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: 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
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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
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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
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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