Since there are 5 axes for the independent variables (v,w,x,y,z), the image illustrated below reflects the actual value of the function f(v,w,x,y,z) at each point (v,w,x,y,z) as viewed from the x-y plane.  Note: All 2D planes cut from the 5D hypervolume are made at the origins of the other 3 axes.  There are actually 1000 possible planes per any 2-axis combination since the other axes would yield 10x10x10 possible combinations of points to observe the relevant 2D plane.  For example, the x-y plane shown below is found at v=0, w=0, and z=0.  There are 1000 possible x-y planes that can be cut along the v, w, and z-axes.

100,000-Node True Results

(Click on image for other 2-D planes)
 
The images at the right are examples of the interpolated grid starting with 2,000, 4,000, 10,000, and 25,000 known nodes randomly extracted from the 100,000 node grid. The value of the function f(v,w,x,y,z) at each point is stored in a netCDF file (version 3.3), and a netCDF viewer (Ncview ) is used to display the results as a 2-D surface plot viewed from the x-y plane. With random distribution of nodes, the 4,000-node set proved to be the smallest set of known nodes to produce acceptable results.