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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TL;DR: In this paper, the performance of standard cubic Hermite interpolation can be improved by interpolating a third point within the parameter interval, and the resulting method is easy to implement and achieves the optimal approximation order 5.
53 citations
TL;DR: This paper uses parametric cubic spline function to develop a numerical method, which is fourth order for a specific choice of the parameter, for computing smooth approximations to the solution for second order boundary value problems.
53 citations
TL;DR: It is shown that, depending upon the orientation of the end tangents t0,t1 relative to the end point displacement vector Δp=p1−p0, the problem of G1 Hermite interpolation by PH cubic segments may admit zero, one, or two distinct solutions.
Abstract: It is shown that, depending upon the orientation of the end tangents $\t_0,
\t_1$ relative to the end point displacement vector $\Delta\p=\p_1-\p_0$, the
problem of $G^1$ Hermite interpolation by PH cubic segments may admit zero,
one, or two distinct solutions. For cases where two interpolants exist, the
bending energy may be used to select among them. In cases where no solution
exists, we determine the minimal adjustment of one end tangent that permits a
spatial PH cubic Hermite interpolant. The problem of assigning tangents to a
sequence of points $\p_0,\ldots,\p_n$ in $\mathbb{R}^3$, compatible with a
$G^1$ piecewise--PH--cubic spline interpolating those points, is also briefly
addressed. The performance of these methods, in terms of overall smoothness
and shape--preservation properties of the resulting curves, is illustrated by
a selection of computed examples.
52 citations
TL;DR: In this article, different types of spatial interpolation for the material-point method are analyzed for the small-strain problem of a vibrating bar and the best results are obtained using quadratic elements.
52 citations
TL;DR: A piecewise rational function in a cubic/cubic form is proposed, which, in each interval, involves four free parameters in its construction that are constrained to preserve the shape of convex, monotone and positive data.
Abstract: This work is a contribution towards the graphical display of 2D data when they are convex, monotone and positive. A piecewise rational function in a cubic/cubic form is proposed, which, in each interval, involves four free parameters in its construction. These four free parameters have a direct geometric interpretation, making their use straightforward. Illustrations of their effect on the shape of the rational function are given. Two of these free parameters are constrained to preserve the shape of convex, monotone and positive data, while the other two parameters are utilized for the modification of positive, monotone and convex curves to obtain a visually pleasing curve. The problem of shape preservation of data lying above a line is also discussed. The method that is presented applies equally well to data or data with derivatives. The developed scheme is computationally economical and pleasing. The error of rational interpolating function is also derived when the arbitrary function being interpolated ...
52 citations