{"id":"https://openalex.org/W136797555","doi":"https://doi.org/10.1007/1-4020-4179-9_154","title":"CLOSED FORM SOLUTION FOR C2 ORIENTATION INTERPOLATION","display_name":"CLOSED FORM SOLUTION FOR C2 ORIENTATION INTERPOLATION","publication_year":2006,"publication_date":"2006-03-10","ids":{"openalex":"https://openalex.org/W136797555","doi":"https://doi.org/10.1007/1-4020-4179-9_154","mag":"136797555"},"language":"en","primary_location":{"id":"doi:10.1007/1-4020-4179-9_154","is_oa":false,"landing_page_url":"https://doi.org/10.1007/1-4020-4179-9_154","pdf_url":null,"source":{"id":"https://openalex.org/S4306463519","display_name":"Kluwer Academic Publishers eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Imaging and Vision","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/A5041898226","display_name":"Vasily Volkov","orcid":null},"institutions":[{"id":"https://openalex.org/I205640436","display_name":"Curtin University","ror":"https://ror.org/02n415q13","country_code":"AU","type":"education","lineage":["https://openalex.org/I205640436"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Vasily Volkov","raw_affiliation_strings":["Curtin University of Technology, Perth, Australia","Curtin Univ. of Technology, Perth, Australia"],"affiliations":[{"raw_affiliation_string":"Curtin University of Technology, Perth, Australia","institution_ids":["https://openalex.org/I205640436"]},{"raw_affiliation_string":"Curtin Univ. of Technology, Perth, Australia","institution_ids":["https://openalex.org/I205640436"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037788925","display_name":"Ling Li","orcid":"https://orcid.org/0000-0001-9722-9503"},"institutions":[{"id":"https://openalex.org/I205640436","display_name":"Curtin University","ror":"https://ror.org/02n415q13","country_code":"AU","type":"education","lineage":["https://openalex.org/I205640436"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Ling Li","raw_affiliation_strings":["Curtin University of Technology, Perth, Australia","Curtin Univ. of Technology, Perth, Australia"],"affiliations":[{"raw_affiliation_string":"Curtin University of Technology, Perth, Australia","institution_ids":["https://openalex.org/I205640436"]},{"raw_affiliation_string":"Curtin Univ. of Technology, Perth, Australia","institution_ids":["https://openalex.org/I205640436"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5041898226"],"corresponding_institution_ids":["https://openalex.org/I205640436"],"apc_list":null,"apc_paid":null,"fwci":2.7884,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.88744476,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1056","last_page":"1062"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9803000092506409,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9797000288963318,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.7706727981567383},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.6999408602714539},{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.6613940596580505},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6074931025505066},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.600456953048706},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5985821485519409},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.5076879262924194},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.47597283124923706},{"id":"https://openalex.org/keywords/monotone-cubic-interpolation","display_name":"Monotone cubic interpolation","score":0.45518606901168823},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.43514516949653625},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3675755262374878},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33961498737335205},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3234136998653412},{"id":"https://openalex.org/keywords/bicubic-interpolation","display_name":"Bicubic interpolation","score":0.3070322871208191},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26221370697021484},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16426676511764526},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.13372310996055603},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.10606342554092407},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09404468536376953},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05811426043510437}],"concepts":[{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.7706727981567383},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.6999408602714539},{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.6613940596580505},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6074931025505066},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.600456953048706},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5985821485519409},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.5076879262924194},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.47597283124923706},{"id":"https://openalex.org/C64485984","wikidata":"https://www.wikidata.org/wiki/Q4044484","display_name":"Monotone cubic interpolation","level":5,"score":0.45518606901168823},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.43514516949653625},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3675755262374878},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33961498737335205},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3234136998653412},{"id":"https://openalex.org/C49608258","wikidata":"https://www.wikidata.org/wiki/Q611705","display_name":"Bicubic interpolation","level":4,"score":0.3070322871208191},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26221370697021484},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16426676511764526},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.13372310996055603},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.10606342554092407},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09404468536376953},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05811426043510437},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/1-4020-4179-9_154","is_oa":false,"landing_page_url":"https://doi.org/10.1007/1-4020-4179-9_154","pdf_url":null,"source":{"id":"https://openalex.org/S4306463519","display_name":"Kluwer Academic Publishers eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Imaging and Vision","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1973484256","https://openalex.org/W1995945562","https://openalex.org/W2001133651","https://openalex.org/W2001450374","https://openalex.org/W2012294177","https://openalex.org/W2118670932","https://openalex.org/W2127186837","https://openalex.org/W2128574024","https://openalex.org/W2147774191","https://openalex.org/W2162870748","https://openalex.org/W2245379371","https://openalex.org/W2899740253","https://openalex.org/W4213187341","https://openalex.org/W4240743460","https://openalex.org/W4310437828"],"related_works":["https://openalex.org/W1974164852","https://openalex.org/W3116540586","https://openalex.org/W2028106580","https://openalex.org/W2009426420","https://openalex.org/W2562597462","https://openalex.org/W1572104243","https://openalex.org/W2380418310","https://openalex.org/W2368242165","https://openalex.org/W2806075104","https://openalex.org/W2583818965"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"present":[2],"a":[3],"simple":[4],"closed":[5],"form":[6],"solution":[7,31],"for":[8],"C2":[9,40],"smooth":[10],"quaternion":[11],"interpolation":[12],"problem.":[13],"In":[14],"contrast":[15],"to":[16],"other":[17],"methods,":[18],"our":[19],"approach":[20],"does":[21],"not":[22],"rely":[23],"on":[24],"cubic":[25],"B-spline":[26],"blending":[27],"functions":[28],"which":[29],"require":[30],"of":[32],"nonlinear":[33],"tridiagonal":[34],"system.":[35],"Instead,":[36],"we":[37],"propose":[38],"using":[39],"interpolatory":[41],"(cardinal)":[42],"basis.":[43],"Our":[44],"method":[45],"outperforms":[46],"all":[47],"alternatives":[48],"and,":[49],"being":[50],"explicit,":[51],"is":[52],"absolutely":[53],"stable.":[54]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
