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COMPUTING
2004

Robust Spherical Parameterization of Triangular Meshes

8 years 10 months ago
Robust Spherical Parameterization of Triangular Meshes
Parameterization of 3D mesh data is important for many graphics and mesh processing applications, in particular for texture mapping, remeshing and morphing. Closed, manifold, genus-0 meshes are topologically equivalent to a sphere, hence this is the natural parameter domain for them. Parameterizing a 3D triangle mesh onto the 3D sphere means assigning a 3D position on the unit sphere to each of the mesh vertices, such that the spherical triangles induced by the mesh connectivity do not overlap. This is called a spherical triangulation. In this paper we formulate a set of necessary and sufficient conditions on the spherical angles of the spherical triangles for them to form a spherical triangulation. We formulate and solve an optimization procedure to produce spherical triangulations which reflect the geometric properties of a given 3D mesh in various ways. AMS Subject Classifications: 68U05, 68U07, 65D18, 51N05.
Alla Sheffer, Craig Gotsman, Nira Dyn
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2004
Where COMPUTING
Authors Alla Sheffer, Craig Gotsman, Nira Dyn
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