Non-uniform subdivision schemes of ωB-spline curves and surfaces with variable parameters. (January 2023) - Lamnii, A.; Nour, M.-Y.; Sbibih, D.; Zidna, A.
Abstract: In this paper, we propose a new non-uniform subdivision scheme that includes a tension parameters sequence. Each tension parameter of the sequence is assigned at each edge of the initial control polygon. The proposed scheme can produce limiting curves that are more consistent with the original data points and the control polygon. It has also the advantage of generating a wide variety of shapes for the limiting curves. Moreover, to produce smooth limit surfaces, the proposed scheme is firstly extended to tensor-product surfaces, then to meshes of arbitrary topology. The convergence and smoothness of the proposed scheme are proven. Numerical results that illustrate the advantages of the proposed non-uniform scheme are given. Highlights: This family of non-uniform subdivision schemes can be used in many engineering applications. It is able to generate a wide variety of shapes for the limiting curves and surfaces. It allows local control of the shape of the resulting limit curves and surfaces. It is extended to mesh of arbitrary topology to generate complex surface subdivisions. It turns out to be the uniform scheme, when the tension parameters are all equal. It turns out to be Doo–Sabin and Catmull–Clark scheme, when the parameters are equal to 1.