A New Computational Approach to Estimate the Subdivision Depth of <italic>n</italic>-Ary Subdivision Scheme

Abstract

The $n$ -ary subdivision scheme has traditionally been designed to generate smooth curve and surface from control polygon. In this paper, we propose a new subdivision depth computation technique for $n$ -ary subdivision scheme. The existing techniques do not ensure the computation of subdivision depth unless some strong condition is assumed on the mask of the scheme. But our technique relaxes the effect of strong condition assumed on the mask of the scheme by increasing the number of convolution steps. Consequently, a more precise subdivision depth technique for a given error tolerance is presented in this paper.

Keywords

• Curves and surfaces
• n-ary subdivision schemes%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">n</italic>-ary subdivision schemes
• convolution
• error
• distance
• subdivision depth