Publication Information

{'id': 'https://openalex.org/W76980395', 'doi': None, 'title': 'Quaternions, Interpolation and Animation', 'display_name': 'Quaternions, Interpolation and Animation', 'publication_year': 2000, 'publication_date': '2000-01-01', 'ids': {'openalex': 'https://openalex.org/W76980395', 'mag': '76980395'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'http://www.dimnp.unipi.it/gabiccini-m/RAR/Hidden/___Quaternions_Interp_and_Animation.pdf', 'pdf_url': None, 'source': None, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': [], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5008183217', 'display_name': 'Erik B. Dam', 'orcid': 'https://orcid.org/0000-0002-8888-2524'}, 'institutions': [{'id': 'https://openalex.org/I124055696', 'display_name': 'University of Copenhagen', 'ror': 'https://ror.org/035b05819', 'country_code': 'DK', 'type': 'education', 'lineage': ['https://openalex.org/I124055696']}], 'countries': ['DK'], 'is_corresponding': False, 'raw_author_name': 'Erik B. Dam', 'raw_affiliation_strings': ['University of Copenhagen - Faculty of Science'], 'affiliations': [{'raw_affiliation_string': 'University of Copenhagen - Faculty of Science', 'institution_ids': ['https://openalex.org/I124055696']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5053757872', 'display_name': 'Martín Koch', 'orcid': 'https://orcid.org/0000-0001-5584-7549'}, 'institutions': [{'id': 'https://openalex.org/I124055696', 'display_name': 'University of Copenhagen', 'ror': 'https://ror.org/035b05819', 'country_code': 'DK', 'type': 'education', 'lineage': ['https://openalex.org/I124055696']}], 'countries': ['DK'], 'is_corresponding': False, 'raw_author_name': 'Martin Koch', 'raw_affiliation_strings': ['University of Copenhagen - Faculty of Science'], 'affiliations': [{'raw_affiliation_string': 'University of Copenhagen - Faculty of Science', 'institution_ids': ['https://openalex.org/I124055696']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5022946341', 'display_name': 'Martin Lillholm', 'orcid': 'https://orcid.org/0000-0002-1402-6899'}, 'institutions': [{'id': 'https://openalex.org/I124055696', 'display_name': 'University of Copenhagen', 'ror': 'https://ror.org/035b05819', 'country_code': 'DK', 'type': 'education', 'lineage': ['https://openalex.org/I124055696']}], 'countries': ['DK'], 'is_corresponding': False, 'raw_author_name': 'Martin Lillholm', 'raw_affiliation_strings': ['University of Copenhagen - Faculty of Science'], 'affiliations': [{'raw_affiliation_string': 'University of Copenhagen - Faculty of Science', 'institution_ids': ['https://openalex.org/I124055696']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 6.134, 'has_fulltext': False, 'cited_by_count': 298, 'citation_normalized_percentile': {'value': 0.999887, 'is_in_top_1_percent': True, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 98, 'max': 99}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11245', 'display_name': 'Advanced Numerical Analysis Techniques', 'score': 0.9869, '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': 0.9869, '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/T10571', 'display_name': 'Robotic Mechanisms and Dynamics', 'score': 0.9509, 'subfield': {'id': 'https://openalex.org/subfields/2207', 'display_name': 'Control and Systems 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': 0.9475, '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/interpolation', 'display_name': 'Interpolation', 'score': 0.6835571}, {'id': 'https://openalex.org/keywords/inverse-quadratic-interpolation', 'display_name': 'Inverse quadratic interpolation', 'score': 0.43859428}], 'concepts': [{'id': 'https://openalex.org/C200127275', 'wikidata': 'https://www.wikidata.org/wiki/Q173853', 'display_name': 'Quaternion', 'level': 2, 'score': 0.8114613}, {'id': 'https://openalex.org/C137800194', 'wikidata': 'https://www.wikidata.org/wiki/Q11713455', 'display_name': 'Interpolation (computer graphics)', 'level': 3, 'score': 0.6835571}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.54217285}, {'id': 'https://openalex.org/C143724316', 'wikidata': 'https://www.wikidata.org/wiki/Q312468', 'display_name': 'Series (stratigraphy)', 'level': 2, 'score': 0.47776878}, {'id': 'https://openalex.org/C177264268', 'wikidata': 'https://www.wikidata.org/wiki/Q1514741', 'display_name': 'Set (abstract data type)', 'level': 2, 'score': 0.46534193}, {'id': 'https://openalex.org/C74050887', 'wikidata': 'https://www.wikidata.org/wiki/Q848368', 'display_name': 'Rotation (mathematics)', 'level': 2, 'score': 0.44895446}, {'id': 'https://openalex.org/C143542097', 'wikidata': 'https://www.wikidata.org/wiki/Q3153554', 'display_name': 'Inverse quadratic interpolation', 'level': 5, 'score': 0.43859428}, {'id': 'https://openalex.org/C28826006', 'wikidata': 'https://www.wikidata.org/wiki/Q33521', 'display_name': 'Applied mathematics', 'level': 1, 'score': 0.42462963}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.41492316}, {'id': 'https://openalex.org/C502989409', 'wikidata': 'https://www.wikidata.org/wiki/Q11425', 'display_name': 'Animation', 'level': 2, 'score': 0.37639657}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.37636188}, {'id': 'https://openalex.org/C188325010', 'wikidata': 'https://www.wikidata.org/wiki/Q861176', 'display_name': 'Trilinear interpolation', 'level': 4, 'score': 0.37327594}, {'id': 'https://openalex.org/C205203396', 'wikidata': 'https://www.wikidata.org/wiki/Q612143', 'display_name': 'Bilinear interpolation', 'level': 2, 'score': 0.3703984}, {'id': 'https://openalex.org/C31447003', 'wikidata': 'https://www.wikidata.org/wiki/Q545002', 'display_name': 'Spline interpolation', 'level': 3, 'score': 0.3655622}, {'id': 'https://openalex.org/C11413529', 'wikidata': 'https://www.wikidata.org/wiki/Q8366', 'display_name': 'Algorithm', 'level': 1, 'score': 0.3649095}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.20767397}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.14764589}, {'id': 'https://openalex.org/C121684516', 'wikidata': 'https://www.wikidata.org/wiki/Q7600677', 'display_name': 'Computer graphics (images)', 'level': 1, 'score': 0.105926484}, {'id': 'https://openalex.org/C199360897', 'wikidata': 'https://www.wikidata.org/wiki/Q9143', 'display_name': 'Programming language', 'level': 1, 'score': 0.06894848}, {'id': 'https://openalex.org/C151730666', 'wikidata': 'https://www.wikidata.org/wiki/Q7205', 'display_name': 'Paleontology', 'level': 1, '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/C86803240', 'wikidata': 'https://www.wikidata.org/wiki/Q420', 'display_name': 'Biology', 'level': 0, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'http://www.dimnp.unipi.it/gabiccini-m/RAR/Hidden/___Quaternions_Interp_and_Animation.pdf', 'pdf_url': None, 'source': None, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 7, 'referenced_works': ['https://openalex.org/W1555837804', 'https://openalex.org/W1561051169', 'https://openalex.org/W1984417059', 'https://openalex.org/W2121378366', 'https://openalex.org/W2503576123', 'https://openalex.org/W2734684709', 'https://openalex.org/W2898916015'], 'related_works': ['https://openalex.org/W2734684709', 'https://openalex.org/W2293451440', 'https://openalex.org/W2211533701', 'https://openalex.org/W2164266004', 'https://openalex.org/W2147774191', 'https://openalex.org/W2145741013', 'https://openalex.org/W2133607347', 'https://openalex.org/W2121349631', 'https://openalex.org/W2090782210', 'https://openalex.org/W2062691475', 'https://openalex.org/W2033819227', 'https://openalex.org/W2018233111', 'https://openalex.org/W2012294177', 'https://openalex.org/W2001133651', 'https://openalex.org/W1989286669', 'https://openalex.org/W1977259876', 'https://openalex.org/W1564897360', 'https://openalex.org/W1527786550', 'https://openalex.org/W1490678064', 'https://openalex.org/W1490482062'], 'abstract_inverted_index': {'The': [0, 141], 'main': [1], 'topics': [2], 'of': [3, 51, 63, 76, 94, 107, 120, 156, 172, 182], 'this': [4, 54, 166], 'technical': [5], 'report': [6, 167], 'are': [7, 29, 146], 'quaternions,': [8, 173, 176], 'their': [9], 'mathematical': [10], 'properties,': [11], 'and': [12, 25, 69, 148, 163, 177], 'how': [13], 'they': [14], 'can': [15], 'be': [16, 125], 'used': [17], 'to': [18], 'rotate': [19], 'objects.': [20], 'We': [21, 41], 'introduce': [22], 'quaternion': [23], 'mathematics': [24], 'discuss': [26], 'why': [27], 'quaternions': [28], 'a': [30, 92, 105, 133, 153, 169], 'better': [31], 'choice': [32], 'for': [33, 47, 60, 97, 136, 180], 'implementing': [34], 'rotation': [35, 174], 'than': [36], 'the': [37, 61, 64, 77, 118, 137, 157], 'well-known': [38], 'matrix': [39], 'implementations.': [40], 'then': [42], 'treat': [43], 'di': [44, 78, 108, 121, 138, 142], 'erent': [45, 79, 143], 'methods': [46, 67, 81, 145, 161], 'interpolation': [48, 66, 80, 86, 100, 144, 178], 'between': [49], 'series': [50, 181], 'rotations.': [52, 183], 'During': [53], 'treatment': [55, 75, 171], 'we': [56, 82, 131, 151], 'give': [57], 'complete': [58], 'proofs': [59], 'correctness': [62], 'important': [65], 'Slerp': [68], 'Squad': [70], '.': [71], 'Inspired': [72], 'by': [73], 'our': [74, 84], 'develop': [83], 'own': [85], 'method': [87], 'called': [88], 'Spring': [89], 'based': [90], 'on': [91], 'set': [93, 106, 119], 'objective': [95], 'constraints': [96], 'an': [98, 129], 'optimal': [99], 'curve.': [101], 'This': [102], 'results': [103], 'in': [104], 'erential': [109, 122, 139], 'equations,': [110], 'whose': [111], 'analytical': [112], 'solution': [113, 135], 'meets': [114], 'these': [115], 'constraints.': [116], 'Unfortunately,': [117], 'equations': [123], 'cannot': [124], 'solved': [126], 'analytically.': [127], 'As': [128], 'alternative': [130], 'propose': [132], 'numerical': [134], 'equations.': [140], 'visualized': [147], 'commented.': [149], 'Finally': [150], 'provide': [152], 'thorough': [154], 'comparison': [155], 'two': [158], 'most': [159], 'convincing': [160], '(Spring': [162], 'Squad).': [164], 'Thereby,': [165], 'provides': [168], 'comprehensive': [170], 'with': [175], 'curves': [179]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W76980395', 'counts_by_year': [{'year': 2024, 'cited_by_count': 9}, {'year': 2023, 'cited_by_count': 13}, {'year': 2022, 'cited_by_count': 11}, {'year': 2021, 'cited_by_count': 27}, {'year': 2020, 'cited_by_count': 20}, {'year': 2019, 'cited_by_count': 19}, {'year': 2018, 'cited_by_count': 16}, {'year': 2017, 'cited_by_count': 17}, {'year': 2016, 'cited_by_count': 20}, {'year': 2015, 'cited_by_count': 20}, {'year': 2014, 'cited_by_count': 20}, {'year': 2013, 'cited_by_count': 13}, {'year': 2012, 'cited_by_count': 8}], 'updated_date': '2025-01-05T08:44:14.423729', 'created_date': '2016-06-24'}