Evolutions of Polygons in the Study of Subdivision Surfaces
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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.
- Evolutions of Polygons in the Study of Subdivision Surfaces
Volume 72, Issue 1-2 , pp 93-103
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- evolving polygons
- circulant matrices
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