Immersion and Embedding of Self-Crossing Loops

dc.contributor.authorMukherjee, Uddipanen_US
dc.contributor.authorM.Gopi,en_US
dc.contributor.authorRossignac, Jareken_US
dc.contributor.editorTracy Hammond and Andy Nealenen_US
dc.date.accessioned2013-10-31T10:24:20Z
dc.date.available2013-10-31T10:24:20Z
dc.date.issued2011en_US
dc.description.abstractThe process of generating a 3D model from a set of 2D planar curves is complex due to the existence of many solutions. In this paper we consider a self-intersecting planar closed loop curve, and determine the 3D layered surface P with the curve as its boundary. Specifically, we are interested in a particular class of closed loop curvesin 2D with multiple self-crossings which bound a surface homeomorphic to a topological disk. Given such a selfcrossingclosed loop curve in 2D, we find the deformation of the topological disk whose boundary is the given loop. Further, we find the surface in 3D whose orthographic projection is the computed deformed disk, thus assigning 3D coordinates for the points in the self-crossing loop and its interior space.We also make theoretical observationsas to when, given a topological disk in 2D, the computed 3D surface will self-intersect.en_US
dc.description.seriesinformationEurographics Workshop on Sketch-Based Interfaces and Modelingen_US
dc.identifier.isbn978-1-4503-0906-6en_US
dc.identifier.issn1812-3503en_US
dc.identifier.urihttps://doi.org/10.2312/SBM/SBM11/031-038en_US
dc.publisherThe Eurographics Associationen_US
dc.titleImmersion and Embedding of Self-Crossing Loopsen_US
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