Tight numerical bounds for digital terrain modeling by interpolatory subdivision schemes Original Research Article

Surface subdivision schemes are used extensively in scientific and practical applications to generate continuous surfaces in an iterative manner, starting from a set of points. The first subdivision step defines the so called control polygon. This initial polygon can be considered as a very coarse approximation to the final surface. Each iterative step is governed by a local averaging rule which is designed to generate new points by taking some weighted averages of the positions of the neighboring vertices from the previous iteration. If the old vertices (i.e. vertices from the previous iteration) are not to be altered, the subdivision scheme is called an interpolatory subdivision scheme. Some of the most popular interpolatory subdivision schemes are the two point, four point and six point subdivision schemes. These subdivision rules define convergent schemes. T