Level sets of weak-morse functions for triangular mesh slicing

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dc.citation.journalTitleMathematicseng
dc.contributor.authorMejia-Parra D.
dc.contributor.authorRuiz-Salguero O.
dc.contributor.authorCadavid C.
dc.contributor.authorMoreno A.
dc.contributor.authorPosada J.
dc.contributor.departmentUniversidad EAFIT. Departamento de Ingeniería Mecánicaspa
dc.contributor.researchgroupLaboratorio CAD/CAM/CAEspa
dc.date.accessioned2021-04-16T22:00:00Z
dc.date.available2021-04-16T22:00:00Z
dc.date.issued2020-01-01
dc.description.abstractIn the context of CAD CAM CAE (Computer-Aided Design, Manufacturing and Engineering) and Additive Manufacturing, the computation of level sets of closed 2-manifold triangular meshes (mesh slicing) is relevant for the generation of 3D printing patterns. Current slicing methods rely on the assumption that the function used to compute the level sets satisfies strong Morse conditions, rendering incorrect results when such a function is not a Morse one. To overcome this limitation, this manuscript presents an algorithm for the computation of mesh level sets under the presence of non-Morse degeneracies. To accomplish this, our method defines weak-Morse conditions, and presents a characterization of the possible types of degeneracies. This classification relies on the position of vertices, edges and faces in the neighborhood outside of the slicing plane. Finally, our algorithm produces oriented 1-manifold contours. Each contour orientation defines whether it belongs to a hole or to an external border. This definition is central for Additive Manufacturing purposes. We set up tests encompassing all known non-Morse degeneracies. Our algorithm successfully processes every generated case. Ongoing work addresses (a) a theoretical proof of completeness for our algorithm, (b) implementation of interval trees to improve the algorithm efficiency and, (c) integration into an Additive Manufacturing framework for industry applications. © 2020 by the authors.eng
dc.identifierhttps://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=12172
dc.identifier.doi10.3390/math8091624
dc.identifier.issn22277390
dc.identifier.otherWOS;000580802400001
dc.identifier.otherSCOPUS;2-s2.0-85091516817
dc.identifier.urihttp://hdl.handle.net/10784/29561
dc.languageeng
dc.publisherMDPI AG
dc.relation.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85091516817&doi=10.3390%2fmath8091624&partnerID=40&md5=4e3de7b8c0e21dc58daa9b99dfc108b9
dc.rightshttps://v2.sherpa.ac.uk/id/publication/issn/2227-7390
dc.sourceMathematics
dc.subject.keywordAdditive manufacturingeng
dc.subject.keywordLevel setseng
dc.subject.keywordMesh slicingeng
dc.subject.keywordMorse theoryeng
dc.titleLevel sets of weak-morse functions for triangular mesh slicingeng
dc.typeinfo:eu-repo/semantics/articleeng
dc.typearticleeng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localArtículospa

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