ihm@nrc.com (Ian Merritt) (10/14/89)
I was looking through the tables and noticed that there is no correspondance between the V&H coordinates given and the latitude and longitude. It appears that the grid is skewed so that its vertical lines do not line up with the meridians on the map, its horizontals don't match the parallels, and to boot, it is numbered from the top down (i.e. 0h is somwehere around 70 degrees latitude, and it increases as north latitude decreases, and 0v is somewhere off the east coast and increases as you move west. Do you know what the basis is for the coordinate system used? Perhaps if not, you could pass this on to John Covert? [Moderator's Note: The above was written to Jon Solomon, who passed it along to the Digest for consideration by all subscribers. PT]
johnl@esegue.segue.boston.ma.us (John R. Levine) (10/15/89)
I can't say anything about the specific coordinate system that the V&H
tapes use, but I can contribute something I learned in a cartography
class a while ago. Using latitude and longitude to compute distances
is not easy because lines of longitude are not parallel. One minute
of longitude is longer in Miami than in Boston, so straightforward
sqrt(x*x + y*y) formulae would tend to overcharge customers in the
north and undercharge customers in the south.
This is closely related to the problem of producing maps on flat
pieces of paper. There are zillions of projections that cartographers
have used to map the curved surface of the earth to a flat map. The
most familar is the Mercator projection which preserves angles at the
cost of severe area and distance distortion. There are also
equal-area projections that distort angles so but make equal areas on
the map correspond to equal areas on the surface of the earth. In a
computer mapping project, I used the Albers equal area projection
which is commonly used for maps of the 48 states; it has an origin in
the Pacific, southwest of California, and distances measured in meters
north and east of that point. Plotting X and Y map coordinates give a
reasonable looking map since the projection has already been done.
The V&H tape uses some other projection that I expect is intended to
make equal distances equal. Any given projection is tuned to the area
that it is intended to display; the Albers projection is tuned for the
lower 48 and does not do very well for Alaska and Hawaii. I'd be
interested to hear if V&H has some non-linear hack for Alaska and
Hawaii, or if they figure that they're so far away from everything
else that the projection errors are unlikely to put many calls in the
wrong rate band.
Regards,
John Levine, johnl@esegue.segue.boston.ma.us, {spdcc|ima|lotus}!esegue!johnllevin@bbn.com (Joel B Levin) (10/17/89)
From johnl@esegue.segue.boston.ma.us: >The V&H tape uses some other projection that I expect is intended to >make equal distances equal. Any given projection is tuned to the area >that it is intended to display; the Albers projection is tuned for the >lower 48 . . . I also have no definitive answer. I have seen the map of the contiguous 48 states displayed against the grid, and an explanation that comes to mind is that the grid is tilted to allow the map to occupy the greatest amount of space within its bounding box, i.e., to maximize the scale used with certain coordinate limits. I don't know why this might be important, though. /JBL