A Novel Numerical Method for Computing Subdivision Depth of Quaternary Schemes - Shahzad, Aamir; Khan, Faheem; Ghaffar, Abdul; Yao, Shao-Wen; İnç, Mustafa; Ali, Shafqat (Mdpi, 2021)
In this paper, an advanced computational technique has been presented to compute the error bounds and subdivision depth of quaternary subdivision schemes. First, the estimation is computed of the error bound between quaternary subdivision limit curves/surfaces and their polygons after kth-level subdivision by using l0 order of convolution. Secondly, by using the error bounds, the subdivision depth of the quaternary schemes has been computed. Moreover, this technique needs fewer iterations (subdivision depth) to get the optimal error bounds of quaternary subdivision schemes as compared to the existing techniques.
Keywords: quaternary subdivision scheme; subdivision models; inequalities; convolution; error bound; subdivision depth; curves and surfaces