Construction and Application of Nine-Tic B-Spline Tensor Product SS

Abstract

In this paper, we propose and analyze a tensor product of nine-tic B-spline subdivision scheme (SS) to reduce the execution time needed to compute the subdivision process of quad meshes. We discuss some essential features of the proposed SS such as continuity, polynomial generation, joint spectral radius, holder regularity and limit stencil. Some results of the SS using surface modeling with the help of computer programming are shown. Author Contributions: Conceptualization, A.G., M.B. and M.I.; methodology, K.S.N. and D.B.; software, A.G., S.M.H. and R.M.; validation, A.G. and K.S.N.; formal analysis, S.M.H., D.B. and R.M.; writing-original draft preparation, A.G., M.I., M.B., S.M.H. and R.M.; writing-review and editing, K.S.N. and D.B. Funding: This research received no external funding. Conflicts of Interest:The authors declare no conflict of interest.

Construction and analysis of unified 4-point interpolating nonstationary subdivision surfaces

“…Fang et al [20] introduced the unified stationary SS of arbitrary order with image controlling variable, but it does not hold up the surfaces like sphere and hyperboloid. Recently, Ghaffar et al [21] have introduced tensor products of nine-tic B-spline. Therefore, the natural way to define refinement operators for quadrilateral nets to modify a tensor product scheme such that special rules for the vicinity of nonregular vertices are found.…”

Progressive Iterative Approximation for Extended B-Spline Interpolation Surfaces

“…Examples of such approaches include [5][6][7][8][9][10][11][12][13][14] and a lot of literatures therein. e emergence of blending bases with shape parameters has enriched the theories and methods of geometric modeling [1,[15][16][17]. Due to the flexibly in shape adjustment, splines with shape parameters have drawn much attention for decades and a large number of splines with shape parameters were exploited (see, for example, [18][19][20]).…”

Generalized 5-Point Approximating Subdivision Scheme of Varying Arity

“…They also proposed a 4-point ternary scheme which creates C 0 interpolating and C 1 , C 2 , C 3 approximating limiting curves, described in [24]. For other recent work on this topic, we may refer to [25][26][27][28][29] and references therein.…”