Planar Parameterization for Closed Manifolds Genus-1 Meshes

dc.contributor.authorSteiner, D.en_US
dc.contributor.authorFischer, A.en_US
dc.contributor.editorGershon Elber and Nicholas Patrikalakis and Pere Bruneten_US
dc.date.accessioned2016-02-17T18:02:45Z
dc.date.available2016-02-17T18:02:45Z
dc.date.issued2004en_US
dc.description.abstractParameterization of 3D meshes is important for many graphics and CAD applications, in particular for texture mapping, re-meshing and morphing. Current parameterization methods for closed manifold genus-n meshes usually involve cutting the mesh according to the object generators, fixing the resulting boundary and then applying the 2D position for each of the mesh vertices on a plane, such that the flattened triangles are not too distorted and do not overlap. Unfortunately, fixing the boundary distorts the resulting parameterization, especially near the boundary. A special case is that of closed manifold genus-1 meshes that have two generators. They can therefore be flattened naturally to a plane without the use of a fixed boundary while still maintaining the continuity of the parameterization. Therefore, in treating genus-1 objects, this attribute must be exploited. This paper introduces a generalized method for planar parameterization of closed manifold genus-1 meshes. As in any planar parameterization with a fixed boundary, weights are assigned over the mesh edges. The type of weights defined depends on the type of mesh characteristics to be preserved. The paper proves that the method satisfies the non-overlapping requirement for any type of positive barycentric weights, including nonsymmetrical weights. Moreover, convergence is guaranteed according to the Gauss- Seidel method. The proposed method is simple to implement, fast and robust. The feasibility of the method will be demonstrated on several complex objects.en_US
dc.description.sectionheadersSurface Parametrization and Approximationen_US
dc.description.seriesinformationSolid Modelingen_US
dc.identifier.doi10.2312/sm.20041379en_US
dc.identifier.isbn3-905673-55-Xen_US
dc.identifier.issn1811-7783en_US
dc.identifier.pages83-91en_US
dc.identifier.urihttps://doi.org/10.2312/sm.20041379en_US
dc.publisherThe Eurographics Associationen_US
dc.subjectPlanar parameterizationen_US
dc.subjectGenusen_US
dc.subjectmeshesen_US
dc.subjectunfixed boundaryen_US
dc.titlePlanar Parameterization for Closed Manifolds Genus-1 Meshesen_US
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