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Robust Spherical Parameterization of Triangular Meshes

In: Geometric Modelling

Author

Listed:
  • 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)

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.

Suggested Citation

  • A. Sheffer & C. Gotsman & N. Dyn, 2004. "Robust Spherical Parameterization of Triangular Meshes," Springer Books, in: Stefanie Hahmann & Guido Brunnett & Gerald Farin & Ron Goldman (ed.), Geometric Modelling, pages 185-193, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-0587-0_15
    DOI: 10.1007/978-3-7091-0587-0_15
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