Evolutions of Polygons in the Study of Subdivision Surfaces

Ivrissimtzis, Ioannis; Seidel, Hans-Peter

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.