From: Sharif Razzaque <sharif@lams.msd.lmsc.lockheed.com>
Newsgroups: info.grass.user
Subject: map projections vs. coordinate systems
Date: 6 Jul 1995 23:48:26 GMT
Organization: Lockheed Martin M & S, Sunnyvale, CASubject: map projections vs. coordinate systems
Hi,I've been reading these mailings for a while and I'm getting really
confused about the map projection discussions. Could you pl= ease
read my following assessment and let me know what you think?___________________________
There is a distinction between a coordinate system & a map
projection. Different coordinate systems are different ways of
referr= ing to the same points on the earth . On the other hand,
different map projections are just different ways of displaying the
earth=
For example, New York has the same lat. & long. (a coord-system)
whether we look at a Mercator, Orthographic, Sinusoidal Equal Ar= ea,
or Lambert Conformal Conic projection.
First, let's separate two classes of coordinate systems: 1) geographic
or good old lat-lon which is a ellipsoidal coordinate system and 2)
rectagular, cartesiand,flat sheet systems like UTM, State Plane
Coordinate Systems. Geocentric X-Y-Z could be added, but lets not get
too confused.
Points in NY can be referred to by geographic coordinates, but most
civil engineers, etc. will probably refer to NY's State Plane system
and the military fighting a battle at the Canadian border would use UTM.
The cartesian coordinates created by a cartographic projection are not
formally referred to as a "coordinate system" unless it is defined
as such by some institution. For example, NY SPCS must be ratified
by the NY legislature.
It seems that GRASS does NOT display maps in different projections.
The programs such as v.proj actually convert maps from one c=
oordinate system to another (i.e. from lat/lon to state-plane). Would
you say this is accurate?
GRASS supports different projections.
Data in one projection cartesian system can be change be changed to
another projection cartesian system by inverse projecting the data
to geographic coordinates and reprojecting in the target projection.
But neither cartesian system need be a official coordinate system
like UTM or SPCS.
Now what really confuses me is that these mail discussions & GRASS
itself uses the word `projection' in situations where `coordin= ate
system' seems more appropriate (like with v.proj). Even worse, I have
seen mail that talks about transforming maps from lat/lon = to mercator
or lambert conic. Lat/Long is a coordinate system (which tells us
nothing about how to display it), while mercator is a = projection
(which tells us nothing about which coordinate system to use).
First, a projection converts geographic data to cartesian data---
data on a plane. Thus any projected data can be viewed on a sheet of
paper or your monitor. Geographic coordinates can only be displayed
on an ellipsoid, *not* on a sheet of paper or your monitor. ANY
attempt to show the earth on a sheet of paper or plane surface
requires a projection.
The obvious reaction is: "but I see lat-lon lines on the map" or
plane surface. This is the gradicule which shows location of
constant parallels and meridians on the sheet. But they, like
everything else, are distorted by the projection.
As to what coordinate system you are using depends upon how you
are making measurements off the map. You can use any system which
is shown on the map. If the graticule is available, you can scale
off points by interpolating lat-lon. Similarly, if the SPCS grid
is printed, you can scale off in SPCS coordinates. But in this case,
it is helpful if the map is projected with the SPCS projection so
the grid will be cartesian on the map. But if you want to scale
SPCS off of a UTM projected map, the SPCS grid will be distorted so
care must be taken (just as trying to scale off geographic coordinates).
As and example, the USGS uses the polyconic projection for many of
its older 7.5' minute quadrangle maps at 1:24,000 and 1:25,000 scale.
These maps often have the UTM grid superimposed and tick marks for
the local SPCS grid system. Thus, I can scale data off the map in
one or all three of these coordinates systems (geographic being the
third). But the sheet itself is printed in a fourth coordinate
system (polyconic).
It certainly would not be unreasonable for a GRASS user to plot
a map with the UTM projection and superimpose a SPCS grid as
well as the UTM grid. A tad confusing, but possible.
Is my understanding of projections & coordinate systems right?
Furthermore, does GRASS indeed use the word `projection' the wrong=
way? Please let me know what you think or if I'm on the wrong track.
Thanks in advance!!
From what I have seen, most usage of the term projection by knowledgable
GRASS user is correct. Heaven help them if it isn't. 
The term projection applies to what kind of distortion method was
used in getting part of the surface on an ellipsoid converted
to a plane surface.
Sharif Razzaque
sharif@lams.msd.lmsc.lockheed.com
phone: (408) 756-4358 & 756-0494
As a recap. Formal "Coordinate Systems" like UTM, SPCS and many non-US
national systems are a way for users to plan in a comfortable,
cartesian coordinate system. All of these systems have an associated
cartographic projection that converts these systems to and from
geographic coordinates.
Maps are displays of geographic areas and *must* use a cartographic
projection which may or may not be the same as a formal coordinate
system covering the same area. It is helpful when the projection
of the map and the formal coordinate system coincide and thus
provide a cartesian display of the grid system on the map.
Gerald (Jerry) I. Evenden Internet: gie@charon.er.usgs.gov
voice: (508)563-6766 Postal: P.O. Box 1027
fax: (508)457-2310 N.Falmouth, MA 02556-1027