README.md

TricubicInterpolations.jl

Julia 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

TricubicInterpolations.jl is written using pure Julia and has no additional dependencies.

Here is a simple example to get you started. We start with

using TricubicInterpolations

We will consider the following function: $$f(x, y, z) = - x^3 + x + y^2 - z.$$ The interpolator object Tricubic 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

f(x, y, z) = - x^3 + x + y^2 - z

X = Y = Z = LinRange(-1, 1, 21)
F = [f(x, y, z) for x=X, y=Y, z=Z]

Then the interpolator is initialised as

t = 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

t(0.5, -0.1, 0.3)

and its derivatives

partial_derivative_x(t, 0.5, -0.1, 0.3)
partial_derivative_y(t, 0.5, -0.1, 0.3)
partial_derivative_z(t, 0.5, -0.1, 0.3)