| This example of interpolation
was done using the Modified Quadratic Shepard's method developed by R.J.
Renka (see Multivariate interpolation of large sets of scattered data,
R.J. Renka, ACM
Trans. on Math. Software 14:2, June 1988, pp. 139-148.) The 3-variable
function f(x,y,z) = [1.25+cos(5.4y)] cos(6z) / [6+6(3x-1)2]
defined on all 8,000 nodes of a 20x20x20 grid was used to create the
true results shown below. Since there are 3 axes for the independent variables
(x,y,z), the image illustrated below reflects the actual value of
the function f(x,y,z) at each point (x,y,z) as viewed from
the y-z plane. Note: All 2D planes cut from the 3D
hypervolume are made at the origin of the 3rd axis. There are actually
10 possible points along the 3rd axis to observe the relevant 2D plane.
For example, the y-z plane shown below is found at x=0.
There are a total of 10 y-z planes that could be cut along the x-axis. |
8000-Node True Results
|
The following images shown below are examples
of the interpolated grid starting with 50, 100, 500, 1000, 2000, and 4000
known nodes randomly extracted from the 8,000 node grid. The value
of the function f(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
y-z plane. With random distribution of nodes, the 2000-node set
proved to be the smallest set of known nodes to produce acceptable results. |