We analyse the mask associated with the 2n-point interpolatory Dubuc-Deslauriers subdivision scheme S-a[n]. Sharp bounds are presented for the magnitude of the coefficients a(2i-1)([n]) of the mask. For scales i is an element of [1, root n] it is shown that vertical bar a(2i-1)([n])vertical bar is comparable to i(-1), and for larger power scales, exponentially decaying bounds are obtained. Using our bounds, we may precisely analyse the summability of the mask as a function of n by identifying which coefficients of the mask contribute to the essential behaviour in n, recovering and refining the recent result of Deng-Hormann Zhang that the operator norm of S-a[n] on l(infinity) grows logarithmically in n.
New minimal bounds are derived for the magnitudes of the derivatives of the rational Bezier paths and the rational rectangular Bezier surface patches of arbitrary degree, which improve previous work of this type in many cases. Moreover, our new bounds are explicitly given by simple and closed-form expressions. An important advantage of the closed-form expressions is that they allow us to prove that our bounds are sharp under certain well-defined conditions. Some numerical examples, highlighting the potential of the new bounds in providing improved estimates, are given in an appendix. (C) 2013 Elsevier Inc. All rights reserved.
New derivative bounds for the rational quadratic Bézier paths are obtained, both for particular weight vectors and for classes of equivalent parametrisations. A comprehensive analysis of our bounds against existing bounds is made.
