{"id":"https://openalex.org/W6907571892","doi":"https://doi.org/10.2312/spbg/spbg06/085-093","title":"Approximating Geodesics on Point Set Surfaces","display_name":"Approximating Geodesics on Point Set Surfaces","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W6907571892","doi":"https://doi.org/10.2312/spbg/spbg06/085-093"},"language":"en","primary_location":{"id":"pmh:oai:kops.uni-konstanz.de:123456789/22995","is_oa":false,"landing_page_url":"http://nbn-resolving.de/urn:nbn:de:bsz:352-229957","pdf_url":null,"source":{"id":"https://openalex.org/S4306401487","display_name":"KOPS (University of Konstanz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189712700","host_organization_name":"University of Konstanz","host_organization_lineage":["https://openalex.org/I189712700"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"BOTSCH,  Mario,  ed. and others. Point-based graphics 2006 [SPBG '06] : Eurographics/IEEE VGTC Symposium proceedings. Aire-la-Ville: Eurographics Association, 2006, pp. 85-94. ISBN 3-905673-32-0. Available under: doi: 10.2312/SPBG/SPBG06/085-093","raw_type":"doc-type:Text"},"type":"other","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.2312/spbg/spbg06/085-093","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Ruggeri, Mauro R.","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ruggeri, Mauro R.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Darom, Tal","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Darom, Tal","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Saupe, Dietmar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Saupe, Dietmar","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Kiryati, Nahum","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kiryati, Nahum","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":null,"topics":[],"keywords":[{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.7756999731063843},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.670799970626831},{"id":"https://openalex.org/keywords/piecewise-linear-manifold","display_name":"Piecewise linear manifold","score":0.5690000057220459},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5335000157356262},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.44119998812675476},{"id":"https://openalex.org/keywords/real-line","display_name":"Real line","score":0.4291999936103821},{"id":"https://openalex.org/keywords/line-segment","display_name":"Line segment","score":0.36160001158714294}],"concepts":[{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.7756999731063843},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7702999711036682},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.670799970626831},{"id":"https://openalex.org/C184175843","wikidata":"https://www.wikidata.org/wiki/Q7191425","display_name":"Piecewise linear manifold","level":3,"score":0.5690000057220459},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5335000157356262},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.44119998812675476},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.4291999936103821},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3962000012397766},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.36160001158714294},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3504999876022339},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.3499000072479248},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.32499998807907104},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.31949999928474426},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.3163999915122986},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.30250000953674316},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.2946999967098236},{"id":"https://openalex.org/C5134670","wikidata":"https://www.wikidata.org/wiki/Q1626444","display_name":"Cut","level":4,"score":0.2937999963760376},{"id":"https://openalex.org/C153008295","wikidata":"https://www.wikidata.org/wiki/Q6535093","display_name":"Level set (data structures)","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27309998869895935},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27149999141693115},{"id":"https://openalex.org/C160824197","wikidata":"https://www.wikidata.org/wiki/Q2071054","display_name":"Linear approximation","level":3,"score":0.26170000433921814}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:kops.uni-konstanz.de:123456789/22995","is_oa":false,"landing_page_url":"http://nbn-resolving.de/urn:nbn:de:bsz:352-229957","pdf_url":null,"source":{"id":"https://openalex.org/S4306401487","display_name":"KOPS (University of Konstanz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189712700","host_organization_name":"University of Konstanz","host_organization_lineage":["https://openalex.org/I189712700"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"BOTSCH,  Mario,  ed. and others. Point-based graphics 2006 [SPBG '06] : Eurographics/IEEE VGTC Symposium proceedings. Aire-la-Ville: Eurographics Association, 2006, pp. 85-94. ISBN 3-905673-32-0. Available under: doi: 10.2312/SPBG/SPBG06/085-093","raw_type":"doc-type:Text"},{"id":"doi:10.2312/spbg/spbg06/085-093","is_oa":true,"landing_page_url":"https://doi.org/10.2312/spbg/spbg06/085-093","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/spbg/spbg06/085-093","is_oa":true,"landing_page_url":"https://doi.org/10.2312/spbg/spbg06/085-093","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,64,71,82,96],"technique":[3],"for":[4,21,34,43,101,136,145],"computing":[5],"piecewise":[6,22,39,67],"linear":[7,23,40,68],"approximations":[8],"of":[9,37,70,106,116],"geodesics":[10,125],"on":[11,122],"point":[12,88],"set":[13],"surfaces":[14,123],"by":[15,75,119],"minimizing":[16],"an":[17],"energy":[18],"function":[19,26],"defined":[20],"path.":[24],"The":[25,104],"considers":[27],"path":[28,41],"length,":[29],"closeness":[30],"to":[31,54,60,81,114,154],"the":[32,35,38,44,87,91],"surface":[33,156],"nodes":[36],"and":[42,56,112,134],"intermediate":[45],"line":[46],"segments.":[47],"Our":[48,130],"method":[49,108,131],"is":[50,73,79,132],"robust":[51],"with":[52],"respect":[53],"noise":[55],"outliers.":[57],"In":[58],"order":[59],"avoid":[61],"local":[62],"minima,":[63],"good":[65],"initial":[66],"approximation":[69],"geodesic":[72],"provided":[74],"Dijkstra\u0092s":[76],"algorithm":[77],"that":[78],"applied":[80,153],"proximity":[83,92],"graph":[84,93,99],"constructed":[85],"over":[86],"set.":[89],"As":[90],"we":[94],"use":[95],"sphere-of-influence":[97],"weighted":[98],"extended":[100],"surfel":[102],"sets.":[103],"convergence":[105],"our":[107],"has":[109,141],"been":[110,142],"studied":[111],"compared":[113],"results":[115],"other":[117,155],"methods":[118],"running":[120],"experiments":[121],"whose":[124],"can":[126,150],"be":[127,152],"computed":[128],"analytically.":[129],"presented":[133],"optimized":[135],"surfel-based":[137],"representations":[138],"but":[139],"it":[140,149],"implemented":[143],"also":[144,151],"MLS":[146],"surfaces.":[147],"Moreover,":[148],"representations,":[157],"e.g.,":[158],"triangle":[159],"meshes,":[160],"radial-basis":[161],"functions,":[162],"etc.":[163]},"counts_by_year":[],"updated_date":"2026-03-25T23:56:10.502304","created_date":"2025-10-10T00:00:00"}