The following is a more elaborative conjecture on what i wish to achieve in C ; here is how far I reached; Any suggestions of how this might be coded actually within C ? (Found it to be more efficient than python or R, however I am not proficient in this language yet.) A 3d grid, about 303030, or a 3d array, so i can define a function of R3 -> R f(x, y, z) = v More precisely, where x, y, z € [0, N] of float values so for f(0.5, 0.5, 0.5) the result would be the trilinear interpolation for the points (0,0,0), (0,0,1), (0,1,0), (0,1,1), (1,0,0), (1,0,1), (1,1,0) and (1,1,1). With v is equal to the value stored in the array if x, y, and z are integer values, or the trilinear interpolation of the closest points in the array where N_i is the number of points - 1 in the i dimension of the array; x € [0, N_x], y € [0, N_y], and z € [0, N_z]. Now let's Imagine a 1d array(which does not exist, only integer indices), one can make up a value by interpolation between closest actual values, and can extend this to 2d, though if you try to get a value for the position 0.3864 for positions 0 and 1 you need the 4 closest points in the end you can extend to any number of dimensions. Providing the values at (0,0), (0,1), (1,0) and (1,1). n is the number of dimensions which have a non integer coordinate, but you get the point with a bilinear interpolation, and you'll need exactly 2ⁿ points where n is the number of dimensions.

(Found C to be more efficient than python or R, however I am not proficient in this language yet.)

I actually wish to code this in c here is a simplified elaboration upon the idea;

I have a 3d grid of floats which via I wish to access this values in parallel by the thousands In random positions. To which then I want to convert this memory bound process into cpu bound; by flattening the 3d array, and approximate it with a finite Fourier expansion or something similar. Then calculate the values at the required positions of this flattened data and use the calculated values to do the trilinear interpolation.