# basic projection question

Gerald I. Evenden gie at charon.er.usgs.gov
Thu Jul 8 09:12:30 EDT 1993

```>Date: Wed, 7 Jul 93 22:05:32 -0500
>Message-Id: <9307080305.AA14794 at bushland.ecn.purdue.edu>
>From: Darrell McCauley <mccauley at ecn.purdue.edu>
>Sender: mccauley at ecn.purdue.edu
>To: grassp-list at max.cecer.army.mil
>Subject: Re: basic projection question
>
>Gerald I. Evenden (gie at charon.er.usgs.gov) writes on 7 Jul 93:
>
...
>
>coordinate system:
>        x,y (for imagery and other unreferenced data)

most imagery I'm familiar with is "referenced" to geographic location!

>        UTM
>        State Plane

both UTM and State Plane are x-y cartesian "systems"

>        Latitude-Longitude

geographic system

>        other projection

a projection per se is NOT a coordinate system.

...

>Second restatement (someone help - I must not be conveying this
>correctly). This is probably more detail than is useful, but
>I must be leaving something out somewhere.
>
>  1. I calculate the following statistic for x,y,z data:
>     (x and y are location - z is perhaps an elevation,
>      or a concentration, or whatever).
>
>     for all points separated by the vector h,
>        sum the squared differences in z values
>        and divide by the number of sample points.
>     call this value '2G'.
>
>     do this again for another vector (the same
>     direction as h, but with the magnitude incremented).
>
>     This gives values of '2G' at several increments
>     of the magnitude of h (called "lags").
>
>     Plot values of '2G' on one axis and ||h|| on another
>     axis. This is called a variogram.
>
>  2. I want to code this into GRASS as a sites program.  Some
>     users may have some data that's not in an x,y coordinate
>     system, and I'd my program to be able to deal with this.
>
>  3. As I understand it, distances are calculated like so:
>     G_begin_distance_calculations();
>     G_distance (x1, y1, x2, y2);
>     This gets me the magnitude of h - G_distance is supposedly
>     smart enough to take care of the details.
>
>  4. WHAT GRASS LIBRARY FUNCTIONS SHOULD I USE SO THAT I CALCULATE
>     THE ANGLE OF h?
>
>--Darrell

Ah, full circle.  Depends if you are in geographic space or cartesian
space! :-)

Sorry, there is no relationship between the angle in cartesian space
and the angle in geographic space UNLESS one knows the details of
the transformation between the two spaces.  One also does not flip
between cartesian and spherical coordinate operators without further
qualifications.  As I pointed out, the angle and the distance must
be qualified as either loxodrome or geodesic in spherical space.

I suggest you stick to cartesian space.

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

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