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Moreover assume that we have an embedded simplical complex <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathcal {A}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>A<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> without boundary, whose vertex set lies on the manifold, is sufficiently dense and such that all simplices in <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathcal {A}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>A<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> have sufficient quality. We prove that if, locally, interiors of the projection of the simplices onto the tangent space do not intersect, then <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathcal {A}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>A<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is a triangulation of the manifold, that is, they are homeomorphic.<\/jats:p>","DOI":"10.1007\/s00454-020-00233-9","type":"journal-article","created":{"date-parts":[[2020,8,10]],"date-time":"2020-08-10T19:05:06Z","timestamp":1597086306000},"page":"666-686","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Local Conditions for Triangulating Submanifolds of Euclidean Space"],"prefix":"10.1007","volume":"66","author":[{"given":"Jean-Daniel","family":"Boissonnat","sequence":"first","affiliation":[]},{"given":"Ramsay","family":"Dyer","sequence":"additional","affiliation":[]},{"given":"Arijit","family":"Ghosh","sequence":"additional","affiliation":[]},{"given":"Andre","family":"Lieutier","sequence":"additional","affiliation":[]},{"given":"Mathijs","family":"Wintraecken","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,8,10]]},"reference":[{"issue":"4","key":"233_CR1","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1007\/PL00009475","volume":"22","author":"N Amenta","year":"1999","unstructured":"Amenta, N., Bern, M.: Surface reconstruction by Voronoi filtering. 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