Robust Spherical Parameterization of Triangular Meshes |
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Authors: | A Sheffer C Gotsman N Dyn |
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Affiliation: | (1) Department of Computer Science, University of British Columbia, 201-2366, Main Mall Vancouver, V6T 1Z4, Canada;(2) Department of Computer Science Technion-Israel Institute of Technology, Center for Graphics and Geometric Computing, Haifa, 32000, Israel;(3) School of Mathematical Sciences, Faculty of Exact Sciences Tel Aviv University, 39040, Tel Aviv, 69978, Israel |
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Abstract: | 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. |
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Keywords: | 68U05 68U07 65D18 51N05 |
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