Local Interpolation by High Resolution Subdivision Schemes 


Daniel Lemire,
Acadia University

Subdivision schemes are used to interpolate data samples locally.
By using temporary placeholders on a dense grid, we improve one of
the best known subdivision scheme (Deslauriers-Dubuc). Interpolated
values require 2 steps to stabilize as they are first interpolated
on a coarse scale through a tetradic filter and then on a finer scale
using a dyadic filter. The interpolants are \( C^{1} \) and can be
made to reproduce polynomials of degree 4 unlike regular subdivision
schemes. These generalized interpolatory subdivision schemes have
minimal support and no additional memory requirement.