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Evolutions of Polygons in the Study of Subdivision Surfaces

In: Geometric Modelling

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  • I. P. Ivrissimtzis

    (MPI — Informatik)

  • H.-P. Seidel

    (MPI — Informatik)

Abstract

We employ the theory of evolving n-gons in the study of subdivision surfaces. We show that for subdivision schemes with small stencils the eigenanalysis of an evolving polygon, corresponding either to a face or to the 1-ring neighborhood of a vertex, complements in a geometrically intuitive way the eigenanalysis of the subdivision matrix. In the applications we study the types of singularities that may appear on a subdivision surface, and we find properties of the subdivision surface that depend on the initial control polyhedron only.

Suggested Citation

  • I. P. Ivrissimtzis & H.-P. Seidel, 2004. "Evolutions of Polygons in the Study of Subdivision Surfaces," Springer Books, in: Stefanie Hahmann & Guido Brunnett & Gerald Farin & Ron Goldman (ed.), Geometric Modelling, pages 93-103, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-0587-0_8
    DOI: 10.1007/978-3-7091-0587-0_8
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