It's called the 'curse of dimensionality', and is why there has been a major change in estimation methods for 'Big Data' (because there isn't enough data for all the dimensions needed! to use Support Vector Machines and kernel methods, and many more (digression ends.) If one needs 30 points to 'fit' a Gaussian to a histogram (and decide if it is a Gaussian), then you'll need 1000 points for 2d and 30,000 points in 3d. In 3d (estimating volume density) it's even worse. Nor does it have a particularly clever algorithm for choosing the upper and lower limits of the grid when the input arguments p and q give the number of x and y axis gridpoints rather than specifying the gridpoints in the corresponding axis.ДЄs a general point, you need many more points to estimate the position and shape of a 2d object (surface) compared to a 1d 'histogram'. I haven't done anything other than give it a rudimentary check for accuracy or subject it to any statistical analysis. I've attached a worksheet giving a rather crude form of griddata (data,p,q), as a demonstration of the principle of creating such a function. You also need to ensure that you have chosen a valid polynomial order for the regression order 10 requires 11^2 points to obtain a fit. The match doesn't appear to be too bad numerically. If you set the number of grid points in your regression to 21, rather than 20, then the surfaces are a good match. Possibly the problem is partly that of appearance. It would be nice if we can use the algorithm used in the 2D surface plot. The interpolation algorithm used in the 2D surface plot looks much better than those two functions. It looks loess function is not stable when the number of data points are more than 800. However, when the number of data points is less than 50, those methods are not stable and the calculations do not converge to a solution. They both worked fine when the number of data points is more than 100. The second one is multivariate fitting by loess. The first one is multivariate fitting by regress. I found a couple of interesting functions in the E-book of the DAEP. This morning I learned about multivariate fitting functions of MathCad 15.

Idl interpolate