Multi-box splines

Timothy Goodman

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    We construct local generators, comprising r functions, for refinable spaces of bivariate Cn-1 spline functions of degree n on meshes comprising all lines through points of the integer lattice in the directions of n + r + 1 pairwise linearly independent vectors with integer components. The generators are characterised by their Fourier transforms. Their shifts are shown to form a Riesz basis if and only if at most r lines in the mesh intersect other than in the integer lattice, which can occur for n = 2r - 1. The symmetry of these generators is studied and examples are given.
    Original languageEnglish
    Pages (from-to)279-301
    Number of pages23
    JournalConstructive Approximation
    Volume25
    Issue number3
    DOIs
    Publication statusPublished - 2007

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