Topic

# Parametric equation

About: Parametric equation is a research topic. Over the lifetime, 2013 publications have been published within this topic receiving 33900 citations.

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TL;DR: In this paper, the Fourier amplitude sensitivity test (FAST) has been extended to include all the interaction terms involving a factor and the main effect of the factor's main effect.

Abstract: A new method for sensitivity analysis (SA) of model output is introduced. It is based on the Fourier amplitude sensitivity test (FAST) and allows the computation of the total contribution of each input factor to the output's variance. The term “total” here means that the factor's main effect, as well as all the interaction terms involving that factor, are included. Although computationally different, the very same measure of sensitivity is offered by the indices of Sobol'. The main advantages of the extended FAST are its robustness, especially at low sample size, and its computational efficiency. The computational aspects of the extended FAST are described. These include (1) the definition of new sets of parametric equations for the search-curve exploring the input space, (2) the selection of frequencies for the parametric equations, and (3) the procedure adopted to estimate the total contributions. We also address the limitations of other global SA methods and suggest that the total-effect indices are id...

1,652 citations

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TL;DR: In this article, a general multivariate normal distribution with a general parametric form of the mean vector and the variance-covariance matrix is proposed, where any parameter of the model may be fixed, free or constrained to be equal to other parameters.

Abstract: SUMMARY It is assumed that observations on a set of variables have a multivariate normal distribution with a general parametric form of the mean vector and the variance-covariance matrix. Any parameter of the model may be fixed, free or constrained to be equal to other parameters. The free and constrained parameters are estimated by maximum likelihood. A wide range of models is obtained from the general model by imposing various specifications on the parametric structure of the general model. Examples are given of areas and problems, especially in the behavioural sciences, where the method may be useful. 1. GENERAL METHODOLOGY 11. The general model We consider a data matrix X = {xOq} of N observations on p response variables and the following model. Rows of X are independently distributed, each having a multivariate normal distribution with the same variance-covariance matrix E of the form

1,115 citations

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TL;DR: In this paper, the problem of moving a manipulator in minimum time along a specified geometric path subject to input torque/force constraints is considered, and the minimum-time solution is deduced in an algorithm form using phase-plane techniques.

Abstract: Conventionally, robot control algorithms are divided into two stages, namely, path or trajectory planning and path tracking (or path control). This division has been adopted mainly as a means of alleviating difficulties in dealing with complex, coupled manipulator dynamics. Trajectory planning usually determines the timing of manipulator position and velocity without considering its dynamics. Consequently, the simplicity obtained from the division comes at the expense of efficiency in utilizing robot's capabilities. To remove at least partially this inefficiency, this paper considers a solution to the problem of moving a manipulator in minimum time along a specified geometric path subject to input torque/force constraints. We first describe the manipulator dynamics using parametric functions which represent geometric path constraints to be honored for collision avoidance as well as task requirements. Second, constraints on input torques/ forces are converted to those on the parameters. Third, the minimum-time solution is deduced in an algorithm form using phase-plane techniques. Finally, numerical examples are presented to demonstrate utility of the trajectory planning method developed.

1,016 citations

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28 Nov 1988TL;DR: This book contains various types of mathematical descriptions of curves and surfaces, such as Ferguson, Coons, Spline, Bzier and B-spline curves and surface, in a unified way so that beginners can easily understand the whole spectrum of parametric curve and surfaces.

Abstract: This book contains various types of mathematical descriptions of curves and surfaces, such as Ferguson, Coons, Spline, Bzier and B-spline curves and surfaces. The materials are classified and arranged in a unified way so that beginners can easily understand the whole spectrum of parametric curves and surfaces. This book will be useful to many researchers, designers, teachers, and students who are working on curves and surfaces. The book can be used as a textbook in computer aided design classes.

825 citations

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TL;DR: Two algorithms for parametric piecewise polynomial evaluation and generation are described and are shown to generalize to new algorithms for obtaining curve and surface intersections and for the computer display of parametric curves and surfaces.

Abstract: Two algorithms for parametric piecewise polynomial evaluation and generation are described. The mathematical development of these algorithms is shown to generalize to new algorithms for obtaining curve and surface intersections and for the computer display of parametric curves and surfaces.

538 citations