Evolutions of Polygons in the Study of Subdivision Surfaces

I. P. Ivrissimtzis () and H.-P. Seidel ()
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I. P. Ivrissimtzis: MPI — Informatik
H.-P. Seidel: MPI — Informatik

A chapter in Geometric Modelling, 2004, pp 93-103 from Springer

Abstract: 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.

Keywords: Subdivision; evolving polygons; circulant matrices; 68U05; 65D17 (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7091-0587-0_8

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DOI: 10.1007/978-3-7091-0587-0_8

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