working in conic projection

[Gerald I. Evenden]

>Date: Sun, 6 Mar 94 19:12:45 EST
>From: simon at artemis.earth.monash.edu.au (Simon Cox)
>To: grassu-list at amber.cecer.army.mil
>Subject: working in conic projection
>
>I would like some advice regarding working in projections other
>than lat-long or UTM.

First, lat-lon is *not* a projection system, it is a coordinate system.
UTM is a definition of a cartesian system and how it relates to the
the lat-lon system.  A *projection* is a mathematical translation
between coordinate systems.

>I have been assigned a project compiling a number of continental scale
>datasets for Australia.  It would probably be easiest to use Lat-Long
>as my base reference system.

And, IMHO, the best way to store the data.

>                             However, displaying or printing Australia
>in rectangular coordinates based on LL is fairly ugly - everything is
>squashed and stretched sideways.

Then, don't do it.  Don't confuse the data with the display.  The display
is used to portray the data in a manner that is coherent to the viewer.
The display may consist of any mechanism to transform the data between
the native data coordinates and the viewing coordinates.

>                                  Furthermore, many of the source data
>are found on hard-copy maps in conic projections - usually with standard
>parallels at 18oS and 36oS.  Thus, digitising these would be best done
>into a system that understands this projection.

No.  Digitizing programs do the inverse of the display: transform the
data out of the viewing space into the application space.

>When establishing a new location, GRASS gives the option "other projection"
>but when you choose this, you are pretty much left on your own.  Is this
>any different to using "x,y" - ie a plain vanilla cartesian system?
>If it _is_ something smarter than this, then how do I use it?  Ie, how do
>I specify the limits of a region, and what units should I use for
>the distance measurement?  Where is the documentation?

Ah, here's the problem.  If the map is properly annotated you should be
able to find all pertinent information in the legend as to projection,
constants used in the projection (standard parallels, etc.) that will
give sufficient information to the digitizing process to convert the
data back to geographic space.  BUT, a lot of people publish maps that do
not convey this data (may these people rot in Hell) and you are going
to have to apply your detailed knowledge in mathematical cartography to
figure out what they did. :-)

>The data will be a combination of raster and vector.  I guess (to repeat)
>I would be happiest referencing this using lat-long, but displaying in
>a simple conic, and being able to input from source material in simple
>conic.  Is GRASS really the tool for me here?

I do not know what you mean by "simple conic."  Equal area, conformal,
equidistant, or none of the above?  Some cartographic references will
use "simple" as equivalent to equidistant (Ptolomy, De l'Isle, ...).
I only mention this to emphasize that the problem of unannotated maps
is not simple.  There are lots of basic conic projections and the
next issue of PROJ.4 will support 9 of 'em and the Russians cooked
up at least as many more.  Fortunately, the first three are the most
frequently used.

>I'm sure I am being very naive, but this is a real problem and people
>are expecting a solution!
>
>Cheers
>
>Simon Cox

Indeed, digitizing from a souce with an unknown base is difficult.
There are some programs that try to analyze digitized points from known
geographic coordinates (such as graticule intersections) and make and
estimate as to projection and projection parameters and they may work
with common projections.  The alternative is to use bivatiate
polynomials based upon least-squares determination of the correction
for known points.

As far as documentation on this subject, you might look at the
first section of Snyder's "Computer-Assisted Map Projection Research,"
USGS Bull. 1629 (1985).

Gerald (Jerry) I. Evenden   Internet: gie at charon.er.usgs.gov
voice: (508)563-6766          Postal: P.O. Box 1027
  fax: (508)457-2310                  N.Falmouth, MA 02556-1027