Estimating error bounds for tensor product binary subdivision volumetric model

Abstract

In this article, by generalizing the techniques of Mustafa, Falai and Deng (2006), we estimate the error bounds between the tensor product binary volumetric model and its control polyhedron after k-fold subdivision. Our bounds are expressed in terms of the first-order differences of the initial control point sequences and constants that depend on the subdivision masks.

Keywords:

• Volumetric subdivision
• Error bound
• Control polyhedron

Acknowledgements

We thank the referees for comments that helped us to improve the error bounds and the presentation of the paper. The first named author is greatly in debt to Professor Chen Falai and Professor Deng Jian Song (Department of Mathematics, University of Science and Techno-logy of China) for their valuable advice, suggestions, moral support, generous assistance and hospitality during his stay in China. This work is supported by the Indigenous PhD Scholarship Scheme of the Higher Education Commission (HEC), Pakistan.