Estimating Error Bounds for Non-stationary Binary Subdivision Curves / Surfaces

Abstract

Error bounds between non-stationary binary subdivision curves/surfaces and their control polygons after k-fold subdivision are estimated. The bounds can be evaluated without recursive subdivision. A computational formula of subdivision depth for non-stationary binary subdivision surfaces is also presented. From this formula one can predict the subdivision depth within a user specified error tolerance. Our results not only remove errors in the results of [3] but also contain the generalization of their results.