A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
The simplest subdivision scheme for smoothing polyhedra
ACM Transactions on Graphics (TOG)
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Refinement operators for triangle meshes
Computer Aided Geometric Design
A generative classification of mesh refinement rules with lattice transformations
Computer Aided Geometric Design
Computer Aided Geometric Design
A family of subdivision schemes with cubic precision
Computer Aided Geometric Design
Full length article: Polynomial reproduction for univariate subdivision schemes of any arity
Journal of Approximation Theory
An heuristic analysis of the classification of bivariate subdivision schemes
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods
Computer Graphics Forum
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We study the support of subdivision schemes: that is, the region of the subdivision surface that is affected by the displacement of a single control point. Our main results cover the regular case, where the mesh induces a regular Euclidean tesselation of the local parameter space. If n is the ratio of similarity between the tesselations 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 (or n2 = 2 because we can always take double steps) 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.