A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes

Abstract

Subdivision schemes are extensively used in scientific and practical applications to produce continuous geometrical shapes in an iterative manner. We construct a numerical algorithm to estimate subdivision depth between the limit curves/surfaces and their control polygons after k-fold subdivisions. In this paper, the proposed numerical algorithm for subdivision depths of binary subdivision curves and surfaces are obtained after some modification of the results given by Mustafa et al in 2006. This algorithm is very useful for implementation of the parametrization.

A Convolution‐Based Computational Technique for Subdivision Depth of Doo‐Sabin Subdivision Surface

“…Reformulation of Successive Convolutions. With the use of analysis developed in [13], there are some useful results, which will be used to construct the new technique for Doo-Sabin surfaces scheme in upcoming sections. Now, we move forward and construct associated constants for the 2 Journal of Mathematics Doo-Sabin surface scheme by using successive convolutions for a one-dimensional array of finite length vectors.…”

“…It is required in all tessellationbased applications such as subdivision surface trimming, finite element polygon generation, Boolean operators, and surface tessellation for rendering. Some novel numerical techniques are presented to estimate the error bounds and subdivision depths only for binary subdivision curves and surfaces [12][13][14]. Still, there is space to extend this work to find the error bound/subdivision depth for well-known subdivision schemes for arbitrary topology.…”

A Novel Numerical Method for Computing Subdivision Depth of Quaternary Schemes

“…The third technique is introduced by Moncayo and Amat [18] and Shahzad et al [19]. It works for binary class of schemes.…”

Analysis of Geometric Properties of Ternary Four-Point Rational Interpolating Subdivision Scheme

“…Zulkifli et al [18] discussed the application of new rational bi-cubic Ball function with six parameters in image interpolation, especially for the gray scale image. For more recent work on SS one may refer to References [19][20][21][22][23].…”