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Evolutions of Polygons in the Study of Subdivision Surfaces

Ivrissimtzis, Ioannis; Seidel, Hans-Peter


Hans-Peter Seidel


We employ the theory of evolving n-gons in the study of subdivision surfaces. We show that for subdivision schemes with small stencils the eige¬nanalysis 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.


Ivrissimtzis, I., & Seidel, H. (2004). Evolutions of Polygons in the Study of Subdivision Surfaces. Computing, 72(1-2), 93-103.

Journal Article Type Article
Publication Date 2004-04
Deposit Date Feb 28, 2008
Journal Computing
Print ISSN 0010-485X
Electronic ISSN 1436-5057
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 72
Issue 1-2
Pages 93-103
Keywords Subdivision, Evolving polygons, Circulant matrices.