{"id":"https://openalex.org/W2010441082","doi":"https://doi.org/10.1007/bf02127699","title":"Barycentric coordinates for convex polytopes","display_name":"Barycentric coordinates for convex polytopes","publication_year":1996,"publication_date":"1996-12-01","ids":{"openalex":"https://openalex.org/W2010441082","doi":"https://doi.org/10.1007/bf02127699","mag":"2010441082"},"language":"en","primary_location":{"id":"doi:10.1007/bf02127699","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02127699","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"type":"article","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/A5113597103","display_name":"Joe Warren","orcid":null},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Joe Warren","raw_affiliation_strings":["Department of Computer Science, Rice University, 77001, Houston, TX, USA","Department of Computer Science, Rice University, Houston, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Rice University, 77001, Houston, TX, USA","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Department of Computer Science, Rice University, Houston, USA#TAB#","institution_ids":["https://openalex.org/I74775410"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5113597103"],"corresponding_institution_ids":["https://openalex.org/I74775410"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":196,"citation_normalized_percentile":{"value":0.18641811,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"6","issue":"1","first_page":"97","last_page":"108"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9297999739646912,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9297999739646912,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9205999970436096,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9023000001907349,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/barycentric-coordinate-system","display_name":"Barycentric coordinate system","score":0.865088701248169},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.8329368829727173},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7183156609535217},{"id":"https://openalex.org/keywords/birkhoff-polytope","display_name":"Birkhoff polytope","score":0.7096878290176392},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6547436118125916},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.6545146107673645},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.505369246006012},{"id":"https://openalex.org/keywords/uniform-k-21-polytope","display_name":"Uniform k 21 polytope","score":0.4912392497062683},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4904622733592987},{"id":"https://openalex.org/keywords/polytope-model","display_name":"Polytope model","score":0.48717302083969116},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.2996692955493927},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.24974820017814636},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.22028738260269165},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1984575390815735},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16376423835754395}],"concepts":[{"id":"https://openalex.org/C128356825","wikidata":"https://www.wikidata.org/wiki/Q738422","display_name":"Barycentric coordinate system","level":2,"score":0.865088701248169},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8329368829727173},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7183156609535217},{"id":"https://openalex.org/C206304794","wikidata":"https://www.wikidata.org/wiki/Q4916482","display_name":"Birkhoff polytope","level":5,"score":0.7096878290176392},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6547436118125916},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.6545146107673645},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.505369246006012},{"id":"https://openalex.org/C16507315","wikidata":"https://www.wikidata.org/wiki/Q7885104","display_name":"Uniform k 21 polytope","level":5,"score":0.4912392497062683},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4904622733592987},{"id":"https://openalex.org/C113391598","wikidata":"https://www.wikidata.org/wiki/Q1681391","display_name":"Polytope model","level":3,"score":0.48717302083969116},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.2996692955493927},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.24974820017814636},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.22028738260269165},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1984575390815735},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16376423835754395},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/bf02127699","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02127699","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.39.6444","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.6444","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.rice.edu/~jwarren/papers/bary.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.49000000953674316,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1978561325","https://openalex.org/W1994631751","https://openalex.org/W2034966370","https://openalex.org/W2911302472","https://openalex.org/W3041834803","https://openalex.org/W3209870235","https://openalex.org/W4247863020","https://openalex.org/W4296942791","https://openalex.org/W4300929448"],"related_works":["https://openalex.org/W2275490733","https://openalex.org/W1968764954","https://openalex.org/W2173724444","https://openalex.org/W2010441082","https://openalex.org/W302405859","https://openalex.org/W24198779","https://openalex.org/W4280592905","https://openalex.org/W4387076217","https://openalex.org/W2044449173","https://openalex.org/W4243575619"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":17},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":18},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}