Synthesis of Reeb Graph and Morse Operators from Level Sets of a Boundary Representation

Simple item page
dc.contributor.authorPareja-Corcho, Juanen_US
dc.contributor.authorMontoya-Zapata, Diegoen_US
dc.contributor.authorCadavid, Carlosen_US
dc.contributor.authorMoreno, Aitoren_US
dc.contributor.authorPosada, Jorgeen_US
dc.contributor.authorArenas-Tobon, Ketzareen_US
dc.contributor.authorRuiz-Salguero, Oscaren_US
dc.contributor.editorPosada, Jorgeen_US
dc.contributor.editorSerrano, Anaen_US
dc.date.accessioned2022-06-22T10:03:45Z
dc.date.available2022-06-22T10:03:45Z
dc.date.issued2022
dc.description.abstractIn the context of Industrie 4.0, it is necessary for several applications, to encode characteristics of a Boundary Representation of a manifold M in an economical manner. Two related characterizations of closed B-Reps (and the solid they represent) are (1) medial axis and (2) Reeb Graph. The medial axis of a solid region is a non-manifold mixture of 1-simplices and 2- simplices and it is expensive to extract. Because of this reason, this manuscript concentrates in the work-flow necessary to extract the Reeb Graph of the B-Rep. The extraction relies on (a) tests of geometric similarities among slices of M and (b) characterization of the topological transitions in the slice sequence of M. The process roughly includes: (1) tilt of the B-Rep to obtain an unambiguous representation of the level sets ofM,(2) identification and classification of the topological transitions that arise between consecutive level sets, (3) sample of Reeb graph vertices inside the material regions defined by the level sets, (4) creation of Reeb graph edges based on the type of topological transition and the 2D similarity among material regions of consecutive levels. Although the Reeb Graph is a topological construct, geometrical processing is central in its synthesis and compliance with the Nyquist-Shannon sampling interval is crucial for its construction. Future work is needed on the extension of our methodology to account for manifolds with internal voids or nested solids.en_US
dc.description.sectionheadersCAD, Simulation, and Grasping
dc.description.seriesinformationSpanish Computer Graphics Conference (CEIG)
dc.identifier.doi10.2312/ceig.20221140
dc.identifier.isbn978-3-03868-186-1
dc.identifier.pages11-15
dc.identifier.pages5 pages
dc.identifier.urihttps://doi.org/10.2312/ceig.20221140
dc.identifier.urihttps://diglib.eg.org:443/handle/10.2312/ceig20221140
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 --> Computer graphics; Shape analysis; Volumetric models
dc.subjectComputing methodologies
dc.subjectComputer graphics
dc.subjectShape analysis
dc.subjectVolumetric models
dc.titleSynthesis of Reeb Graph and Morse Operators from Level Sets of a Boundary Representationen_US
Files
Original bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
011-015.pdf
Size:
3.98 MB
Format:
Adobe Portable Document Format
Download
Collections
CEIG2022