Robust Spherical Parameterization of Triangular Meshes

A. Sheffer (), C. Gotsman () and N. Dyn ()
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A. Sheffer: University of British Columbia, Department of Computer Science
C. Gotsman: Technion-Israel Institute of Technology, Center for Graphics and Geometric Computing, Department of Computer Science
N. Dyn: Tel Aviv University, School of Mathematical Sciences

A chapter in Geometric Modelling, 2004, pp 185-193 from Springer

Abstract: 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.

Keywords: Parameterization; mesh processing; spherical parametrization; spherical embedding; 68U05; 68U07; 65D18; 51N05 (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-3-7091-0587-0_15

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