basic projection question

[Gerald I. Evenden]

>Date: Wed, 7 Jul 93 15:53:37 -0500
>From: Darrell McCauley <mccauley at ecn.purdue.edu>
>Sender: mccauley at ecn.purdue.edu
>To: grassp-list at max.cecer.army.mil
>In-Reply-To: <9307071359.AA01312 at charon.er.usgs.gov>
>Subject: Re:  basic projection question
>
>Gerald I. Evenden (gie at charon.er.usgs.gov) writes on 7 Jul 93:
>
>>You have totally lost me.
>
>and you were the only reply :-(
>
>Let me re-phrase the question. Forget about spheres
>and ellipsoids and earth for a second. I am coding up
>an algorithm that was written for points in a plane
>(call it x-y).  A line extends through two points,
>(x1,y1) and (x2,y2), both of which are in the first
>quadrant of a Cartesian coordinate system.  This line
>crosses the y-axis at some point. The angle 't'
>between the line and the axis is what I am interested
>in.
>
>     |           * (x2, y2)
>     |          /
>     |         /
>     |        *  (x1, y2)
>     |       /
>     |      /
>     -----------------------
>     |    /
>     |   /
>     |t /
>     | /
>     |/
>     |
>    /|
>   / |
>
>Calculation of the angle is straightforward in the
>x-y plane.

Certainly, the above is clear and elementary as long as we are
discussing a cartesian system.

>            Now enter the complexities of geo
>referenced data, an funny-shaped earth, etc. How would
>this angle be calculated using GRASS library
>functions? (Assuming that the data is in one of 
>the supported coordinate systesms.)

We are starting to issue several buzz words here and I think we need to
clarify our dictionaries.  We talk about "geo referenced data" and
"supported coordinate systems" and I am not sure what exactly you mean.
As far as I am concerned there are two basic systems for describing
a geographic point: the common spherical system using latitude, longitude
and height above the geoid and the x-y-z system usually associated with
satelite computations.  There are different datums or origin references
but I don't think you are concerned with these.

I am interpreting the phrase "supported coodinate systems" as really
meaning *transformations* between geographic coordinates and a
cartesian x-y system.  Certainly, UTM is one of the most common GRASS
transformations used and if you include the proj system that comes with
GRASS, there are at least 75 more that are also supported.

>I suspect that most users of this program that I'm
>writing will never have anything by x-y
								  ~~
                                  but ?
>(unreferenced) data, but I was hoping to do what
>is right-n-proper by including support for lat-long
>data.

"Unreferenced data?"  What do you mean?

I must assume by that sentence that you expect users to have cartesian
data for which they have no idea what the relationship is to the
geographic (lat-lon) coordinate system and how to transform such data
to same.  I hope this is not true, for if it is, I fail to see any
value in the data.

>--Darrell

Getting back to the angle per se.  Given that the angle is computed
in the cartesian system, what is its purpose in the geographic system?
Very few cartesian systems will give the above angular determination
any special significant in geographic space.  One case where it will,
is for the Mercator projection where what you have described is a
rhumb line and its azimuth.  That's why the Mercator projection is
still used for navigation charts.  But outside of navigation, I don't
think many users are interested in rhumb lines.

One of us just doesn't understand the problem.

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