{"id":"https://openalex.org/W6888814518","doi":"https://doi.org/10.2312/compaesth/compaesth05/133-141","title":"Straight away on Curved Spaces","display_name":"Straight away on Curved Spaces","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W6888814518","doi":"https://doi.org/10.2312/compaesth/compaesth05/133-141"},"language":"en","primary_location":{"id":"doi:10.2312/compaesth/compaesth05/133-141","is_oa":true,"landing_page_url":"https://doi.org/10.2312/compaesth/compaesth05/133-141","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"other","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.2312/compaesth/compaesth05/133-141","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Marty, Alain","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Marty, Alain","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T10715","display_name":"Distributed and Parallel Computing Systems","score":0.14259999990463257,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10715","display_name":"Distributed and Parallel Computing Systems","score":0.14259999990463257,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.13809999823570251,"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/T10933","display_name":"Real-Time Systems Scheduling","score":0.06930000334978104,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.7064999938011169},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.619700014591217},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6068000197410583},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5181000232696533},{"id":"https://openalex.org/keywords/curved-space","display_name":"Curved space","score":0.4814999997615814},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.47290000319480896},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"Differential geometry","score":0.4690000116825104},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4453999996185303},{"id":"https://openalex.org/keywords/jordan-curve-theorem","display_name":"Jordan curve theorem","score":0.42660000920295715}],"concepts":[{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.7064999938011169},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6597999930381775},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.619700014591217},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6068000197410583},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5181000232696533},{"id":"https://openalex.org/C111410970","wikidata":"https://www.wikidata.org/wiki/Q5196078","display_name":"Curved space","level":2,"score":0.4814999997615814},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.47290000319480896},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.4690000116825104},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4555000066757202},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4453999996185303},{"id":"https://openalex.org/C70251129","wikidata":"https://www.wikidata.org/wiki/Q260928","display_name":"Jordan curve theorem","level":2,"score":0.42660000920295715},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41999998688697815},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.41760000586509705},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4133000075817108},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.38269999623298645},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33160001039505005},{"id":"https://openalex.org/C15001198","wikidata":"https://www.wikidata.org/wiki/Q3241394","display_name":"Toroid","level":3,"score":0.32409998774528503},{"id":"https://openalex.org/C83677898","wikidata":"https://www.wikidata.org/wiki/Q1878538","display_name":"Hyperbolic space","level":2,"score":0.3228999972343445},{"id":"https://openalex.org/C2779668893","wikidata":"https://www.wikidata.org/wiki/Q2250422","display_name":"Constant curvature","level":3,"score":0.31439998745918274},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.3142000138759613},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.296999990940094},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C203231007","wikidata":"https://www.wikidata.org/wiki/Q192768","display_name":"Paraboloid","level":3,"score":0.2712000012397766},{"id":"https://openalex.org/C53622353","wikidata":"https://www.wikidata.org/wiki/Q1518913","display_name":"Family of curves","level":2,"score":0.2558000087738037},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.25540000200271606}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2312/compaesth/compaesth05/133-141","is_oa":true,"landing_page_url":"https://doi.org/10.2312/compaesth/compaesth05/133-141","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.2312/compaesth/compaesth05/133-141","is_oa":true,"landing_page_url":"https://doi.org/10.2312/compaesth/compaesth05/133-141","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.6068862676620483,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Two":[0],"points":[1],"of":[2,13,48,55,81,108,157,207],"a":[3,26,30,82,98,120,126,136,142,151,172,221,228,234,239,243,264],"Euclidean":[4,50,83],"space":[5,84],"can":[6,223,271],"always":[7],"be":[8,43,75,119,133,224,272],"connected":[9],"by":[10,125,263,274,294],"the":[11,14,16,34,46,49,53,60,64,71,109,155,181,199,216,225,248,267,280,285,289,295],"simplest":[12],"curves,":[15],"straight":[17,38,89],"line.":[18],"This":[19,115],"curve":[20,101,257],"is":[21,40,123],"unique":[22],"(it\u0092s":[23],"required),":[24],"with":[25],"constant":[27,111],"direction":[28],"and":[29,85,147,177],"minimal":[31,113],"length":[32],"between":[33],"two":[35],"points.":[36],"The":[37,167],"line":[39,90],"known":[41,117],"to":[42,63,74,95,118,150,160,197,227],"fundamental":[44,100],"in":[45,77,135,154,187,266,288],"building":[47],"geometry,":[51],"for":[52,97,175],"production":[54],"all":[56],"imaginable":[57],"figures,":[58],"from":[59],"simple":[61,137],"triangle":[62],"most":[65],"complex":[66,255],"curved":[67,78,161,179,212],"shapes.":[68],"And":[69],"when":[70],"figures":[72,158],"have":[73,300],"immersed":[76,276],"shapes,":[79,180],"out":[80],"without":[86],"its":[87,103],"useful":[88],"tool,":[91],"it":[92],"seems":[93],"natural":[94],"search":[96],"similar":[99],"possessing":[102],"basic":[104],"properties":[105],":":[106,214,232],"uniqueness":[107],"curve,":[110,116],"direction,":[112],"length.":[114],"geodesic":[121,222],"line,":[122],"defined":[124],"differential":[127],"system":[128],"whose":[129],"solutions":[130],"cannot":[131],"generally":[132],"expressed":[134],"way,":[138],"(let\u0092s":[139],"say":[140],"as":[141],"finite":[143],"degree":[144],"polynomial":[145],"expression),":[146],"so":[148],"leads":[149],"great":[152],"complexity":[153],"definition":[156],"belonging":[159],"spaces.":[162],"But":[163],"other":[164],"approachs":[165],"exist...":[166],"present":[168],"contribution,":[169],"based":[170],"on":[171,204,211,238],"conceptual":[173],"tool":[174],"creating":[176],"managing":[178],"Pascalian":[182],"Forms,":[183],"or":[184],"pForms,":[185],"(published":[186],"Editions":[188],"de":[189,200],"l\u0092Esperou":[190],"/":[191,193],"Montpellier":[192],"2004),":[194],"an":[195,253],"attempt":[196],"generalize":[198],"Casteljau":[201],"algorithm,":[202],"focuses":[203],"three":[205],"cases":[206],"\"straight":[208],"lines\"":[209],"drawn":[210],"shapes":[213,287],"1)":[215],"first":[217],"case":[218,250,282],"shows":[219,251,283],"how":[220,252,284],"solution":[226],"very":[229],"practical":[230],"problem":[231],"applying":[233],"long":[235],"thin":[236],"plank":[237],"toroidal":[240],"roof":[241],"upon":[242],"swimming":[244],"pool":[245],";":[246,278],"2)":[247],"second":[249],"apparently":[254],"spatial":[256],"(the":[258],"Threefoil":[259],"Knot":[260],"Curve)":[261],"followed":[262],"staircase":[265],"MC":[268],"Escher":[269],"style":[270],"simplified":[273],"using":[275,303],"pSegments":[277],"3)":[279],"third":[281],"natural/organic":[286],"Sagrada":[290],"Familia":[291],"Temple":[292],"dreamed":[293],"catalan":[296],"architect":[297],"A.":[298],"Gaudi":[299],"been":[301],"mastered":[302],"ruled":[304],"surfaces":[305],"(pSurfaces).":[306]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}