Evolutions of Polygons in the Study of Subdivision Surfaces

Ivrissimtzis, Ioannis; Seidel, Hans-Peter

doi:10.1007/s00607-003-0049-8

Evolutions of Polygons in the Study of Subdivision Surfaces

Ivrissimtzis, Ioannis; Seidel, Hans-Peter

Authors

Dr Ioannis Ivrissimtzis ioannis.ivrissimtzis@durham.ac.uk
Associate Professor

Hans-Peter Seidel

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 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.

Citation

Ivrissimtzis, I., & Seidel, H. (2004). Evolutions of Polygons in the Study of Subdivision Surfaces. Computing, 72(1-2), 93-103. https://doi.org/10.1007/s00607-003-0049-8

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
DOI	https://doi.org/10.1007/s00607-003-0049-8
Keywords	Subdivision, Evolving polygons, Circulant matrices.