map projections vs. coordinate systems

[Gerald I. Evenden]

>From: Sharif Razzaque <sharif at 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, CA
>
>Subject: 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!!