A New Family of Interpolatory Non-Stationary Subdivision Schemes for Curve Design in Geometric Modeling

摘要

Univariate subdivision schemes are efficient iterative methods to generate smooth limit curves starting from a sequence of arbitrary points. Aim of this paper is to present and investigate a new family of 6-point interpolatory non-stationary subdivision schemes capable of reproducing important curves of great interest in geometric modeling and engineering applications, if starting from uniformly spaced initial samples. This new family can reproduce conic sections since it is obtained by a parameter depending affine combination of the cubic exponential B-spline symbol generating functions in the space V4,Υ = {1,X, e~(tx),e(-tx)} with t ∈ {0,s, is|s > 0}. Moreover, the free parameter can be chosen to reproduce also other interesting analytic curves by imposing the algebraic conditions for the reproduction of an additional pair of exponential polynomials giving rise to different extensions of the space V_4,Υ.