{"id":"https://openalex.org/W2826399","doi":null,"title":"Constant Affine Velocity Predicts the 1/3 Power Law of Drawing and Planar Motion Perception","display_name":"Constant Affine Velocity Predicts the 1/3 Power Law of Drawing and Planar Motion Perception","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W2826399","mag":"2826399"},"language":"en","primary_location":{"id":"mag:2826399","doi":null,"is_oa":false,"landing_page_url":"http://www.hpl.hp.com/techreports/95/HPL-95-67.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5054643754","display_name":"Frank Earl Pollick","orcid":"https://orcid.org/0000-0002-7212-4622","observed_orcids":["https://orcid.org/0000-0002-7212-4622"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Frank Pollick","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-7212-4622","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5025218580","display_name":"Guillermo Sapiro","orcid":"https://orcid.org/0000-0001-9190-6964","observed_orcids":["https://orcid.org/0000-0001-9190-6964"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guillermo Sapiro","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-9190-6964","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1899,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.44317447,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10982","display_name":"Motor Control and Adaptation","score":0.9320999979972839,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10982","display_name":"Motor Control and Adaptation","score":0.9320999979972839,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10427","display_name":"Visual perception and processing mechanisms","score":0.06270000338554382,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10914","display_name":"Tactile and Sensory Interactions","score":0.0032999999821186066,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/affine-invariance","display_name":"affine invariance","score":0.8259999752044678},{"id":"https://openalex.org/keywords/freehand-drawing","display_name":"freehand drawing","score":0.7160000205039978},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"affine transformation","score":0.7609999775886536},{"id":"https://openalex.org/keywords/arc-length","display_name":"arc length","score":0.39800000190734863},{"id":"https://openalex.org/keywords/motor-control","display_name":"motor control","score":0.40700000524520874}],"concepts":[{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.8485403060913086},{"id":"https://openalex.org/C202411454","wikidata":"https://www.wikidata.org/wiki/Q4688941","display_name":"Affine geometry of curves","level":4,"score":0.8288998603820801},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6287742853164673},{"id":"https://openalex.org/C18516315","wikidata":"https://www.wikidata.org/wiki/Q4688950","display_name":"Affine shape adaptation","level":4,"score":0.5857420563697815},{"id":"https://openalex.org/C207221997","wikidata":"https://www.wikidata.org/wiki/Q938614","display_name":"Affine combination","level":3,"score":0.5841694474220276},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5569747686386108},{"id":"https://openalex.org/C95565831","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine coordinate system","level":4,"score":0.5293189883232117},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5285519361495972},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.5214523673057556},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5185554623603821},{"id":"https://openalex.org/C6408098","wikidata":"https://www.wikidata.org/wiki/Q17021115","display_name":"Harris affine region detector","level":5,"score":0.4998645782470703},{"id":"https://openalex.org/C154610627","wikidata":"https://www.wikidata.org/wiki/Q382491","display_name":"Affine plane (incidence geometry)","level":3,"score":0.4740923345088959},{"id":"https://openalex.org/C112128483","wikidata":"https://www.wikidata.org/wiki/Q382504","display_name":"Affine hull","level":4,"score":0.4514339566230774},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.45138034224510193},{"id":"https://openalex.org/C87040749","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Power law","level":2,"score":0.44471973180770874},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.43778783082962036},{"id":"https://openalex.org/C62623296","wikidata":"https://www.wikidata.org/wiki/Q686291","display_name":"Affine group","level":3,"score":0.4190611243247986},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40125536918640137},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.3071334958076477},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2899708151817322},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1953580379486084},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.13916540145874023},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12133046984672546},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.05773663520812988},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.052937448024749756},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C43809302","wikidata":"https://www.wikidata.org/wiki/Q1060874","display_name":"Plane curve","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2826399","doi":null,"is_oa":false,"landing_page_url":"http://www.hpl.hp.com/techreports/95/HPL-95-67.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4073262842","display_name":"STRUCTURE AND REGULATION OF A PROTEIN KINASE/PHOSPHATASE","funder_award_id":"R01GM033927","funder_id":"https://openalex.org/F4320337354","funder_display_name":"National Institute of General Medical Sciences"}],"funders":[{"id":"https://openalex.org/F4320337354","display_name":"National Institute of General Medical Sciences","ror":"https://ror.org/04q48ey07"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W1587069887","https://openalex.org/W2105763874"],"related_works":["https://openalex.org/W2564471646","https://openalex.org/W2067193840","https://openalex.org/W2320004782","https://openalex.org/W2053809049","https://openalex.org/W3092181564","https://openalex.org/W2790707682","https://openalex.org/W2263734429","https://openalex.org/W2008886640","https://openalex.org/W4409107201","https://openalex.org/W2004831791"],"abstract_inverted_index":{"AbstractNumerous":[0],"studies":[1,101],"have":[2],"shown":[3],"that":[4,50,73,93,120,142],"the":[5,20,28,42,55,60,74,94,100,152,157],"power":[6,96],"of":[7,16,24,53,77,102,122,154,161],"1/3":[8,44,95],"is":[9,33,65,85],"important":[10],"in":[11,19,99],"relating":[12],"Euclidean":[13,56],"velocity":[14,30,57,84,118],"toradius":[15],"curvature":[17,32],"(R)":[18],"production":[21,158],"and":[22,31,35,104,159],"perception":[23,160],"planar":[25,105,162],"movement.":[26],"Although":[27],"relationbetween":[29],"clear":[34],"very":[36],"intuitive,":[37],"no":[38],"valid":[39],"explanation":[40],"for":[41,151],"specific":[43],"valuewas":[45],"found":[46],"yet.":[47],"We":[48],"show":[49],"if":[51],"instead":[52],"computing":[54],"we":[58,71,131],"compute":[59],"affine":[61,68,82,117,124,147,155],"one,":[62],"avelocity":[63],"which":[64],"invariant":[66,83],"to":[67,135],"transformations,":[69],"then":[70],"obtain":[72],"unique":[75],"function":[76],"R":[78,87],"whichwill":[79],"give":[80],"an":[81,133],"precisely":[86],"1/":[88],"3":[89],"\u2022":[90],"This":[91],"means":[92],"law,":[97],"experimentallyfound":[98],"hand-drawing":[103],"motion":[106,109],"perception,":[107],"implies":[108,119],"at":[110,115,145],"constant":[111,116,146],"affinevelocity.":[112],"Since":[113],"drawing":[114],"curves":[121],"equal":[123,129],"length":[125],"will":[126],"be":[127],"drawnin":[128],"time,":[130],"performed":[132,144],"experiment":[134],"further":[136],"support":[137],"this":[138],"result.":[139],"Results":[140],"showed":[141],"drawingwas":[143],"velocity.":[148],"Possible":[149],"reasons":[150],"appearance":[153],"transformationsin":[156],"movement":[163],"are":[164],"discussed.":[165]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2016-06-24T00:00:00"}
