After my study on map projection I realized that it is very difficult to choose a projection that allows to compute simultaneously the distances between a great deal of points if these points are located all over the world. Equidistant projections allows only to compute distance between couple of points. Then I decided to use the following solution. My data set can be split in smaller datasets:
- United States territory;
- the whole EURASIA;
- the territory encompassing the African continent and the Europe.
In ArcGIS 9.3 (ArcInfo license) I projected each dataset with the Lambert Azimuthal Equal Area projection properly “centered” for each case. For each dataset I loaded a new layer with the Tissot's Indicatrix shapefile and computed the areas of each ellipse. I considered as "not distorted" (as regards the area, and the distances) all that territories over which the ellipses’ areas do not differ more than the 5% from the ellipse nearest to the center of the projection and when the ellipses' shape do not reasonably differ from a circular one. After having seen that my points were enclosed in this “not distorted” territory, I computed the point distance. Do you think my procedure was reasonably correct or have some advice about a better map projection for my purpose?