Mesh Parameterization Meets Intrinsic Triangulations

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dc.contributor.authorAkalin, Korayen_US
dc.contributor.authorFinnendahl, Ugoen_US
dc.contributor.authorSorkine-Hornung, Olgaen_US
dc.contributor.authorAlexa, Marcen_US
dc.contributor.editorHu, Ruizhenen_US
dc.contributor.editorLefebvre, Sylvainen_US
dc.date.accessioned2024-06-20T07:54:58Z
dc.date.available2024-06-20T07:54:58Z
dc.date.issued2024
dc.description.abstractA parameterization of a triangle mesh is a realization in the plane so that all triangles have positive signed area. Triangle mesh parameterizations are commonly computed by minimizing a distortion energy, measuring the distortions of the triangles as they are mapped into the parameter domain. It is assumed that the triangulation is fixed and the triangles are mapped affinely. We consider a more general setup and additionally optimize among the intrinsic triangulations of the piecewise linear input geometry. This means the distortion energy is computed for the same geometry, yet the space of possible parameterizations is enlarged. For minimizing the distortion energy, we suggest alternating between varying the parameter locations of the vertices and intrinsic flipping. We show that this process improves the mapping for different distortion energies at moderate additional cost. We also find intrinsic triangulations that are better starting points for the optimization of positions, offering a compromise between the full optimization approach and exploiting the additional freedom of intrinsic triangulations.en_US
dc.description.number5
dc.description.sectionheadersParametrization and Curves
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume43
dc.identifier.doi10.1111/cgf.15134
dc.identifier.issn1467-8659
dc.identifier.pages12 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.15134
dc.identifier.urihttps://diglib.eg.org/handle/10.1111/cgf15134
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectCCS Concepts: Computing methodologies → Computer graphics; Mesh models; Mesh geometry models
dc.subjectComputing methodologies → Computer graphics
dc.subjectMesh models
dc.subjectMesh geometry models
dc.titleMesh Parameterization Meets Intrinsic Triangulationsen_US
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