Regularity of irregular subdivision

Journal Article (Journal Article)

We study the smoothness of the limit function for one-dimensional unequally spaced interpolating subdivision schemes. The new grid points introduced at every level can lie in irregularly spaced locations between old, adjacent grid points and not only midway as is usually the case. For the natural generalization of the four-point scheme introduced by Dubuc and Dyn, Levin, and Gregory, we show that, under some geometric restrictions, the limit function is always C1; under slightly stronger restrictions we show that the limit function is almost C2, the same regularity as in the regularly spaced case.

Full Text

Duke Authors

Cited Authors

  • Daubechies, I; Guskov, I; Sweldens, W

Published Date

  • January 1, 1999

Published In

Volume / Issue

  • 15 / 3

Start / End Page

  • 381 - 426

International Standard Serial Number (ISSN)

  • 0176-4276

Digital Object Identifier (DOI)

  • 10.1007/s003659900114

Citation Source

  • Scopus