Spline subdivision schemes for convex compact sets

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:119

Article

Dyn, N ; Farkhi, E

关键词: convex sets;    support functions;    Minkowski addition;    set-valued functions;    spline subdivision;    shape preservation;    approximation;   

DOI  :  10.1016/S0377-0427(00)00375-7

来源: Elsevier

【 摘 要 】

The application of spline subdivision schemes to data consisting of convex compact sets, with addition replaced by Minkowski 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 coefficients. 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 finite collections of their parallel cross-sections. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

【 授权许可】

Free