To instantiate the class, pass it a source field — e. Of course, if an analytic solution is available there is no need to interpolate — this is simply a useful calibration tool! The tricubic interpolation method values smoothness of the interpolated function and its first derivatives over absolute accuracy [ 4 ]. From Wikipedia, the free encyclopedia. It can be seen that for a given level of accuracy the analytic solution can tolerate a larger grid spacing — this is due to the high gradients at the interface between two materials in finite-element or boundary volume integral [ 12 ] analysis. Simply altering the mass and magnetic moment parameters would allow other species to be modelled. If the functions defining the acceleration due to a potential are replaced, trajectories in alternative systems could easily be modelled, for example, the motion of charges in electric fields, or masses moving under gravity. 
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Tricubic interpolation - Wikipedia
These example files also illustrate the expected input format of the data. It has also been tested on Enthought Canopy v2. ARBTools was developed in Python 2. It is often necessary to smoothly interpolate vector or scalar fields known as a set of discrete data points across a grid. The tricubic method described by Lekien and Marsden libragy 4 ] implements cubic spline interpolation in three dimensions, in an efficient and accurate way.
Figure 1 shows an interpolation example. For example; a cubic volume 20 mm on a side with a grid spacing of 0.
Numerical integrators for solving particle trajectories are included, but the core interpolator can be used for any scalar or vector field. The tricubic interpolator is equivalent to:. The core of ARBTools is the tricubic interpolator, which can be used with any suitably-formatted input field, for many possible tasks — for example, visualising the shape of a three-dimensional potential or extracting coherent Lagrangian structures from a time-dependent two-dimensional flow.
It can be seen that for a given level of accuracy the analytic solution can tolerate a larger grid spacing — this is due to the high gradients at the interface between two materials in finite-element or boundary tricugic integral [ 12 ] analysis.
Simply altering the mass and magnetic moment parameters would allow other species to be modelled. Unlike other interpolation methods in which the gradients are recovered via finite-differences, in the tricubic scheme the approximating polynomial function can be analytically differentiated.
A fourth-order Runge-Kutta [ 10 ] algorithm is implemented for numerically solving particle motion.
Computing in Science and Engineering For one- and two-dimensional problems cubic and bicubic spline librarry exist for example, in the SciPy interpolate library [ 1 ]but three-dimensional problems are more difficult.
The only additional system requirements are NumPy. The included Runge-Kutta integrator can be easily modified to solve particle motion in alternative systems — for example, we have recently discussed simulating the operation of an atomic tweezer apparatus with a colleague.
If no keyword is passed, the interpolator defaults to vector mode. Any version of Python from 2.
The potentials are calculated, for example using finite element analysis methods, as a series of data points on a grid, which librafy be interpolated to return the required values for an arbitrary point within the region of interest. The cubic interpolation article indicates that the method is equivalent to a sequential application of one-dimensional cubic interpolators.
Michael Thomas Flanagan's Java Library: TriCubic Spline Interpolation
Separate query methods are included for dealing with interpolation of a single point, or for multiple simultaneous coordinates. In general, consideration of the nature of the data set being interpolated and its structure will inform the grid spacing chosen, which is a compromise between inaccuracy and unwieldiness.
Two query modes are implemented: PhD thesis, Durham University. This software was developed for use in modelling the three-dimensional motion of paramagnetic neutral particles through Zeeman decelerators [ 2 ] and magnetic traps [ 3 ].
The interpolator has been designed to be imported as a library in Python, and the output from the evaluation methods can easily be passed into third-party code, or output to file for use in non-Python systems. ARBTools has been used with large datasets on the Durham university supercomputer.
Tricubic interpolation
Although produced for the specific application of modelling low-field-seeking neutral particles, this software has been developed to be more general. Journal of Open Research Software 7 1: Example magnetic fields, as both magnitudes and vectors, are available to download along with scripts illustrating the use of the interpolator.
Journal of Open Research Software7 1 The quadrupole electric field produced by four point charges was calculated as a grid of 3 data points; the left plot is a 2D slice through pibrary central plane.
This page was last edited on 26 Marchat
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