# Surface design using locally interpolating subdivision schemes

# Abstract

Non-uniform multivariate subdivision schemes
are constructed, which
generate limit functions interpolating some of
the initial control points.
Our schemes differ from the known interpolatory subdivision schemes,
in that only some of the original control points are interpolated,
and not the control points in every level.
These new schemes are combinations of a non-interpolatory schemes
with different local schemes near some of the original control points.
They generate smooth surfaces interpolating given points,
using stencils of small support.
Next, it is shown how to modify known subdivision schemes so that
the limit surfaces generated by them interpolate given
normal vectors at given interpolation points.

#### Size of gzipped file: 317 kb

### BiBTeX entry

@article(AdiLevin:2000:loc-intrp,

author = "A. Levin",

title = "Surface design using locally interpolating subdivision schemes",

journal = "Journal of Approximation Theory",

year = 2000,

pages = "98--120",

volume = "104(1)",

)