key":"S0218195920500090BIB029","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-016-9811-5"},{"key":"S0218195920500090BIB030","volume-title":"Delaunay Mesh Generation","author":"Cheng S.-W.","year":"2012"},{"key":"S0218195920500090BIB031","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-04319-2_4"},{"key":"S0218195920500090BIB032","doi-asserted-by":"publisher","DOI":"10.1016\/j.finel.2009.06.017"},{"key":"S0218195920500090BIB033","first-page":"237","author":"Scott P. R.","year":"2000","journal-title":"Bulletin of the Australian Mathematical Society"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195920500090","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,17]],"date-time":"2021-08-17T10:34:51Z","timestamp":1629196491000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195920500090"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9]]},"references-count":32,"journal-issue":{"issue":"03n04","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["10.1142\/S0218195920500090"],"URL":"https:\/\/doi.org\/10.1142\/s0218195920500090","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9]]}}}