{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T09:36:02Z","timestamp":1742981762978,"version":"3.40.3"},"publisher-location":"Cham","reference-count":13,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030227494"},{"type":"electronic","value":"9783030227500"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-030-22750-0_49","type":"book-chapter","created":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T18:11:13Z","timestamp":1559931073000},"page":"543-550","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Rendering Non-Euclidean Space in Real-Time Using Spherical and Hyperbolic Trigonometry"],"prefix":"10.1007","author":[{"given":"Daniil","family":"Osudin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chris","family":"Child","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang-Hui","family":"He","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,6,8]]},"reference":[{"key":"49_CR1","unstructured":"Heath, T.L.: Euclid\u2019s Elements. Dover, New York (1956). (translated)"},{"key":"49_CR2","unstructured":"Todhunter, I.: Spherical Trigonometry For the use of colleges and schools. Project Gutenberg License (1886). (republished 12 November 2006)"},{"key":"49_CR3","volume-title":"The Elements of Non-Euclidean Plane Geometry and Trigonometry","author":"HS Carslaw","year":"1916","unstructured":"Carslaw, H.S.: The Elements of Non-Euclidean Plane Geometry and Trigonometry. Longmans, Green and Co., London (1916)"},{"key":"49_CR4","unstructured":"Traver, T.: Trigonometry in the hyperbolic plane (2014). Accessed December 2017, Manuscript"},{"key":"49_CR5","volume-title":"The VNR Concise Encyclopedia of Mathematics","author":"W Gellert","year":"1989","unstructured":"Gellert, W., Gottwald, S., Hellwich, M., K\u00e4stner, H., K\u00fcstner, H.: The VNR Concise Encyclopedia of Mathematics, 2nd edn. Van Nostrand Reinhold, New York (1989). ch. 12","edition":"2"},{"key":"49_CR6","doi-asserted-by":"publisher","first-page":"236","DOI":"10.1016\/0315-0860(79)90124-1","volume":"6","author":"J Gray","year":"1979","unstructured":"Gray, J.: Non-Euclidean geometry\u2013a re-interpretation. Historia Mathematica 6, 236\u2013258 (1979)","journal-title":"Historia Mathematica"},{"key":"49_CR7","doi-asserted-by":"crossref","unstructured":"Osudin, D., Child, C., He, Y.-H.: Rendering non-Euclidean space in realtime using spherical and hyperbolic trigonometry (2019). https:\/\/youtu.be\/A1ZCFh5qfNg","DOI":"10.1007\/978-3-030-22750-0_49"},{"key":"49_CR8","unstructured":"Brent, R.P.: Multiple-precision zero-finding methods and the complexity of elementary function evaluation (2010). http:\/\/arxiv.org\/abs\/1004.3412v2. Accessed 26 Aug 2018"},{"key":"49_CR9","unstructured":"Rochet, F.: Fast trigonometry functions using lookup tables (2004). http:\/\/www.flipcode.com\/archives\/Fast_Trigonometry_Functions_Using_Lookup_Tables.shtml. Accessed 30 Aug 2018"},{"key":"49_CR10","doi-asserted-by":"crossref","unstructured":"Gartner, G., Huang, H.: Recent research developments in modern cartography in Europe, Issue 1: EuroCarto 2015 (2015)","DOI":"10.1080\/23729333.2016.1187908"},{"key":"49_CR11","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1111\/2041-210X.12316","volume":"6","author":"C Sutherland","year":"2015","unstructured":"Sutherland, C., Fuller, A.K., Royle, J.A.: Modelling non-Euclidean movement and landscape connectivity in highly structured ecological networks. Methods Ecol. Evol. 6, 169\u2013177 (2015)","journal-title":"Methods Ecol. Evol."},{"key":"49_CR12","doi-asserted-by":"publisher","first-page":"1585","DOI":"10.1002\/joc.3786","volume":"34","author":"C Frei","year":"2013","unstructured":"Frei, C.: Interpolation of temperature in a mountainous region using nonlinear profiles and non-Euclidean distances. Int. J. Climatol. 34, 1585\u20131605 (2013). https:\/\/doi.org\/10.1002\/joc.3786","journal-title":"Int. J. Climatol."},{"key":"49_CR13","unstructured":"Zeno Rogue Games: Hyperrogue (2019). http:\/\/roguetemple.com\/z\/hyper\/"}],"container-title":["Lecture Notes in Computer Science","Computational Science \u2013 ICCS 2019"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-22750-0_49","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,7]],"date-time":"2023-06-07T03:46:57Z","timestamp":1686109617000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-22750-0_49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783030227494","9783030227500"],"references-count":13,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-22750-0_49","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"8 June 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ICCS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Computational Science","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Faro","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Portugal","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2019","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12 June 2019","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 June 2019","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"iccs-computsci2019","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.iccs-meeting.org\/iccs2019\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}