C2rational quartic interpolation spline with local shape preserving property

Abstract

Please cite this article as: Y.P. Zhu; X.L. Han, C 2 rational quartic interpolation spline with local shape preserving property, Appl. Math. Lett. (2015), http://dx. AbstractWe present an explicit representation of a general C 2 rational quartic interpolation spline with three families of local shape parameters. Sufficient conditions for the proposed interpolant to preserve locally the shape of positive, monotonic, and/or convex set of data are given. The approximation order of the interpolant is O(h 2 ) or O(h 3 ).

Progressive Iterative Approximation for Extended B-Spline Interpolation Surfaces

“…. , u m− 1 ) and and N s (t; λ 2 ) 􏼈 􏼉 3 s�0 be the λ-B-spline bases defined as in (1). en, for u ∈ [u i , u i+1 ], i � 1, 2, .…”

“…If we want the λ-B-spline surface to interpolate the boundary control points, we have to add several control vertices according to 3 s�0 be the λ-Bspline bases defined as in (1). Given a set of organized data points p ij 􏽮 􏽯 i�0,...,n i�0,...,m to be interpolated, we assign a pair of parameters (u i , v j ) to the (i, j)th point p ij , where…”

“…Data interpolation plays important roles in scientific research and engineering applications. How to solve interpolation curves/surfaces efficiently has been one of the most popular topics in computer-aided geometric design (see [1][2][3]). Oftentimes, one has to solve a linear system to obtain the interpolation curves or 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]).…”