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We show that from the 3D Delaunay triangulation, it is possible to derive a distance measure among regions lying in adjacent slices. Such distance is used to define a positive integer parameter, called \u03b2, responsible for establishing the connections. Varying \u03b2 thus allows the construction of different models from a given set of cross-sectional regions: small values of \u03b2 causes closer regions to be connected into a single component, and as \u03b2 increases, more distant regions are connected together. The algorithm, named \u03b2-connection, is described, and examples are provided that illustrate its applicability in solid modeling and model reconstruction from real data. The underlying reconstruction method is effective, which jointly with the \u03b2-connection correspondence strategy, improve the usability of volumetric reconstruction techniques considerably.<\/jats:p>","DOI":"10.1145\/1095878.1095879","type":"journal-article","created":{"date-parts":[[2005,11,7]],"date-time":"2005-11-07T16:00:45Z","timestamp":1131379245000},"page":"1239-1258","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":10,"title":["Beta-connection"],"prefix":"10.1145","volume":"24","author":[{"given":"Luis Gustavo","family":"Nonato","sequence":"first","affiliation":[{"name":"Universidade de S\u00e3o Paulo, Trabalhador S\u00e3o-Carlense, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alex Jesus","family":"Cuadros-Vargas","sequence":"additional","affiliation":[{"name":"Universidade de S\u00e3o Paulo, Trabalhador S\u00e3o-Carlense, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rosane","family":"Minghim","sequence":"additional","affiliation":[{"name":"Universidade de S\u00e3o Paulo, Trabalhador S\u00e3o-Carlense, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maria Cristina F.","family":"De Oliveira","sequence":"additional","affiliation":[{"name":"Universidade de S\u00e3o Paulo, Trabalhador S\u00e3o-Carlense, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2005,10]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/116873.116880"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1006\/gmip.1996.0044"},{"key":"e_1_2_1_3_1","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/S0045-7825(99)00030-4","article-title":"Tetrahedral meshes from planar cross-sections","volume":"179","author":"Bajaj C.","year":"1999","unstructured":"Bajaj , C. , Coyle , E. , and Lin , K. 1999 . 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