ARAP Revisited Discretizing the Elastic Energy using Intrinsic Voronoi Cells

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dc.contributor.authorFinnendahl, Ugoen_US
dc.contributor.authorSchwartz, Matthiasen_US
dc.contributor.authorAlexa, Marcen_US
dc.contributor.editorHauser, Helwig and Alliez, Pierreen_US
dc.date.accessioned2023-10-06T11:58:56Z
dc.date.available2023-10-06T11:58:56Z
dc.date.issued2023
dc.description.abstractAs‐rigid‐as‐possible (ARAP) surface modelling is widely used for interactive deformation of triangle meshes. We show that ARAP can be interpreted as minimizing a discretization of an elastic energy based on non‐conforming elements defined over dual orthogonal cells of the mesh. Using the Voronoi cells rather than an orthogonal dual of the extrinsic mesh guarantees that the energy is non‐negative over each cell. We represent the intrinsic Delaunay edges extrinsically as polylines over the mesh, encoded in barycentric coordinates relative to the mesh vertices. This modification of the original ARAP energy, which we term , remedies problems stemming from non‐Delaunay edges in the original approach. Unlike the spokes‐and‐rims version of the ARAP approach it is less susceptible to the triangulation of the surface. We provide examples of deformations generated with iARAP and contrast them with other versions of ARAP. We also discuss the properties of the Laplace‐Beltrami operator implicitly introduced with the new discretization.en_US
dc.description.number6
dc.description.sectionheadersORIGINAL ARTICLES
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume42
dc.identifier.doi10.1111/cgf.14790
dc.identifier.issn1467-8659
dc.identifier.urihttps://doi.org/10.1111/cgf.14790
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf14790
dc.publisher© 2023 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd.en_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectmodelling
dc.subjectdeformations
dc.subjectpolygonal modelling
dc.titleARAP Revisited Discretizing the Elastic Energy using Intrinsic Voronoi Cellsen_US
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