README.md

tricubic

Python implementation of a tricubic interpolator in three dimensions. The scheme is based on Lekien and Marsden (2005), "Tricubic interpolation in three dimensions," Int. J. Numer. Meth. Eng. 63, 455.

Usage

tricubic requires the numpy package, so make sure that this is installed on your system.

Here is a simple example to get you started. The interpolator is an object that can be imported as

from tricubic import Tricubic

We will consider the following function: $$f(x, y, z) = - x^3 + x + y^2 - z.$$ The Tricubic object accepts four inputs (X, Y, Z, F), which are the samples of the three independent variables $(x, y, z)$ and the one dependent variable $f$. These can be generated for our function as

import numpy as np

def f(x, y, z): return - x**3 + x + y**2 - z

X, Y, Z = np.linspace(-1, 1, 21)
x, y, z = np.meshgrid(X, Y, Z, indexing='ij')
F = f(x, y, z)

Then the interpolator object is initialised as

interp = Tricubic(X, Y, Z, F)

The interpolator can be called at a point, say $(0.5, -0.1, 0.3)$, for an estimate of the function

interp(0.5, -0.1, 0.3)

and its derivatives

interp(0.5, -0.1, 0.3, dx=True)
interp(0.5, -0.1, 0.3, dy=True)
interp(0.5, -0.1, 0.3, dz=True)

Due to the local nature of the interpolation scheme, it does not accept arrays as inputs.

Testing

To test, run

python -m unittest tests.test

in the root directory.