Estimating error bounds of Bajaj's solid models and their control hexahedral meshes

In this article, we estimate error bounds between the surface boundary patch of Bajaj et al's solid models (The Visual Computer 18, 343–356, 2002) and their boundary of control hexahedral meshes after $k$-fold subdivision. Our bounds are express in terms of the maximal differences of the initial control point sequences and constants. The bound is independent of the process of subdivision and can be evaluated without recursive subdivision. From this error bound one can predict the subdivision depth within a user specified error tolerance.