Tim Hattrell

This is VERY slow compared to what it could be. You will want a fine grid because of the coarse aggregation. Also very much data, otherwise there will be many holes in the resulting grid. This code may be reasonable for problems with very noisy data, where an interpolant will produce a mess. Beware surfaces with high curvature, as the averaging will flatten them out.

Why use a triple loop over all the cells to do what 3 calls to floor will do for you? I.e., since the grid is equally spaced, subtract the minimum, divide by the spacing, then call floor, and add 1. This provides an index in each dimension for every data point. Now use any strategy you want to accumulate the mean of all points in a given cell. Since this works in 3-d, sparse or accumarray are not options (unless you use a reshape, which will then work very efficiently.)