Improved error estimate for extraordinary Catmull–Clark subdivision surface patches

Distance between a Catmull-Clark subdivision surface and its limit mesh

“…We denote by M k i and M k the second order norms of Π k i and Π k , respectively. The second order norms M k 0 and M 0 satisfy the following inequality Huang and Wang 2006]:…”

“…Multistep convergence rate r k (n) was introduced and estimated in ] with a matrix based technique, then improved in [Huang and Wang 2006] with an optimization based approach.…”

“…The bounds on the maximal distance between a CCSS patch and its control mesh in terms of the maximum norm of the second order differences (called second order norm) of the control points have been studied in Huang and Wang 2006]. Though some techniques such as matrix based ] and optimization based [Huang and Wang 2006] are adopted to improve the distance estimate, for an extraordinary CCSS patch, the subdivision depth for a given error tolerance is still very large.…”

“…Though some techniques such as matrix based ] and optimization based [Huang and Wang 2006] are adopted to improve the distance estimate, for an extraordinary CCSS patch, the subdivision depth for a given error tolerance is still very large.…”

The distance of a subdivision surface to its control polyhedron

“…the estimate does not match observations and is not practically useful. Similar estimates, ever more sophisticated in the details, can be found in [3,5,4,9,10].…”