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.
Papers published on a yearly basis
Papers
More filters
Book•
08 Sep 2005
TL;DR: This paper presents a probabilistic procedure called "Spline Interpolation–Bezier Approximation–Subdivision Methods", which automates the very labor-intensive and therefore time-heavy and expensive process of solving the inequality of the following types of inequality:.
Abstract: Basic Theory.- Linear Interpolation.- Polynomial Interpolation.- Hermite Interpolation.- Spline Interpolation.- Bezier Approximation.- B-Spline Approximation.- Subdivision Methods.- Sweep Surfaces.
317 citations
314 citations
TL;DR: In this paper, a method for producing monotone piecewise cubic interpolants to monotonous data is described, which is completely local and which is extremely simple to implement.
Abstract: A method is described for producing monotone piecewise cubic interpolants to monotone data which is completely local and which is extremely simple to implement.
294 citations
TL;DR: A parametric cubic spline interpolation scheme for planar curves which is based on an idea of Sabin for the construction of C^1 bicubic parametric spline surfaces is described, a natural generalization of [standard] Hermite interpolation.
276 citations
TL;DR: This paper addresses two interrelated problems concerning the planar three degree-of-freedom motion of a vehicle, namely, the path planning problem and the guidance problem, and derives a new κ-exponentially stable integral LOS guidance law, capable of eliminating the effect of constant external disturbances for straight-line path following.
Abstract: This paper addresses two interrelated problems concerning the planar three degree-of-freedom motion of a vehicle, namely, the path planning problem and the guidance problem. The monotone cubic Hermite spline interpolation (CHSI) technique by Fritsch and Carlson is employed to design paths that provide the user with better shape control and avoid wiggles and zigzags between the two successive waypoints. The conventional line-of-sight (LOS) guidance law is modified by proposing a time-varying equation for the lookahead distance, which is a function of the cross-track error. This results in a more flexible maneuvering behavior that can contribute to reaching the desired path faster as well as obtaining a diminished oscillatory behavior around the desired path. The guidance system along with a heading controller form a cascaded structure, which is shown to be $\kappa$ -exponentially stable when the control task is to converge to the path produced by the aforementioned CHSI method. In addition, the issue of compensating for the sideslip angle $\beta$ is discussed and a new $\kappa$ -exponentially stable integral LOS guidance law, capable of eliminating the effect of constant external disturbances for straight-line path following, is derived.
267 citations