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On the support of recursive subdivision

Ivrissimtzis, Ioannis; Sabin, Malcolm; Dodgson, Neil


Malcolm Sabin

Neil Dodgson


We study the support of subdivision schemes: that is, the region of the subdivision surface, which is affected by the displacement of a single control point. Our main results cover the regular case, where the mesh induces a regular Euclidean tessellation of the local parameter space. If n is the ratio of similarity between the tessellations at steps k and k-1 of the refinement, we show that n determines the extent of this region and largely determines whether its boundary is polygonal or fractal. In particular, if n = 2 the support is a convex polygon whose vertices can easily be determined. In other cases, whether the boundary of the support is fractal or not depends on whether there are sufficient points with non-zero coefficients in the edges of the convex hull of the mask. If there are enough points on every such edge, the support is again a convex polygon. If some edges have enough points and others do not, the boundary can consist of a fractal assembly of an unbounded number of line segments.


Ivrissimtzis, I., Sabin, M., & Dodgson, N. (2004). On the support of recursive subdivision. ACM Transactions on Graphics, 23(4), 1043-1060.

Journal Article Type Article
Publication Date 2004-10
Deposit Date Jan 23, 2009
Journal ACM Transactions on Graphics
Print ISSN 0730-0301
Publisher Association for Computing Machinery (ACM)
Peer Reviewed Peer Reviewed
Volume 23
Issue 4
Pages 1043-1060
Keywords Cantor set.