Abstract and Applied Analysis
Volume 2011 (2011), Article ID 203453, 22 pages
http://dx.doi.org/10.1155/2011/203453
Research Article

Subdivision Depth Computation for Tensor Product 𝑛 -Ary Volumetric Models

Ghulam Mustafa and Muhammad Sadiq Hashmi

Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan

Received 22 October 2010; Revised 27 January 2011; Accepted 28 February 2011

Academic Editor: Yoshikazu Giga

Copyright © 2011 Ghulam Mustafa and Muhammad Sadiq Hashmi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We offer computational formula of subdivision depth for tensor product 𝑛 -ary ( 𝑛 ⩾ 2 ) volumetric models based on error bound evaluation technique. This formula provides and error control tool in subdivision schemes over regular hexahedron lattice in higher-dimensional spaces. Moreover, the error bounds of Mustafa et al. (2006) are special cases of our bounds.