An Approach to the Decomposition of Solids with Voids via Morse Theory

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dc.contributor.authorPareja-Corcho, Juanen_US
dc.contributor.authorMontoya-Zapata, Diegoen_US
dc.contributor.authorMoreno, Aitoren_US
dc.contributor.authorCadavid, Carlosen_US
dc.contributor.authorPosada, Jorgeen_US
dc.contributor.authorArenas-Tobon, Ketzareen_US
dc.contributor.authorRuiz-Salguero, Oscaren_US
dc.contributor.editorBanterle, Francescoen_US
dc.contributor.editorCaggianese, Giuseppeen_US
dc.contributor.editorCapece, Nicolaen_US
dc.contributor.editorErra, Ugoen_US
dc.contributor.editorLupinetti, Katiaen_US
dc.contributor.editorManfredi, Gildaen_US
dc.date.accessioned2023-11-12T15:37:41Z
dc.date.available2023-11-12T15:37:41Z
dc.date.issued2023
dc.description.abstractThe decomposition of solids is a problem of interest in areas of engineering such as feature recognition or manufacturing planning. The problem can be stated as finding a set of smaller and simpler pieces that glued together amount to the initial solid. This decomposition can be guided by geometrical or topological criteria and be applied to either surfaces or solids (embedded manifolds). Most topological decompositions rely on Morse theory to identify changes in the topology of a manifold. A Morse function f is defined on the manifold and the manifold's topology is studied by studying the behaviour of the critical points of f . A popular structure used to encode this behaviour is the Reeb graph. Reeb graph-based decompositions have proven to work well for surfaces and for solids without inner voids, but fail to consider solids with inner voids. In this work we present a methodology based on the handle-decomposition of a manifold that can encode changes in the topology of solids both with and without inner voids. Our methodology uses the Boundary Representation of the solid and a shape similarity criteria to identify changes in the topology of both the outer and inner boundary(ies) of the solid. Our methodology is defined for Morse functions that produce parallel planar level sets and we do not consider the case of annidated solids (i.e. solids within other solids). We present an algorithm to implement our methodology and execute experiments on several datasets. Future work includes the testing of the methodology with functions different to the height function and the speed up of the algorithm's data structure.en_US
dc.description.sectionheadersRepresentation of 3D shapes
dc.description.seriesinformationSmart Tools and Applications in Graphics - Eurographics Italian Chapter Conference
dc.identifier.doi10.2312/stag.20231302
dc.identifier.isbn978-3-03868-235-6
dc.identifier.issn2617-4855
dc.identifier.pages135-144
dc.identifier.pages10 pages
dc.identifier.urihttps://doi.org/10.2312/stag.20231302
dc.identifier.urihttps://diglib.eg.org:443/handle/10.2312/stag20231302
dc.publisherThe Eurographics Associationen_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectCCS Concepts: Computing methodologies -> Shape analysis; Volumetric models; Mesh models
dc.subjectComputing methodologies
dc.subjectShape analysis
dc.subjectVolumetric models
dc.subjectMesh models
dc.titleAn Approach to the Decomposition of Solids with Voids via Morse Theoryen_US
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