Topic
Monotone cubic interpolation
About: Monotone cubic interpolation is a research topic. Over the lifetime, 1740 publications have been published within this topic receiving 38111 citations.
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24 Jun 2010
TL;DR: This article addresses the problem of interpolating data points lying on a regular grid by C1-continuous L1-bicubic spline surfaces by developing an interpolation scheme based on four linear directions so as to construct the interpolation surface.
Abstract: In this article, we address the problem of interpolating data points lying on a regular grid by C1-continuous L1-bicubic spline surfaces. Our algorithm is based on a local univariate L1 minimization method which enable us to calculate first derivative values for C1-cubic spline curves. In order to construct the interpolation surface, we calculate four derivative values at each data point using this local method. At is was shown in [17], our local interpolation L1 cubic spline curve algorithm preserves well the shape of the data even for abrupt changes.The sequential computational complexity of this local method is linear and the parallel computational complexity is O(1). Consequently, we can address in this manner data on large grids. In order to keep this linear complexity for spline surface interpolation, we define an interpolation scheme based on four linear directions so as to construct our L1-bicubic surface. Some image interpolation examples show the efficiency of this non linear interpolation scheme.
5 citations
13 Nov 2014
TL;DR: In this paper, the authors compare contemporary practices of global approximation using cubic B-splines in conjunction with double multiplicity of inner knots (-continuous) with older ideas of utilizing local Hermite interpolation of third degree.
Abstract: We compare contemporary practices of global approximation using cubic B-splines in conjunction with double multiplicity of inner knots (-continuous) with older ideas of utilizing local Hermite interpolation of third degree. The study is conducted within the context of the Galerkin-Ritz formulation, which forms the background of the finite element structural analysis. Numerical results, concerning static and eigenvalue analysis of rectangular elastic structures in plane stress conditions, show that both interpolations lead to identical results, a finding that supports the view that they are mathematically equivalent.
5 citations
Proceedings Article•
15 Feb 2006TL;DR: In this paper, a nonlinear interpolation based on Hermite interpolation is used to compute adaptively derivatives from signal discrete data, and a multiresolution based on the Hermite method is performed.
Abstract: This paper is devoted to the construction of a nonlinear interpolation in order to compute adaptively derivatives from signal discrete data. Using these derivatives a multiresolution based on Hermite interpolation is performed. The way in which the derivatives are approximated is crucial.
5 citations
TL;DR: In this article, the authors reformulated the construction of bicubic splines as the minimisation of an appropriate integral subject to certain constraints, such as the polar singularity.
5 citations
01 Aug 2000
Abstract: In the present paper, C1-piecewise rational cubic spline function involving tension parameters is considered which produces a monotonie interpolant to a given monotonie data set. It is observed that under certain conditions the interpolant preserves the convexity property of the data set. The existence and uniqueness of a C2-rational cubic spline interpolant are established. The error analysis of the spline interpolant is also given.
5 citations