Evolutions of polygons in the study of subdivision surfaces

Authors:
I. P. Ivrissimtzis;H.-P. Seidel
Affiliations:
MPI - Informatik, Stuhlsatzenhausweg, Saarbrücken, Germany;MPI - Informatik, Stuhlsatzenhausweg, Saarbrücken, Germany
Venue:
Computing - Geometric modelling dagstuhl 2002
Year:
2004

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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.