https://github.com/fgittins/tricubic

Python implementation of a tricubic interpolator in three dimensions.
https://github.com/fgittins/tricubic

Last synced: 14 days ago
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Python implementation of a tricubic interpolator in three dimensions.

• Host: GitHub
• URL: https://github.com/fgittins/tricubic
• Owner: fgittins
• License: mit
• Created: 2023-07-05T17:22:11.000Z (over 1 year ago)
• Default Branch: main
• Last Pushed: 2023-10-11T11:14:50.000Z (over 1 year ago)
• Last Synced: 2024-11-10T08:15:47.830Z (2 months ago)
• Language: Jupyter Notebook
• Size: 1.07 MB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# 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](https://doi.org/10.1002/nme.1296).

## 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.