Ivrissimtzis, I. and Sabin, M. and Dodgson, N. (2004) 'On the support of recursive subdivision.', ACM transactions on graphics., 23 (4). pp. 1043-1060.
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.
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|Publisher Web site:||http://dx.doi.org/10.1145/1027411.1027417|
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|Date of first online publication:||October 2004|
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