How to “flatten” or “index” 3D-array in 1D array?

Here is a solution in Java that gives you both:

• from 3D to 1D
• from 1D to 3D

Below is a graphical illustration of the path I chose to traverse the 3D matrix, the cells are numbered in their traversal order:

Conversion functions:

public int to1D( int x, int y, int z ) {
    return (z * xMax * yMax) + (y * xMax) + x;
}

public int[] to3D( int idx ) {
    final int z = idx / (xMax * yMax);
    idx -= (z * xMax * yMax);
    final int y = idx / xMax;
    final int x = idx % xMax;
    return new int[]{ x, y, z };
}