Map Projections Minimizing Distance Errors
Abstract
It is useful to have mathematical criteria for evaluating errors in map projections. The Chebyshev criterion for minimizing rms (root mean square) local scale factor errors for conformal maps has been useful in developing conformal map projections of continents. Any local error criterion will be minimized ultimately by map projections with multiple interruptions, on which some pairs of points that are close on the globe are far apart on the map. Since it is as bad to have two points on the map at two times their proper separation as to have them at half their proper separation, it is the rms logarithmic distance, s, between random points in the mapped region that we will minimize. The best previously known projection of the entire sphere for distances is the Lambert equalarea azimuthal with an rms logarithmic distance error of s=0.343. For comparison, the Mercator has s=0.444, and the Mollweide has s=0.390. We present new projections: the "Gott equalarea elliptical" with perfect shapes on the central meridian, the "GottMugnolo equalarea elliptical" and the "GottMugnolo azimuthal" with rms logarithmic distance errors of s=0.365, s=0.348, and s=0.341 respectively, which improve on previous projections of their type. The "GottMugnolo azimuthal" has the lowest distance errors of any map and is produced by a new technique using "forces" between pairs of points on a map which make them move so as to minimize s. The "Gott equalarea elliptical" projection produces a particularly attractive map of Mars, and the "GottMugnolo azimuthal" projection produces an interesting map of the moon.
 Publication:

arXiv eprints
 Pub Date:
 August 2006
 arXiv:
 arXiv:astroph/0608500
 Bibcode:
 2006astro.ph..8500G
 Keywords:

 Astrophysics
 EPrint:
 PDF from Microsoft Word, with imported JPEG figures