We offer computational formula of subdivision depth for tensor product -ary 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.
Ghulam Mustafa. Muhammad Sadiq Hashmi. "Subdivision Depth Computation for Tensor Product -Ary Volumetric Models." Abstr. Appl. Anal. 2011 1 - 22, 2011. https://doi.org/10.1155/2011/203453