{"id":"https://openalex.org/W3175062468","doi":"https://doi.org/10.1007/s42979-021-00770-x","title":"Conversion Between Cubic Bezier Curves and Catmull\u2013Rom Splines","display_name":"Conversion Between Cubic Bezier Curves and Catmull\u2013Rom Splines","publication_year":2021,"publication_date":"2021-07-31","ids":{"openalex":"https://openalex.org/W3175062468","doi":"https://doi.org/10.1007/s42979-021-00770-x","mag":"3175062468"},"language":"en","primary_location":{"id":"doi:10.1007/s42979-021-00770-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s42979-021-00770-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s42979-021-00770-x.pdf","source":{"id":"https://openalex.org/S4210174798","display_name":"SN Computer Science","issn_l":"2661-8907","issn":["2661-8907","2662-995X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SN Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s42979-021-00770-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Soroosh Tayebi Arasteh","orcid":"https://orcid.org/0000-0003-1015-7733"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]},{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]},{"id":"https://openalex.org/I2801543288","display_name":"Lemuel Shattuck Hospital","ror":"https://ror.org/01wpqwr25","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I2801543288"]}],"countries":["DE","US"],"is_corresponding":true,"raw_author_name":"Soroosh Tayebi Arasteh","raw_affiliation_strings":["Department of Electrical, Electronic, and Communication Engineering, Information Technology (LIKE), Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Am Wolfsmantel 33, 90158, Erlangen, Germany","Harvard Medical School, 25 Shattuck St, Boston, MA, 02115, USA"],"raw_orcid":"https://orcid.org/0000-0003-1015-7733","affiliations":[{"raw_affiliation_string":"Department of Electrical, Electronic, and Communication Engineering, Information Technology (LIKE), Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Am Wolfsmantel 33, 90158, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"Harvard Medical School, 25 Shattuck St, Boston, MA, 02115, USA","institution_ids":["https://openalex.org/I2801543288","https://openalex.org/I136199984"]}]},{"author_position":"last","author":{"id":null,"display_name":"Adam Kalisz","orcid":null},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Adam Kalisz","raw_affiliation_strings":["Department of Electrical, Electronic, and Communication Engineering, Information Technology (LIKE), Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Am Wolfsmantel 33, 90158, Erlangen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical, Electronic, and Communication Engineering, Information Technology (LIKE), Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Am Wolfsmantel 33, 90158, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I136199984","https://openalex.org/I181369854","https://openalex.org/I2801543288"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.0346,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.72091218,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"2","issue":"5","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.0010999999940395355,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T13267","display_name":"Advanced Theoretical and Applied Studies in Material Sciences and Geometry","score":0.0010999999940395355,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/b\u00e9zier-curve","display_name":"B\u00e9zier curve","score":0.7800999879837036},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5307999849319458},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.52920001745224},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics","score":0.45660001039505005},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4447999894618988},{"id":"https://openalex.org/keywords/graphics","display_name":"Graphics","score":0.4083000123500824},{"id":"https://openalex.org/keywords/geometric-design","display_name":"Geometric design","score":0.37290000915527344},{"id":"https://openalex.org/keywords/control-point","display_name":"Control point","score":0.35530000925064087}],"concepts":[{"id":"https://openalex.org/C206423108","wikidata":"https://www.wikidata.org/wiki/Q214728","display_name":"B\u00e9zier curve","level":2,"score":0.7800999879837036},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5881999731063843},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5307999849319458},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.52920001745224},{"id":"https://openalex.org/C77660652","wikidata":"https://www.wikidata.org/wiki/Q150971","display_name":"Computer graphics","level":2,"score":0.45660001039505005},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4447999894618988},{"id":"https://openalex.org/C21442007","wikidata":"https://www.wikidata.org/wiki/Q1027879","display_name":"Graphics","level":2,"score":0.4083000123500824},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40790000557899475},{"id":"https://openalex.org/C40319758","wikidata":"https://www.wikidata.org/wiki/Q5535477","display_name":"Geometric design","level":2,"score":0.37290000915527344},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36579999327659607},{"id":"https://openalex.org/C2777774050","wikidata":"https://www.wikidata.org/wiki/Q16945110","display_name":"Control point","level":2,"score":0.35530000925064087},{"id":"https://openalex.org/C104065381","wikidata":"https://www.wikidata.org/wiki/Q1002535","display_name":"Geometric modeling","level":2,"score":0.351500004529953},{"id":"https://openalex.org/C184389593","wikidata":"https://www.wikidata.org/wiki/Q603159","display_name":"Curve fitting","level":2,"score":0.33570000529289246},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31790000200271606},{"id":"https://openalex.org/C119823426","wikidata":"https://www.wikidata.org/wiki/Q184793","display_name":"Computer Aided Design","level":2,"score":0.31150001287460327},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.30979999899864197},{"id":"https://openalex.org/C107457265","wikidata":"https://www.wikidata.org/wiki/Q7546460","display_name":"Smoothing spline","level":4,"score":0.3084000051021576},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.3034999966621399},{"id":"https://openalex.org/C65559279","wikidata":"https://www.wikidata.org/wiki/Q16667694","display_name":"Cubic function","level":2,"score":0.29739999771118164},{"id":"https://openalex.org/C78383375","wikidata":"https://www.wikidata.org/wiki/Q4951620","display_name":"Box spline","level":4,"score":0.296099990606308},{"id":"https://openalex.org/C91429207","wikidata":"https://www.wikidata.org/wiki/Q5192245","display_name":"Cubic form","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2831000089645386},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C15945459","wikidata":"https://www.wikidata.org/wiki/Q2083109","display_name":"B-spline","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25540000200271606},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s42979-021-00770-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s42979-021-00770-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s42979-021-00770-x.pdf","source":{"id":"https://openalex.org/S4210174798","display_name":"SN Computer Science","issn_l":"2661-8907","issn":["2661-8907","2662-995X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SN Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2011.08232","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.08232","pdf_url":"https://arxiv.org/pdf/2011.08232","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:ub.uni-erlangen.de-opus:22445","is_oa":true,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bvb:29-opus4-224458","pdf_url":null,"source":{"id":"https://openalex.org/S4306402340","display_name":"OPUS FAU (Kooperativer Bibliotheksverbund Berlin-Brandenburg (KOBV), on behalf of the Universit\u00e4tsbibliothek Erlangen-N\u00fcrnberg)","issn_l":null,"issn":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s42979-021-00770-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s42979-021-00770-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s42979-021-00770-x.pdf","source":{"id":"https://openalex.org/S4210174798","display_name":"SN Computer Science","issn_l":"2661-8907","issn":["2661-8907","2662-995X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SN Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320873","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3175062468.pdf","grobid_xml":"https://content.openalex.org/works/W3175062468.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W26013093","https://openalex.org/W326547310","https://openalex.org/W1553284676","https://openalex.org/W2017721907","https://openalex.org/W2061176333","https://openalex.org/W2064028512","https://openalex.org/W2066812414","https://openalex.org/W2077758943","https://openalex.org/W2094963988","https://openalex.org/W2150325883","https://openalex.org/W2159031840","https://openalex.org/W2200993670","https://openalex.org/W2946914738","https://openalex.org/W2955208387","https://openalex.org/W3120734124"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Splines":[1],"are":[2,41],"one":[3],"of":[4,8,22,48,82,86,88,99,118,122,132],"the":[5,16,20,42,46,72,79,83,89,106,110,116,119,123,135],"main":[6],"methods":[7],"mathematically":[9],"representing":[10],"complicated":[11],"shapes,":[12],"which":[13,102,145],"have":[14],"become":[15],"primary":[17],"technique":[18],"in":[19,45,149],"fields":[21],"Computer":[23],"Graphics":[24],"(CG)":[25],"and":[26,38,60,141,155],"Computer-Aided":[27],"Geometric":[28],"Design":[29],"(CAGD)":[30],"for":[31],"modeling":[32],"complex":[33],"surfaces.":[34],"Among":[35],"all,":[36],"B\u00e9zier":[37,59,92],"Catmull\u2013Rom":[39,61,90],"splines":[40],"most":[43],"common":[44],"sub-fields":[47],"engineering.":[49],"In":[50],"this":[51,150],"paper,":[52],"we":[53,75],"focus":[54],"on":[55],"conversion":[56,73],"between":[57],"cubic":[58,93],"curve":[62],"segments,":[63],"rather":[64],"than":[65],"going":[66],"through":[67],"their":[68],"properties.":[69],"By":[70],"deriving":[71],"equations,":[74],"aim":[76],"at":[77],"converting":[78],"original":[80,111],"set":[81,98,117],"control":[84,100,120,133],"points":[85,121],"either":[87],"or":[91],"curves":[94],"to":[95,104,127,143],"a":[96],"new":[97],"points,":[101,134],"corresponds":[103],"approximately":[105],"same":[107],"shape":[108],"as":[109,115],"curve,":[112],"when":[113],"considered":[114],"other":[124],"curve.":[125],"Due":[126],"providing":[128],"simple":[129],"linear":[130],"transformations":[131],"method":[136],"is":[137,146],"very":[138],"simple,":[139],"efficient,":[140],"easy":[142],"implement,":[144],"further":[147],"validated":[148],"paper":[151],"using":[152],"some":[153],"numerical":[154],"visual":[156],"examples.":[157]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2021-07-05T00:00:00"}