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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: This work considers the problem of G^2 two-point Hermite interpolation by a rational cubic and places necessary and sufficient conditions on the weights of the rational cubic curve which ensures that if the data suggest a C -shaped curve, therational cubic interpolates a C-shaped curve without loops, cusps, or inflections.
Abstract: We consider the problem of G^2 two-point Hermite interpolation by a rational cubic. Given two points with tangent vectors and curvatures, the necessary and sufficient conditions are placed on the w...
6 citations
TL;DR: Two new functional Monte Carlo algorithms are constructed for the numerical solution of three-dimensional Dirichlet boundary value problems for the linear and nonlinear Helmholtz equations using first Monte Carlo methods followed by an appropriate interpolation scheme.
Abstract: Here we construct two new functional Monte Carlo algorithms for the numerical solution of three-dimensional Dirichlet boundary value problems for the linear and nonlinear Helmholtz equations. These algorithms are based on estimating the solution and, if necessary, its partial derivatives at grid nodes using first Monte Carlo methods followed by an appropriate interpolation scheme. This allows us to obtain an approximation of the solution in the entire domain, which is not commonly done with Monte Carlo. The Monte Carlo methods used in this paper include the random walk on spheres method and the walk in balls process (with possible branching in the nonlinear case) and the stochastic application of Green's formula. For global approximation, cubic spline interpolation is used. One of the proposed approximation algorithms is based on Hermite cubic spline interpolation and utilizes estimates of the solution and its first partial derivatives. The other algorithm is based on Lagrange tricubic spline interpolation on a uniform grid and needs only estimates of the solution. An important problem is to find the optimal values of the interpolation algorithm parameters, such as the number of grid nodes and the sample volume. For this we use a stochastic optimization approach; i.e., for both of the proposed approximation algorithms we construct upper bounds of the approximation errors and minimize computational cost functions constrained by a fixed error criterion with a stochastic technique. To study the effectiveness of these proposed methods, we make a comparison between three functional algorithms, which are based on the use of the Hermite cubic splines, on the Lagrange tricubic splines, and on more common multilinear interpolation.
6 citations
TL;DR: In this paper, the Hermite interpolation problem with equally spaced nodes on the unit circle was studied and conditions for the derivatives were obtained in order that the interpolants uniformly converge to continuous functions.
Abstract: We study the Hermite interpolation problem with equally spaced nodes on the unit circle. We obtain new conditions for the derivatives in order that the Hermite interpolants uniformly converge to continuous functions. As a consequence we obtain some improvements in the case of the bounded interval.
6 citations
Journal Article•
TL;DR: Panoramic annular lens (PAL) project the view of the entire 360° around the optical axis onto an annular plane as mentioned in this paper, which plays important roles in the applications of robot vision, surveillance and virtual reality.
Abstract: Panoramic annular lens(PAL) project the view of the entire 360° around the optical axis onto an annular plane.Due to the super wide field of view,panoramic imaging system plays important roles in the applications of robot vision,surveillance and virtual reality.An annular image from PAL needs to be unwrapped to conventional rectangular image without distortion.The problem of the decreased resolution from outer circles to inner ones needs to be resolved during unwrapping procedure.The PAL image is restored according to the imaging feature of panoramic annular lens.Referenced to the highest resolution,the image adopts cubic spline interpolation function with the optimal parameter.Compared with nearest and bilinear interpolations,cubic spline interpolation with optimal parameter can restore the detail of the image better,and decrease the computational cost.
6 citations
TL;DR: In this article, the authors presented the cubic trigonometric interpolation curves with two parameters generated over the space {1, sint, cost, sin 2t, sin 3t, cost 2, sin 4t, cos 3t, cos 4t] and showed that the optimal interpolation curve can be determined by an energy optimization model.
Abstract: This paper presents the cubic trigonometric interpolation curves with two parameters generated over the space {1, sint, cost, sin2t, sin3t, cos3t} The new curves can not only automatically interpolate the given data points without solving equation systems, but are also C2 and adjust their shape by altering values of the two parameters The optimal interpolation curves can be determined by an energy optimization model The corresponding interpolation surfaces have characteristics similar to the new curves
6 citations