{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,6]],"date-time":"2026-08-06T19:43:03Z","timestamp":1786045383810,"version":"3.56.0"},"reference-count":31,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2010,8,25]],"date-time":"2010-08-25T00:00:00Z","timestamp":1282694400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Computer Graphics Forum"],"published-print":{"date-parts":[[2011,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p> <jats:italic>The Hermite radial basis functions (HRBF) implicits reconstruct an implicit function which interpolates or approximates scattered multivariate Hermite data (i.e. unstructured points and their corresponding normals). Experiments suggest that HRBF implicits allow the reconstruction of surfaces rich in details and behave better than previous related methods under coarse and\/or non\u2010uniform samplings, even in the presence of close sheets. HRBF implicits theory unifies a recently introduced class of surface reconstruction methods based on radial basis functions (RBF), which incorporate normals directly in their problem formulation. Such class has the advantage of not depending on manufactured offset\u2010points to ensure existence of a non\u2010trivial implicit surface RBF interpolant. In fact, we show that HRBF implicits constitute a particular case of Hermite\u2013Birkhoff interpolation with radial basis functions, whose main results we present here. This framework not only allows us to show connections between the present method and others but also enable us to enhance the flexibility of our method by ensuring well\u2010posedness of an interesting combined interpolation\/regularization approach.<\/jats:italic> <\/jats:p>","DOI":"10.1111\/j.1467-8659.2010.01785.x","type":"journal-article","created":{"date-parts":[[2010,8,29]],"date-time":"2010-08-29T20:45:01Z","timestamp":1283114701000},"page":"27-42","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":81,"title":["Hermite Radial Basis Functions Implicits"],"prefix":"10.1111","volume":"30","author":[{"given":"I.","family":"Mac\u00eado","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J. P.","family":"Gois","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L.","family":"Velho","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2010,8,25]]},"reference":[{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1145\/1516522.1516531"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2003.1175093"},{"key":"e_1_2_7_4_2","unstructured":"ATLAS:Automatically tuned linear algebra software June 2010.https:\/\/2.zoppoz.workers.dev:443\/http\/math\u2010atlas.sourceforge.net\/."},{"key":"e_1_2_7_5_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1018932227617"},{"key":"e_1_2_7_6_2","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599361771"},{"key":"e_1_2_7_7_2","volume-title":"Functional Analysis","author":"Bachman G.","year":"2000"},{"key":"e_1_2_7_8_2","volume-title":"Proceedings of the International Conference on Computer Graphics and Interactive Techniques","author":"Carr J. C.","year":"2001"},{"key":"e_1_2_7_9_2","doi-asserted-by":"publisher","DOI":"10.1145\/1391989.1391995"},{"key":"e_1_2_7_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-007-9008-7"},{"key":"e_1_2_7_11_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2008.60"},{"key":"e_1_2_7_12_2","first-page":"85","volume-title":"Splines Minimizing Rotation\u2010Invariant Semi\u2010Norms in Sobolev Spaces, vol. 571 of\u2002Lecture Notes in Mathematics","author":"Duchon J.","year":"1977"},{"key":"e_1_2_7_13_2","first-page":"131","volume-title":"Surface Fitting and Multiresolution Methods","author":"Fasshauer G.","year":"1997"},{"key":"e_1_2_7_14_2","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073227"},{"key":"e_1_2_7_15_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2010.01663.x"},{"key":"e_1_2_7_16_2","doi-asserted-by":"publisher","DOI":"10.1145\/1275808.1276406"},{"key":"e_1_2_7_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2008.07.013"},{"key":"e_1_2_7_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00371-008-0297-x"},{"key":"e_1_2_7_19_2","doi-asserted-by":"publisher","DOI":"10.1364\/AO.47.002091"},{"key":"e_1_2_7_20_2","volume-title":"Proceedings of SMA'01","author":"Morse B. S.","year":"2001"},{"key":"e_1_2_7_21_2","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882293"},{"key":"e_1_2_7_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.gmod.2004.06.003"},{"key":"e_1_2_7_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11432-009-0032-x"},{"key":"e_1_2_7_24_2","unstructured":"POV\u2010Ray:Persistence of vision ray tracer June 2010.https:\/\/2.zoppoz.workers.dev:443\/http\/www.povray.org\/."},{"key":"e_1_2_7_25_2","first-page":"261","article-title":"Real\u2010time ray tracing of implicit surfaces on the gpu","volume":"99","author":"Singh J. M.","year":"2009","journal-title":"IEEE Transactions on Visualization and Computer Graphics"},{"key":"e_1_2_7_26_2","doi-asserted-by":"publisher","DOI":"10.1145\/1186562.1015816"},{"key":"e_1_2_7_27_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2006.149"},{"key":"e_1_2_7_28_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019105612985"},{"key":"e_1_2_7_29_2","doi-asserted-by":"publisher","DOI":"10.1145\/571647.571650"},{"key":"e_1_2_7_30_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02123482"},{"key":"e_1_2_7_31_2","volume-title":"Scattered Data Approximation","author":"Wendland H.","year":"2005"},{"key":"e_1_2_7_32_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2006.00983.x"}],"container-title":["Computer Graphics Forum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.1467-8659.2010.01785.x","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/j.1467-8659.2010.01785.x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,16]],"date-time":"2023-10-16T04:41:07Z","timestamp":1697431267000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/10.1111\/j.1467-8659.2010.01785.x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,8,25]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,3]]}},"alternative-id":["10.1111\/j.1467-8659.2010.01785.x"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1111\/j.1467-8659.2010.01785.x","archive":["Portico"],"relation":{},"ISSN":["0167-7055","1467-8659"],"issn-type":[{"value":"0167-7055","type":"print"},{"value":"1467-8659","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,8,25]]},"assertion":[{"value":"2010-08-25","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}