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Interpolation is the process of estimating the values of a function, when the function's values are known only at a particular set of points. Questions on interpolation in one or more dimensions, as well as algorithms for doing so, should have this tag.
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Bilinear interpolation for large grids
You could try the GNU Scientific Library: https://www.gnu.org/software/gsl/doc/html/interp.html#id5
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Interpolation question
matches both the data $y_i$ and the first derivatives $y'_i$ at the nodes $x_i$,
\begin{align}
f(x_i) &= y_i \\
\frac{d}{dx} f(x_i) &= y'_i
\end{align}
At first I thought that piecewise cubic Hermite interpolation … Does anyone know of a reference for doing an interpolation like this, and whether there exists a high-quality implementation in some numerical library? …