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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.


Papers
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Journal ArticleDOI
TL;DR: Two methods based on the use of natural and quasi cubic spline interpolations for approximating the solution of the second kind Fredholm integral equations are proposed.

17 citations

Proceedings Article
01 Jan 1974

17 citations

Journal ArticleDOI
TL;DR: In this paper, a cubic spline method for linear second-order boundary value problems is presented, which is a Petrov-Galerkin method using a cubic trial space, a piecewise-linear test space, and a simple quadrature rule for the integration.
Abstract: A cubic spline method for linear second-order two-point boundary-value problems is analysed. The method is a Petrov-Galerkin method using a cubic spline trial space, a piecewise-linear test space, and a simple quadrature rule for the integration, and may be considered a discrete version of the H 1 -Galerkin method. The method is fully discrete, allows an arbitrary mesh, yields a linear system with bandwidth five, and under suitable conditions is shown to have an o(h 4−i ) rate of convergence in the W p i norm for i = 0, 1, 2, 1 ≤ p ≤ ∞. The H 1 -Galerkin method and orthogonal spline collocation with Hermite cubics are also discussed

17 citations

Journal ArticleDOI
TL;DR: In this paper, a path-planning interpolation methodology is presented with which the user may analytically specify the desired path to be followed by any planar industrial robot, and the trajectory-planner can be implemented as part of kinematic and kinetic simulation software, and also has the potential application for controlling machine tools in cutting along free-form curves.
Abstract: A new path-planning interpolation methodology is presented with which the user may analytically specify the desired path to be followed by any planar industrial robot. The user prescribes a set of nodal points along a general curve to be followed by the chosen working point on the end-effector of the mechanism. Given these specified points along the path and additional prescribed kinematical requirements, Overlapping Cubic Arcs are fitted in the Cartesian domain and a cubic Spline interpolation curve is fitted in the time-domain. Further user-specified information is used to determine how the end-effector orientation angle should vary along the specified curve. The proposed trajectory-planning methodology is embodied in a computer-algorithm (OCAS), which outputs continuous graphs for positions, velocities and accelerations in the time-domain. If a varying end-effector orientation angle is specified, the OCAS-algorithm also generates continuous orientation angle, orientation angular velocity and orientation angular acceleration curves in the time-domain. The trajectory-planning capabilities of the OCAS-algorithm are tested for cases where the prescribed nodal points lie along curves defined by analytically known non-linear functions, as well as for nodal points specified along a non-analytical (free-form) test-curve. The proposed trajectory-planner may be implemented as part of kinematic and kinetic simulation software, and it also has the potential application for controlling machine tools in cutting along free-form curves. Copyright © 2003 John Wiley & Sons, Ltd.

17 citations

Journal ArticleDOI
TL;DR: A C 1 cubic spline space defined over a triangulation with Powell-Sabin refinement is considered, which has some local C 2 super-smoothness and can be seen as a close extension of the classical cubic Clough-Tocherspline space.

17 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202316
202227
20191
201812
201740
201652