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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01 Jan 2003
TL;DR: In this paper, the authors present a parameterization and an interpolation method for quintic splines, which result in a smooth and consistent feedrate profile for C3 splines.
Abstract: This paper presents a parameterization and an interpolation method for quintic splines, which result in a smooth and consistent feedrate profile. The discrepancy between the spline parameter and the actual arc length leads to undesirable feed fluctuations and discontinuity, which elicit themselves as high frequency acceleration and jerk harmonics, causing unwanted structural vibrations and excessive tracking error. Two different approaches are presented that alleviate this problem: The first approach is based on modifying the spline toolpath so that it is optimally parameterized with respect to its arc length. The second approach is based on scheduling the spline parameter to accurately yield the desired arc displacement (i.e. feedrate), either by approximation of the relationship between the arc length and the spline parameter with a feed correction polynomial, or by solving the spline parameter iteratively in real-time at each interpolation step. The two approaches are compared to nearly arc length parameterized C3 quintic spline interpolation in terms of feedrate consistency and experimental tracking accuracy.Copyright © 2003 by ASME
51 citations
TL;DR: A local cubic splines interpolation method based on a domain decomposition, e.g. Hermite boundary conditions between the domains, using ad hoc reconstruction of the derivatives, provide a good approximation of the global solution.
51 citations
TL;DR: The degree of smoothness attained is C2 which is more powerful than a previous C1 method and the rational spline scheme has a unique representation.
51 citations
TL;DR: In this article, a numerical technique is presented for the solution of Fokker-Planck equation using the cubic B-spline scaling functions, which is easy to implement and produces very accurate results.
Abstract: In this article a numerical technique is presented for the solution of Fokker-–Planck equation. This method uses the cubic B-spline scaling functions. The method consists of expanding the required approximate solution as the elements of cubic B-spline scaling function. Using the operational matrix of derivative, the problem will be reduced to a set of algebraic equations. Some numerical examples are included to demonstrate the validity and applicability of the technique. The method is easy to implement and produces very accurate results. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 25: 418–429, 2009
51 citations
01 Oct 1985
TL;DR: Hardy's multiquadric interpolation (MQI) scheme is a global, continuously differentiable interpolation method for solving scattered data interpolation problems as discussed by the authors, which is capable of producing monotonic, extremely accurate interpolating functions, integrals, and derivatives.
Abstract: Hardy's multiquadric interpolation (MQI) scheme is a global, continuously differentiable interpolation method for solving scattered data interpolation problems. It is capable of producing monotonic, extremely accurate interpolating functions, integrals, and derivatives. Derivative estimates for a variety of one and two-dimensional surfaces were obtained. MQI was then applied to the spherical blast wave problem of von Neumann. The numerical solution agreed extremely well with the exact solution. 17 refs., 3 figs., 2 tabs.
51 citations