{"id":"https://openalex.org/W1952933606","doi":"https://doi.org/10.1007/978-0-85729-811-9_5","title":"Square Root and Logarithm of Rotors in 3D Conformal Geometric Algebra Using Polar Decomposition","display_name":"Square Root and Logarithm of Rotors in 3D Conformal Geometric Algebra Using Polar Decomposition","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1952933606","doi":"https://doi.org/10.1007/978-0-85729-811-9_5","mag":"1952933606"},"language":"en","primary_location":{"id":"doi:10.1007/978-0-85729-811-9_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-85729-811-9_5","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Guide to Geometric Algebra in Practice","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036491534","display_name":"Leo Dorst","orcid":"https://orcid.org/0000-0003-3680-2745"},"institutions":[{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Leo Dorst","raw_affiliation_strings":["Informatics Institute, University of Amsterdam, Science Park 107, Amsterdam, 1098 XG, Netherlands","Intelligent Systems Laboratory, University of Amsterdam, Amsterdam, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Informatics Institute, University of Amsterdam, Science Park 107, Amsterdam, 1098 XG, Netherlands","institution_ids":["https://openalex.org/I887064364"]},{"raw_affiliation_string":"Intelligent Systems Laboratory, University of Amsterdam, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I887064364"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007319685","display_name":"Robert J. Valkenburg","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert Valkenburg","raw_affiliation_strings":["Industrial Research Limited, Auckland, New Zealand"],"affiliations":[{"raw_affiliation_string":"Industrial Research Limited, Auckland, New Zealand","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036491534"],"corresponding_institution_ids":["https://openalex.org/I887064364"],"apc_list":null,"apc_paid":null,"fwci":6.4093,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.96719933,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"81","last_page":"104"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9833999872207642,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.972599983215332,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/conformal-map","display_name":"Conformal map","score":0.8029372692108154},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6786589622497559},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6670487523078918},{"id":"https://openalex.org/keywords/subalgebra","display_name":"Subalgebra","score":0.6563135385513306},{"id":"https://openalex.org/keywords/square-root","display_name":"Square root","score":0.5428653955459595},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.47218576073646545},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4433942437171936},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4374791979789734},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.4132993221282959},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.41174548864364624},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.288891077041626},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17704826593399048}],"concepts":[{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.8029372692108154},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6786589622497559},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6670487523078918},{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.6563135385513306},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.5428653955459595},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47218576073646545},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4433942437171936},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4374791979789734},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.4132993221282959},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.41174548864364624},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.288891077041626},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17704826593399048},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/978-0-85729-811-9_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-85729-811-9_5","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Guide to Geometric Algebra in Practice","raw_type":"book-chapter"},{"id":"pmh:oai:dare.uva.nl:openaire_cris_publications/eb412e6e-e614-440c-ab74-9d42f8d52596","is_oa":false,"landing_page_url":"https://dare.uva.nl/personal/pure/en/publications/square-root-and-logarithm-of-rotors-in-3d-conformal-geometric-algebra-using-polar-decomposition(eb412e6e-e614-440c-ab74-9d42f8d52596).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Dorst, L & Valkenburg, R J 2011, Square root and logarithm of rotors in 3D conformal geometric algebra using polar decomposition. in L Dorst & J Lasenby (eds), Guide to Geometric Algebra in Practice. pp. 25-46. https://doi.org/10.1007/978-0-85729-811-9_5","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:dare.uva.nl:publications/eb412e6e-e614-440c-ab74-9d42f8d52596","is_oa":false,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/square-root-and-logarithm-of-rotors-in-3d-conformal-geometric-algebra-using-polar-decomposition(eb412e6e-e614-440c-ab74-9d42f8d52596).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Dorst, L & Valkenburg, R J 2011, Square root and logarithm of rotors in 3D conformal geometric algebra using polar decomposition. in L Dorst & J Lasenby (eds), Guide to Geometric Algebra in Practice. pp. 25-46. https://doi.org/10.1007/978-0-85729-811-9_5","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W122875470","https://openalex.org/W1879706276","https://openalex.org/W2082565556","https://openalex.org/W2102277366","https://openalex.org/W2116021467","https://openalex.org/W2169467475","https://openalex.org/W4298680854"],"related_works":["https://openalex.org/W4327856465","https://openalex.org/W1670763528","https://openalex.org/W2756546235","https://openalex.org/W2016872916","https://openalex.org/W2171772926","https://openalex.org/W2051675810","https://openalex.org/W2003747419","https://openalex.org/W3040896577","https://openalex.org/W1975727149","https://openalex.org/W1973938972"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3}],"updated_date":"2026-03-17T09:09:15.849793","created_date":"2025-10-10T00:00:00"}
