Compact, convex sets inRnand a new banach lattice. I.- Theory.

Margolis, Beatriz

doi:10.1080/01630569008816388

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A Class Of Shape Preserving Subdivision Schemes1

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“…Conjecture: Any of the subdivision methods (8) with m > 1 applied to initial compact sets, fF 0 j g generates as a limit a convex-valued multifunction, given by F 1 (t) = X j2Z coF 0 j B m (t ; j)…”

Section: A Class Of Shape Preserving Subdivision Schemesmentioning

confidence: 99%

Spline subdivision schemes for convex compact sets

Dyn

Farkhi

2000

Journal of Computational and Applied Mathematics

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N i r a D y n a n d E l z a F arkhi The application of spline subdivision schemes to data consisting of convex compact sets, with addition replaced by M i n k owski sums of sets, is investigated. These methods generate in the limit set-valued functions, which can be expressed explicitly in terms of linear combinations of integer shifts of B-splines with the initial data as coe cients. The subdivision techniques are used to conclude that these limit set-valued spline functions have shape preserving properties similar to those of the usual spline functions. This extension of subdivision methods from the scalar setting to the set-valued case has application in the approximate reconstruction of 3-D bodies from nite collections of their parallel cross-sections.

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Section: A Class Of Shape Preserving Subdivision Schemesmentioning

confidence: 99%