Algorithmic display tool

What the tool is and how to invoke it

This module discusses a tool for displaying various features of the Natgrid algorithm. This tool is available only with the NCAR Graphics distribution.

The tool is an executable called "nnalg". If you are using NCAR Graphics and have properly set NCARG_ROOT, "nnalg" will be in your search path.

"nnalg" takes a single argument which is the name of a special file created by the Fortran subroutine NATGRIDS or the C function c_natgrids. This file contains data appropriate for displaying various features of the Natgrid algorithm. By default, this file is not created. In order to create it, you need to set the value of the control parameter adf to 1. You can additionally override the default file name of "nnalg.dat" by using the parameter alg. Example 8 shows an example of how to create a data file with a user-specified name.

To invoke "nnalg", simply type the command:

nnalg data_file

where "data_file" is a file that has been created by the Fortran subroutine NATGRIDS or the C function c_natgrids.

By editing the data file, you have many options for what is displayed and how the plot appears. All of these options are discussed below.

What can be displayed

The features that can be displayed are:

The input data points
The natural neighbor circumcircles and their centers
The Delaunay triangulation, derived from the natural neighbor circumcircles
The Voronoi polygons
The first order natural neighbors of a given input point (or points)
The second order natural neighbors of a given input point (or points)

The first four items in the above list are displayed in the default case. The plot in Example 8 illustrates plotting these four items.

Note that there is a very interesting relationship between the natural neighbor circumcircles, the Delaunay triangulation, and the Voronoi polygons: the aggregate of the triangles created within each circumcircle form a Delaunay triangulation; lines connecting the circumcircle centers that are perpendicular to the edges in the Delaunay triangulation form the Voronoi polygons.

Where the plot will be displayed

Using the file example8.dat for reference, the first non-comment line in the integer flags section controls where the output will be dispatched upon executing nnalg example8.dat. By default the plot will be displayed in an X11 window that is created at execution time. The other choices you have are producing an NCAR CGM file (with name "gmeta"), or a PostScript file (with name "gmeta1.ps").

Controlling what gets plotted

The integer flags section of example8.dat controls what gets plotted. The comments there are intended to be self-explanatory. The pseudo data are internally calculated as extreme points that lie on a least-squares plane fitted to the original data. The pseudo data points are used for extrapolation. If you choose to display them, what you will usually get is the interesting part of the plot squeezed into a tiny area with only the pseudo points being meaningfully displayed.

Changing colors

The color information section of example8.dat allows you to assign colors to various plot components, as described.

Changing sizes

The scale factors section of example8.dat allows you to scale various aspects of the plot, as described.

Changing the plot view window

The user coordinate specification section of example8.dat allows you to change what part of the plot you want to look at. The default setting of all zeros tells nnalg to compute data minimums and maximums and look at an area slightly larger than that.

In the non-default case, the four numbers in the user coordinate specification line control what part of the plot you want to look at. The numbers specify, in user coordinates, the minimum X coordinate value, the maximum X coordinate value, the minimum Y coordinate value, and the maximum Y coordinate value, respectively, of the viewing window. If any single value is changed, then no default applies and all four values will be used to determine the extent of the viewing area.

Plotting first and second order natural neighbors

Sometimes it is of interest to see what input data points are being used to calculate an interpolated value. These points are the natural neighbors. This could shed light on why an interpolated value might appear to be different from what is expected. This is particularly important for interpolated values near the convex hull of a dataset where the convex hull differs significantly from the bounding polygon.

Example 9 takes you through a sequence of plots illustrating the plotting of first and second order natural neighbors.