Topological Initialization of Injective Integer Grid Maps

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dc.contributor.authorLivesu, Marcoen_US
dc.contributor.editorCabiddu, Danielaen_US
dc.contributor.editorSchneider, Teseoen_US
dc.contributor.editorAllegra, Darioen_US
dc.contributor.editorCatalano, Chiara Evaen_US
dc.contributor.editorCherchi, Gianmarcoen_US
dc.contributor.editorScateni, Riccardoen_US
dc.date.accessioned2022-11-08T11:44:42Z
dc.date.available2022-11-08T11:44:42Z
dc.date.issued2022
dc.description.abstractInteger Grid Maps (IGM) are a class of mappings characterized by integer isolines that align up to unit translations and rotations of multiples of 90 degrees. They are widely used in the context of remeshing, to lay a quadrilateral grid onto the mapped surface. Computing an IGM is notoriously a challenging task, because it requires to solve a numerical problem with mixed discrete and continuous variables which is known to be NP-Hard. As a result, state of the art methods rely on heuristics that may occasionally fail to produce a valid quadrilateral mesh. Existing pipelines incorporate a final sanitization step which attempts to fix such defects, but no guaranteees can be given in this regard. In this paper we propose a simple topological construction that allows to reduce the problem of computing an IGM to the one of mapping a topological disk to a convex domain. This is a much easier problem to deal with, because it does not endow integer translational and rotational constraints, permitting to obtain a parameterization that is guaranteed to incorporate all the correct integer transitions and to not contain degenerate or inverted elements. Despite provably correct, the so generated maps contain a considerable amount of geometric distortion and a poor quad connectivity, making this technique more suitable for a robust initialization rather than for the computation of an application-ready IGM. In the article we present the details of our construction, also analyzing its geometric and topological properties.en_US
dc.description.sectionheadersGeometry Processing
dc.description.seriesinformationSmart Tools and Applications in Graphics - Eurographics Italian Chapter Conference
dc.identifier.doi10.2312/stag.20221254
dc.identifier.isbn978-3-03868-191-5
dc.identifier.issn2617-4855
dc.identifier.pages41-48
dc.identifier.pages8 pages
dc.identifier.urihttps://doi.org/10.2312/stag.20221254
dc.identifier.urihttps://diglib.eg.org:443/handle/10.2312/stag20221254
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 -> Mesh models
dc.subjectComputing methodologies
dc.subjectMesh models
dc.titleTopological Initialization of Injective Integer Grid Mapsen_US
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