Nabble - GIS-List

Re: excel 2007 - no dbf

2009-12-17T07:00:44Z

You have a few options depending on what version of ArcGIS you are using.
The last several versions (9.3, 9.2) have been able to directly load an
Excel spreadsheet. You can work directly from the spreadsheet similarly to
how you worked with a DBF. However, there are some limitations such as
they are read-only. Here is the online help for opening spreadsheets in
ArcGIS:

http://webhelp.esri.com/arcgisdesktop/9.2/index.cfm?TopicName=Working_with_Microsoft_Excel_files_in_ArcGIS

As with DBF, there are rules for field names such as they cannot contain
spaces. I have been able to export the spreadsheet table to DBF within
ArcMap and ArcCatalog. You can also export to comma-delimited and
tab-delimited text files. Or, if your spreadsheet contains X&Y
coordinates, you can create an event layer and even export to a feature
class or shapefile.

If you still need to be able to save from Excel to DBF, there is an Excel
plug-in for 2007 that I can recommend called SaveDBF. It is not free and
requires a "donation", but it works quite well.
http://thexlwiz.blogspot.com/2009/09/update-savedbf-add-in.html

Another option that has worked for me is to save your spreadsheet as a
comma-delimited (CSV) or tab-delimited (TXT) file in Excel. Either of
these can be loaded into ArcMap directly - though still keep in mind that
ArcMap will be picky about field names. Another issue with the text files
is that ArcMap will use the first row of values to determine the type of
values in each column. For example, if you have a column (field) of values
that are supposed to be of type double or floating point, but the first
value just happens to be an integer, ArcMap will probably return an error
when it gets to the first value that is a floating point value. There are
ways around this - such as moving a row that has correctly formatted
values in all columns to the top just below the headings.

I hope this helps!

Jennifer

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5th gvSIG Conference. Reports, posters and articles

2009-12-17T04:12:20Z

We would like to inform you of the availability of presentations,
posters and articles presented during the 5th gvSIG Conference [1]
which under the motto "We keep growing" brought together 500 attendees
from 27 countries.

The magazine Open Planet 3 [2] and the Live-DVD given during the
Conference [3] are available too.

Videos of presentations and workshops will be published shortly, in
Spanish as well as in English.

[1] http://jornadas.gvsig.org/comunicaciones/reports
[2] http://jornadas.gvsig.org/descargas/magazine
[3] http://jornadas.gvsig.org/descargas/live-dvd-1

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Re: excel 2007 - no dbf

2009-12-16T21:54:51Z

hi julia

try these steps

1. You can create your database in Excel 2007,
2. Save as Excel 97-2003 file
3. Import this file through data interoperability tool, if you have
4. it gets imported in geodatabase format, then you can open the sheet as new table

otherwise if you dont have this extension, you can save excel file as Text file and open the database in ARC GIS.

Hope it works for you

regards
hrishikesh

On Thu, 17 Dec 2009 06:04:43 +0530 wrote
>Other than going to third party software solutions, the only work around that I have found is to do the following:

- In Excel 2007, Go to "file > Save As.." and choose .csv

- Now open Access 2007 and Choose import data and select the csv file

- The data then loads into a table and from there you can export the data from Access into a DBF file! Choosing either DBF3, DBF4, DBF5

Not fun, but effective.

I hope this helps!

Analisa

-----Original Message-----
From: gislist-bounces+analisag=ecotrust.org@... [mailto:gislist-bounces+analisag=ecotrust.org@...] On Behalf Of Julia Reisemann
Sent: Wednesday, December 16, 2009 9:45 AM
To: gislist@...
Subject: [gislist] excel 2007 - no dbf

I use excel often to deal with/create dbfs for ArcGIS. Excel 2007
doesn't allow dbfs. So what do I do?

Suggestions are appreciated.

Thanks,

Julia

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**************************************************
R. HRISHIKESH MAHADEV
MS, M.Tech, B.E
Manager
**************************************************
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Re: excel 2007 - no dbf

2009-12-16T16:38:44Z

Other than going to third party software solutions, the only work around that I have found is to do the following:

- In Excel 2007, Go to "file > Save As.." and choose .csv

- Now open Access 2007 and Choose import data and select the csv file

- The data then loads into a table and from there you can export the data from Access into a DBF file! Choosing either DBF3, DBF4, DBF5

Not fun, but effective.

I hope this helps!

Analisa

-----Original Message-----
From: gislist-bounces+analisag=ecotrust.org@... [mailto:gislist-bounces+analisag=ecotrust.org@...] On Behalf Of Julia Reisemann
Sent: Wednesday, December 16, 2009 9:45 AM
To: gislist@...
Subject: [gislist] excel 2007 - no dbf

I use excel often to deal with/create dbfs for ArcGIS. Excel 2007
doesn't allow dbfs. So what do I do?

Suggestions are appreciated.

Thanks,

Julia

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Re: excel 2007 - no dbf

2009-12-16T10:57:39Z

The latest versions of ArcGIS import excel 2007 files directly. You can
then export the table which will create the .dbf file. You can then
make additions or corrections in the original excel file and re-import
the file and repeat the process.

Ritchie

-----Original Message-----
From: gislist-bounces+ritchie.eyster=ars.usda.gov@...
[mailto:gislist-bounces+ritchie.eyster=ars.usda.gov@...]
On Behalf Of Virginia Morris
Sent: Wednesday, December 16, 2009 11:59 AM
To: True, Diane
Cc: gislist@...
Subject: Re: [gislist] excel 2007 - no dbf

I've been doing the same thing as Diane - but I googled 'excel 2007 to
dbase
conversion' and found links to both free and proprietary conversion
programs. It might also be worthwhile to investigate some of these ...

On Wed, Dec 16, 2009 at 11:55 AM, True, Diane <truecd@...>
wrote:

> I "save as" Excel 2003 format, then open the workbook in ArcCatalog.
You

> can view the tables or export to .dbf in ArcCatalog.
>
>
> -----Original Message-----
> From: gislist-bounces+truecd=missouri.edu@... [mailto:
> gislist-bounces+truecd <gislist-bounces%2Btruecd>=missouri.edu@
> lists.geocomm.com] On Behalf Of Julia Reisemann
> Sent: Wednesday, December 16, 2009 11:45 AM
> To: gislist@...
> Subject: [gislist] excel 2007 - no dbf
>
> I use excel often to deal with/create dbfs for ArcGIS. Excel 2007
> doesn't allow dbfs. So what do I do?
>
>
>
> Suggestions are appreciated.
>
>
>
> Thanks,
>
>
>
> Julia
>
> _______________________________________________
> gislist mailing list
> gislist@...
> http://lists.geocomm.com/mailman/listinfo/gislist
>
> _________________________________
> This list is brought to you by
> The GeoCommunity
> http://www.geocomm.com/
> _______________________________________________
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>
> _________________________________
> This list is brought to you by
> The GeoCommunity
> http://www.geocomm.com/
>

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Re: excel 2007 - no dbf

2009-12-16T09:59:05Z

I've been doing the same thing as Diane - but I googled 'excel 2007 to dbase
conversion' and found links to both free and proprietary conversion
programs. It might also be worthwhile to investigate some of these ...

On Wed, Dec 16, 2009 at 11:55 AM, True, Diane <truecd@...> wrote:

> I "save as" Excel 2003 format, then open the workbook in ArcCatalog. You
> can view the tables or export to .dbf in ArcCatalog.
>
>
> -----Original Message-----
> From: gislist-bounces+truecd=missouri.edu@... [mailto:
> gislist-bounces+truecd <gislist-bounces%2Btruecd>=missouri.edu@
> lists.geocomm.com] On Behalf Of Julia Reisemann
> Sent: Wednesday, December 16, 2009 11:45 AM
> To: gislist@...
> Subject: [gislist] excel 2007 - no dbf
>
> I use excel often to deal with/create dbfs for ArcGIS. Excel 2007
> doesn't allow dbfs. So what do I do?
>
>
>
> Suggestions are appreciated.
>
>
>
> Thanks,
>
>
>
> Julia
>
> _______________________________________________
> gislist mailing list
> gislist@...
> http://lists.geocomm.com/mailman/listinfo/gislist
>
> _________________________________
> This list is brought to you by
> The GeoCommunity
> http://www.geocomm.com/
> _______________________________________________
> gislist mailing list
> gislist@...
> http://lists.geocomm.com/mailman/listinfo/gislist
>
> _________________________________
> This list is brought to you by
> The GeoCommunity
> http://www.geocomm.com/
>

Re: excel 2007 - no dbf

2009-12-16T09:55:02Z

I "save as" Excel 2003 format, then open the workbook in ArcCatalog. You can view the tables or export to .dbf in ArcCatalog.

-----Original Message-----
From: gislist-bounces+truecd=missouri.edu@... [mailto:gislist-bounces+truecd=missouri.edu@...] On Behalf Of Julia Reisemann
Sent: Wednesday, December 16, 2009 11:45 AM
To: gislist@...
Subject: [gislist] excel 2007 - no dbf

I use excel often to deal with/create dbfs for ArcGIS. Excel 2007
doesn't allow dbfs. So what do I do?

Suggestions are appreciated.

Thanks,

Julia

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excel 2007 - no dbf

2009-12-16T09:45:25Z

I use excel often to deal with/create dbfs for ArcGIS. Excel 2007
doesn't allow dbfs. So what do I do?

Suggestions are appreciated.

Thanks,

Julia

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GPS Almanac Updates (GeoXT)

2009-12-08T13:36:55Z

Hello, I'd like to get an understanding of GPS almanacs. More specifically,
how they are updated. I use a Trimble GeoXT and sometimes there are large
gaps between its use.

1. How do I know if I have the latest almanac? Will the GPS not function
w/out the latest? If it WILL function w/out the latest, is the quality of
the output now as good? I am currently working w/an almanac dated 8/16/09.
2. How is the almanac update process initiated? Is it initiated the when
the GPS is activated by any program (ArcPad) or does the GPS have to be
initiated by a specific/proprietary program such as "GPS Controller" for
Trimble products.
3. The GeoXT updates its almanac over the air. Can an update also be done
manually off the internet? If so, where can an update be downloaded from?
And does each GPS manufacturer have a different file format for this update.

Any and all input would be great.

Thank you,
Sachin

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Re: Vacancies in UAE

2009-12-08T04:29:40Z

Dear Sir,
I am writing this letter in reference to the vacancy available with your esteemed organization for the post of ‘GIS surveyor'. I am highly pleased to apply for this job that I am also enclosing my resume with this cover letter.
I have a bachelor’s degree as well as a master’s degree in Geo-Science from an esteemed University. I am very well versed in field geology, observing aerial & satellite images, understanding important seismic, geophysical and topographical data. I have an extensive experience in this field and I have full knowledge of GIS packages. In addition, my desire for learning with being an active and creative person will hopefully qualify me in being employed as an element in your firm.
I would be very obliged if you can arrange for an interview where I can further discuss about my qualifications and skills. I am enclosing my resume with this cover letter. Please go through it and let me know the career prospects.
Thanks for taking the time to consider my application.
Sincerely,
Yunus Ali.P

DARPA Network Challenge

2009-12-02T13:50:56Z

DARPA, the folks that originally inverted the Internet, are having a wacky
spatially-related contest this weekend involving GPS:
http://networkchallenge.darpa.mil/

There has already been much speculation about using GIS or remote sensing to located the
balloons, but much of it is hindered by the fact that there is no good/fast/widely
available imagery one could search. One could probably eliminate much of the US by
buffering the road network, since the rules state the targets will be visible from a road,
but it still leaves a huge unknown area. One team claims to have even predicted where 1-5
of the balloons will be based "(thanks to help from Mekow334 and HotJazz, our expert
balloon sleuths, who know their way around a satellite and a GPS log like nobody else!)"

I'm somewhat skeptical, since their countdown clock isn't even counting down to the
right time.

I’ve established a team of my own, called Team DeciNena. We will win because we have the
wittiest name. ;)

No, seriously, whomever wins will be using a mixture of all sorts of tactics from team
recruiting to passive data mining. I'm sure there will be a lot of disinformation out
there, and it will be important to combat it. We are using a mashup of GIS/GoogleMaps
technologies in a Drupal-based Content Management System to coordinate our team. If we get
a report, we can spatially query our member database to find other nearby team members who
can confirm the report. We're also experimenting with Google Wave to see if it has
anything interesting to offer.

Join us, it's free, and you could actually win something. We're even sharing some reward
money with those team participants who DON'T themselves find a balloon.

http://decinena.com

--
Chris 'Xenon' Hanson, omo sanza lettere Xenon AlphaPixel.com
PixelSense Landsat processing now available! http://www.alphapixel.com/demos/
"There is no Truth. There is only Perception. To Perceive is to Exist." - Xen
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Re: Identify

2009-12-02T02:55:30Z

| I have a strange problem I am using ARC view 9.1 and I have lost my
| Identify box (the button is still there and still works) but no box comes
| up to show the information. I have tried reloading Arc view and even a
| complete shut down of my work station/computer. any suggestions? thank
| you

Carl,
Could it be that the box is displayed off screen?
(to get it back, do this - start ArcMap fresh, click with the identify tool anywhere so that it should pop up. Next - alt-space (system menu) and press 'm' (for move, only works on English windows) - and one of the arrow keys. Then you should be able to move this window with your mouse.

Also try deleting your normal.mxt in the application data folder.

Cheers,
Hugo

--
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-------------------------------------------------------------
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Phone: +46 75 7575284
Nordpil Fax: +46 8 6747020
http://nordpil.com Mobile: +46 733 467111
Skype: callto:hugo.ahlenius

vCard: http://nordpil.com/hugoahlenius.vcf
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Identify

2009-12-01T08:39:11Z

To all;

I do not know why the identify box went away or where it was hidden. However I just got it back by loading an arc map session I used several monts ago (I tried reloading a new clean .mxt file which did not work). I tried some of the other suggestion that were made, the ones that I coul implement did not work, however thank you all for all of your help.

Carl Nelson
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Identify

2009-12-01T07:11:06Z

To all;

I have a strange problem I am using ARC view 9.1 and I have lost my Identify box (the button is still there and still works) but no box comes up to show the information. I have tried reloading Arc view and even a complete shut down of my work station/computer. any suggestions? thank you

Carl Nelson
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Re: saving to a personal geodatabase

2009-11-25T13:43:21Z

Hi Rick:

I have sometimes seen similar behaviour when the destination disk gets
physically or logically full (i.e. via disk quotas). The second case is
particularly frustrating because the quotas, as they are administered at
my institution, can be somewhat invisible so no one has a clue what went
wrong.

I don't know if that is the source of your students' frustration, but
it might be worth checking which students were writing to their own
drives and which were writing to your institution's disks.

Joe

--

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

On sabbatical in 2009

Joseph M. Piwowar, Ph.D.
Associate Professor
Canada Research Chair in Geomatics & Sustainability
Geography Graduate Coordinator
Director, TERRA Lab
Department of Geography
University of Regina
Regina, SK S4S 0A2
Canada

joe.piwowar@...
http://uregina.ca/piwowarj
tel: +1.306.585.5273
fax: +1.306.585.4815

"Discovery consists of
seeing what everybody has seen and
thinking what nobody has thought."
~ Albert von Szent-Gyorgyi
PBefore printing, think about the environment / Avant l'impression,
pensez à l'environnement.

>>> On 2009.11.25 at 3:28 PM, "RICK GRAY"
<RGRAY@...> wrote:
> I know this is probably best answered by ESRI directly, but I've
found that
> this list is usually just as knowledgeable and often quicker to
respond.
>
> The first group of students had to hand in their GIS projects today.
>
> A couple of my students have tried importing files into a personal
> geodatabase as required, but have run into a problem. They can import
some
> files, but not others, yet the files are all of the same type (i.e.
> shapefiles or orthophotos). Other students have no issue with the
same files.
>
> In one case ArcCatalog goes through the import process as if
everything is
> OK, but the geodatabase does not have the new file. There are no
error
> messages. In this case it was a 1.7 MB photo. But shape files
imported easily
> and there are already 2 other photos of the same type and size in the

> geodatabase. The geodatabase was nowhere near its size limitation
(probably
> only 4-5 MB of data in it). We checked to see if they had sufficient
space in
> the hard drive and they had lots.
>
> In another case, the students simply got error messages that it could
not
> write to the geodatabase. All students are working with the same
basic file
> set and most have had no problems.
>
> The third and most troubling case was that one group of students
tried
> importing the raster images into the geodatabase but when it was
taking too
> long they canceled the process. Now their geodatabase is corrupted
and cannot
> be accessed which means that their project cannot be run. Is there
possibly a
> workaround to fix this?
>
> I know some of my descriptions are perhaps a bit vague, but this all

> occurred in class a couple of hours ago and I am just now getting a
chance to

> send the email.
>
> Hopefully someone can point me to answers.
>
> Thanks a million,
> Rick Gray
>
> _______________________________________________
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>
> _________________________________
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saving to a personal geodatabase

2009-11-25T13:28:30Z

I know this is probably best answered by ESRI directly, but I've found that this list is usually just as knowledgeable and often quicker to respond.

The first group of students had to hand in their GIS projects today.

A couple of my students have tried importing files into a personal geodatabase as required, but have run into a problem. They can import some files, but not others, yet the files are all of the same type (i.e. shapefiles or orthophotos). Other students have no issue with the same files.

In one case ArcCatalog goes through the import process as if everything is OK, but the geodatabase does not have the new file. There are no error messages. In this case it was a 1.7 MB photo. But shape files imported easily and there are already 2 other photos of the same type and size in the geodatabase. The geodatabase was nowhere near its size limitation (probably only 4-5 MB of data in it). We checked to see if they had sufficient space in the hard drive and they had lots.

In another case, the students simply got error messages that it could not write to the geodatabase. All students are working with the same basic file set and most have had no problems.

The third and most troubling case was that one group of students tried importing the raster images into the geodatabase but when it was taking too long they canceled the process. Now their geodatabase is corrupted and cannot be accessed which means that their project cannot be run. Is there possibly a workaround to fix this?

I know some of my descriptions are perhaps a bit vague, but this all occurred in class a couple of hours ago and I am just now getting a chance to send the email.

Hopefully someone can point me to answers.

Thanks a million,
Rick Gray

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Re: multiring buffers in ArcMap

2009-11-19T14:15:03Z

Thanks, Jeremy.

These things seem so simple when you know how to do them. Unfortunately the
Help in ArcMap isn't very good about many things. Even knowing now that there is
a buffer wizard, I cannot find any reference to it in Help.

Cheers,
Rick

BTW, for anyone (like me) that didn't know how to do this, there are very
straightforward instructions at
http://ic.ucdavis.edu/information/BufferWizardArcGIS9.pdf

>>> Jeremy Olynik <jeremy_olynik@...> 11/19/2009 4:15 PM >>>

Hi Rick,

You can simply add the buffer wizard through customizing a toolbar. Locate the
buffer wizard icon and drag it on to a toolbar. It has an option to create
multiple ring buffers.

> Date: Thu, 19 Nov 2009 16:08:11 -0500
> From: rgray@...
> To: gislist@...
> Subject: [gislist] multiring buffers in ArcMap
>
> In ArcView 3 it was easy to create, for example, a buffer with 20 rings at 1
meter each.
>
> In ArcMap 9 I can only figure out how to enter individual ring distances in
the Multiring Buffer tool in ArcToolbox. Because of the number of rings
required, and the desire to try multiple variations, this is painfully slow.

>
> Is there a way in ArcMap to do what I want?
>
> Rick Gray
> _______________________________________________
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>
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multiring buffers in ArcMap

2009-11-19T13:08:11Z

In ArcView 3 it was easy to create, for example, a buffer with 20 rings at 1 meter each.

In ArcMap 9 I can only figure out how to enter individual ring distances in the Multiring Buffer tool in ArcToolbox. Because of the number of rings required, and the desire to try multiple variations, this is painfully slow.

Is there a way in ArcMap to do what I want?

Rick Gray
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Re: Projections, co-ordinate systems, datums, spheroids, geoids etc.

2009-11-19T10:25:13Z

Thank you to everyone for responding in the list! This way those of us who
hadn't asked the question (yet) also had the chance to learn - and I have
suggested that some friends also check out this thread.

On Thu, Nov 19, 2009 at 11:26 AM, Landon Blake <lblake@...> wrote:

> Bill,
>
> This was an excellent post. I think you should write a white paper. :]
>
> Landon
> Office Phone Number: (209) 946-0268
> Cell Phone Number: (209) 992-0658
>
> -----Original Message-----
> From: gislist-bounces+lblake=ksninc.com@...
> [mailto:gislist-bounces+lblake <gislist-bounces%2Blblake>=ksninc.com@
> lists.geocomm.com] On Behalf
> Of Quantitative Decisions
> Sent: Wednesday, November 18, 2009 11:54 AM
> To: gislist@...
> Subject: Re: [gislist] Projections, co-ordinate systems, datums,
> spheroids, geoids etc.
>
> This morning Gilllian McGregor asked,
> >I would like to clarify the use and definition of a range of terms ...
> I
> >would like to understand better, with regard to ... a better
> definition,
> >when they are used and why they are used and how they relate to one
> another.
>
> The terms include
>
> Geoid
> Ellipsoid
> Datum
> Coordinate system
> Projection.
>
>
> A helpful respondent wrote:
>
> >A projection is the systematic mathematical transformation of the
> "round"
> >surface so that it will lay flat. Different projections try to minimize
>
> >what gets distorted and by how much and which you utilize will be
> >partially dependent on what you want to display in your final map (is
> >preserving area more important than direction, etc).
>
> This is excellent. Although everything that followed it was helpful for
>
> the intuition and consistent with what is taught and "known" among GIS
> professionals, it nevertheless bears closer examination in the
> details. Let's look.
>
>
> >There are 3 "developable surfaces" that projections are based on - the
> >cylinder, the cone and the plane.
>
> This is true for some projections but not all. Many modern projections,
>
> such as many of those developed by the late John Snyder at the USGS, are
>
> not "based" on any developable surface in any fundamental or important
> way.
>
> An equivalent way to think of a "projection" of any surface is that it
> assigns a pair of real numbers to each point on the surface. When you
> interpret those numbers as Cartesian coordinates in the plane, you have
> drawn a map. That's all there is to map projection.
>
> (BTW, there are many more developable surfaces than these three. By
> definition these are surfaces that can be "unrolled": they have
> everywhere
> zero Gaussian curvature but are not necessarily planar. One example is
> the
> elliptical cylinder related to a transverse Mercator projection from an
> ellipsoid. For more fanciful examples, take any sheet of paper and roll
>
> its corners and edges into any shape you can without creating folds.)
>
>
> >Different people (Clarke, etc.) have defined the spheroid or ellipsoid
> >mathematically and this goes into the projection formula.
>
> This is less a matter of mathematics than of measurement. A spheroid is
> an
> imaginary surface coincident with the earth (and rotating and moving
> through the universe with it). At any given time, the spheroid provides
> a
> way of identifying all points in the universe by means of two things: a
> point on the spheroid itself and a distance up or down, perpendicular to
>
> the spheroid, from that point.
>
> What makes a spheroid useful is that it has a simple mathematical
> description, unlike the actual surface of a planet. Thus, ellipsoids of
>
> revolution (or sometimes triaxial ellipsoids) are used as references for
>
> the spheroids of planets and planetoids because of their mathematical
> simplicity. Having elected to use, say, an ellipsoid of revolution, one
>
> then makes measurements of selected points on the planet's surface and
> finds an ellipsoid that best approximates those measured points in some
> sense.
>
> There are many ellipsoids in use for mapping the earth because (a)
> historically measurements have gotten better, (b) the earth's surface is
>
> constantly changing shape, (c) criteria to compare the ellipsoid with
> the
> measured locations can vary, and--most importantly--(d) many different
> sets
> of measurements have focused on relatively small patches of the earth's
> surface. An ellipsoid that fits one patch well does not necessarily fit
>
> the rest of the earth's surface well. That's why an ellipsoid suitable
> for
> the UK is unlikely to be used for distant South Africa, for instance.
>
>
> > To refine it even more, we use the term geoid to explain the bumps
> and
> > hollows of the ocean depths and mountain peaks.
>
> No, this is incorrect. There is a unique geoid defined as a particular
> a
> gravitational equipotential surface. As such, it depends on the
> distribution of mass within a planet, not on the form its surface
> takes. On the earth, the geoid varies only a little from any decent
> ellipsoid; the variation rarely exceeds 100 meters. That obviously does
>
> not "explain" ocean depths or mountain peaks, which are local variations
>
> two orders of magnitude greater. Moreover, the geoid's undulations do
> not
> exactly follow all mountain ranges or ocean floors, although there is a
> close correlation.
>
> Of the many possible such equipotential surfaces for the earth
> (differing
> only in height), the geoid is the one along which the surface of the
> oceans
> would lie were there no winds, waves, currents, or tides. (See the
> Wikipedia article at http://en.wikipedia.org/wiki/Geoid .)
> Equipotential
> surfaces of gravity are of interest in geodesy primarily because at any
> point within the influence of earth's gravitation, "up" is always
> perpendicular to the equipotential surface at that point. Because the
> "up"
> direction is used to measure things like geodetic latitude and
> longitude,
> which by definition are determined by the direction perpendicular to the
>
> *ellipsoid*, any deviations between the geoid and whatever ellipsoid is
> being used will oblige us to make corrections in geodetic measurements.
>
> BTW, the mechanism we use to represent the ocean floor and mountain
> peaks,
> as well as everything in between, is called a digital elevation model
> (or
> digital terrain model).
>
>
> >Again, this must be at a fairly coarse resolution because your computer
>
> >would be crunching numbers for days if we wanted to be extremely
> accurate.
>
> There's nothing the matter with this statement, but it reflects a
> philosophy that IMHO reverses priorities, although I'm sure that's not
> what
> was intended. It seems to suggest that the accuracy we accept in our
> work
> should be determined by the computer's capabilities. Yes, compromises
> must
> be made, but especially with today's power, it should work the other
> way:
> you, as the user of the data, should begin by determining the accuracy
> you
> need. Then you set up a system capable of delivering that accuracy. If
>
> you need the submicron-level accuracy that would be delivered by using a
>
> geoid instead of an ellipsoid, then you should compute with the geoid.
> It
> wouldn't cost you days: the calculations aren't that much more involved
> (but it's a real pain to program and simply not worth the effort). The
> real point is that imprecision in all the other data we have is vastly
> greater than the imprecision created by using an ellipsoid instead of
> the
> geoid.
>
>
> >Then we get to the datum. This is the mathematical surface that fits
> >closely to the mean sea level of the earth and to which ground control
> >point are referenced. Here in North America our maps used to use NAD27
>
> >(North American Datum 1927) as a final refinement.
>
> These statements actually are contradictory, because NAD27 is neither a
> mathematical surface nor a refinement at all: it's actually a gross,
> unintended distortion of a datum.
>
> A datum, in its broadest sense, is a system set up to let us find (via
> measurement) the point on an ellipsoid (and elevation relative to that
> point) corresponding to any physical point on or near the earth's
> surface. This can be done in many ways. For NAD27 it consists of a
> network of thousands of points laid across the US. To each point was
> associated, once and for all (although with great inaccuracy for today's
>
> needs) a point on the Clarke 1866 ellipsoid. To locate any point in
> North
> America, a surveyor finds one or more nearby points in this network and
> makes measurements relative to them. With the capabilities afforded by
> modern instruments (e.g., GPS), to define a datum it now suffices to
> provide an ellipsoid and a single reference location, reference
> direction,
> and reference height on the earth's surface. The example of NAD27
> reminds
> us that this is not the only way to establish a datum, though.
>
> The fact that NAD27 is not a mathematical surface, nor even a refinement
> of
> one, is made apparent by NADCON and VERTCON, the apparatus needed to
> relate
> NAD27 to other datums. These algorithms require a database that
> essentially records the errors (usually at quarter degree intervals)
> made
> within the NAD27 geodetic reference network across North America. The
> errors often reach hundreds of meters, especially in northwestern US and
>
> outside the conterminous US. Older datums in Canada and Australia
> require
> similar methods of correction.
>
>
> >In 83, a new datum (NAD 83) used our new knowledge, based on satellite
> >measurements, to more accurately pinpoint the centre of the earth as
> the
> >reference point, which helped to remove the error as you moved across
> the
> >continent. Again, this is just a mathematical refinement to the
> projection
> >when used at a more local level.
>
> The new datum was needed in part because of the large errors introduced
> in
> the network of NAD 27 reference points, not to "pinpoint the center of
> the
> earth." Indeed, even today many datums use ellipsoids whose centers do
> *not* coincide with that of the earth, and this is on purpose: it's not
> an
> error. The reason is that these datums attempt to approximate one small
>
> patch of the earth, such as a single country, as well as possible, and
> in
> so doing it just turns out that the ellipsoid is not concentric with the
>
> geoid. This is why we need those seven-parameter datum transformations:
>
> three parameters to shift the ellipsoids, three to rotate them, and one
> to
> rescale their size.
>
> None of this has anything to do with projections. We're talking about
> establishing ways to identify points on the earth with points on an
> ellipsoid, period. The projection comes only when you decide to make a
> map. You make a map in two steps: the datum supplies you with a point
> on
> the ellipsoid, then a mathematical formula--the projection
> itself--derives
> Cartesian coordinates (x,y) from that point.
>
>
> >A Mercator projection uses the cylinder as its developable surface. If
> you
> >picture wrapping a tube around the globe with its open ends at the
> poles,
> >and "projecting" a light from the centre of the globe outwards onto the
>
> >tube, you sort of get the image.
>
> Yes, but the "sort of" hides some important details. The Mercator
> projection also includes an exponential distortion of the north-south
> distances, even after this geometric projection operation is carried
> out:
> it is _not_ the same as the light-and-shadow process described. This is
>
> true of many projections: although in some loose intuitive sense they
> are
> "based" on geometric projections onto a developable surface, that's not
> really how they work. That's why we need the more general mathematical
> idea of projection introduced earlier.
>
>
> >Because the tube touches only at the equator, that is the point where
> the
> >distortion will be the least. Hence the world maps we used to always
> see
> >had the lands at the top and bottom greatly stretched because they used
> a
> >Mercator projection (Greenland isn't really as big as Brazil).
>
> Again, sort of. The distortion in the Mercator projection has little to
> do
> with tubes or "touching" the equator. It is inherent in the mathematics
> of
> the projection. The distortion is a phenomenon better understood by
> considering the map scale in two directions at every point: east-west
> and
> north-south. The Mercator has the special property of being conformal,
> which implies those two scales are always equal. Up and down the map,
> from
> north to south, the common scale will increase with increasing distance
> from the equator. It becomes unbounded as the poles are approached.
>
>
> >To make a "transverse" Mercator, we simply rotate the cylinder or tube
> to
> >run crosswise to the globe.
>
> A minor point: that method works when using a perfect sphere for the
> datum;
> mathematically it's more complicated for an ellipsoid, because a
> meridian
> then has the shape of an ellipse, not of a circle.
>
>
> >Now the area of least distortion follows a meridian from north to
> south.
> >We then decide (well, somebody decided) that a 6 degree swath is as
> wide
> >as we need for one zone in order to minimize distortion.
>
> This does not by any means "minimize" distortion. You can make
> distortion
> smaller still in many ways, such as by using narrower zones. This point
>
> goes back to the philosophical issue raised earlier: the design of UTM
> began with a target for scale accuracy. In turns out this target is met
> by
> using reference circles approximately 500 km apart and limiting the
> projection to a swath approximately 800 km wide (seven degrees at the
> equator). Successive swaths in the UTM system overlap at the equator by
>
> one degree apiece, whence 60 swaths are needed to cover the lower
> latitudes
> of the globe. (A different projection altogether is used for the polar
> regions in UTM.)
>
> BTW, there's more to UTM than this. It also includes a hierarchical,
> tree-like organization of regions within each UTM zone. However, this
> additional structure is rarely used within GIS. It can become important
>
> for interpreting certain military coordinates.
>
>
> >As for a coordinate system, that is merely a method of identifying a
> >location (x,y and perhaps z) on your globe or map. We use degrees,
> minutes
> >and seconds for the 3D globe because that has been the tradition.
>
> Thus, fundamentally, a 3D coordinate function consists of the following:
>
> (1) A set of points, "M", in 3D Euclidean space endowed with its
> Cartesian coordinates (x,y,z).
>
> (2) A mechanism to associate a unique point near the earth's surface
>
> with each (x,y,z) in M.
>
> (3) Units of measurement, such as feet, meters, or degrees, for x,
> y,
> and z.
>
> Typically, the mechanism in (2) is "adapted" to the ellipsoid in the
> sense
> that the ellipsoid itself is a level surface of the z coordinate and, to
> a
> good approximation, 'z' can be interpreted as height relative to the
> ellipsoid. Consequently, (x,y) can be taken as coordinates for the
> ellipsoid itself and 'z' can be taken as elevation.
>
> If this sounds like a "projection," you're hearing right: there's a
> projection lurking here. Remember that a projection assigns coordinates
> to
> physical points. A coordinate function as just defined does the
> opposite:
> it assigns physical points to coordinates. But in most cases you can go
> in
> reverse: each physical point usually has only one set of
> coordinates. Assigning those coordinates to the point and forgetting
> about
> the 'z' part constitutes a projection. It's a subtle difference, but it
>
> affords ample opportunity for confusion.
>
> BTW, in mathematics a coordinate function is usually defined in the same
>
> way a "projection" is defined here. This is not the place to unravel
> differences in terminology. The important thing is to understand the
> distinction being made between assigning coordinates to points and
> assigning points to coordinates. Both mechanisms are important and
> useful;
> both are very closely related; but they are distinct things.
>
> The idea of "coordinate system" generalizes this: it can comprise more
> than
> one coordinate function. UTM is the archetypical example: it includes
> more
> than 60 coordinate functions. To designate a point on the earth in UTM,
>
> then, you have to specify one of its coordinate function (which amounts
> to
> naming the UTM zone) along with the (x, y) or (x, y, z) coordinates that
>
> will be interpreted in terms of that coordinate function. The State
> Plane
> systems in the U.S. provide another example of a coordinate system that
> is
> not merely one coordinate function.
>
> Best,
>
> Bill Huber
> Quantitative Decisions
>
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Re: Projections, co-ordinate systems, datums, spheroids, geoids etc.

2009-11-19T09:26:28Z

Bill,

This was an excellent post. I think you should write a white paper. :]

Landon
Office Phone Number: (209) 946-0268
Cell Phone Number: (209) 992-0658

-----Original Message-----
From: gislist-bounces+lblake=ksninc.com@...
[mailto:gislist-bounces+lblake=ksninc.com@...] On Behalf
Of Quantitative Decisions
Sent: Wednesday, November 18, 2009 11:54 AM
To: gislist@...
Subject: Re: [gislist] Projections, co-ordinate systems, datums,
spheroids, geoids etc.

This morning Gilllian McGregor asked,
>I would like to clarify the use and definition of a range of terms ...
I
>would like to understand better, with regard to ... a better
definition,
>when they are used and why they are used and how they relate to one
another.

The terms include

Geoid
Ellipsoid
Datum
Coordinate system
Projection.

A helpful respondent wrote:

>A projection is the systematic mathematical transformation of the
"round"
>surface so that it will lay flat. Different projections try to minimize

>what gets distorted and by how much and which you utilize will be
>partially dependent on what you want to display in your final map (is
>preserving area more important than direction, etc).

This is excellent. Although everything that followed it was helpful for

the intuition and consistent with what is taught and "known" among GIS
professionals, it nevertheless bears closer examination in the
details. Let's look.

>There are 3 "developable surfaces" that projections are based on - the
>cylinder, the cone and the plane.

This is true for some projections but not all. Many modern projections,

such as many of those developed by the late John Snyder at the USGS, are

not "based" on any developable surface in any fundamental or important
way.

An equivalent way to think of a "projection" of any surface is that it
assigns a pair of real numbers to each point on the surface. When you
interpret those numbers as Cartesian coordinates in the plane, you have
drawn a map. That's all there is to map projection.

(BTW, there are many more developable surfaces than these three. By
definition these are surfaces that can be "unrolled": they have
everywhere
zero Gaussian curvature but are not necessarily planar. One example is
the
elliptical cylinder related to a transverse Mercator projection from an
ellipsoid. For more fanciful examples, take any sheet of paper and roll

its corners and edges into any shape you can without creating folds.)

>Different people (Clarke, etc.) have defined the spheroid or ellipsoid
>mathematically and this goes into the projection formula.

This is less a matter of mathematics than of measurement. A spheroid is
an
imaginary surface coincident with the earth (and rotating and moving
through the universe with it). At any given time, the spheroid provides
a
way of identifying all points in the universe by means of two things: a
point on the spheroid itself and a distance up or down, perpendicular to

the spheroid, from that point.

What makes a spheroid useful is that it has a simple mathematical
description, unlike the actual surface of a planet. Thus, ellipsoids of

revolution (or sometimes triaxial ellipsoids) are used as references for

the spheroids of planets and planetoids because of their mathematical
simplicity. Having elected to use, say, an ellipsoid of revolution, one

then makes measurements of selected points on the planet's surface and
finds an ellipsoid that best approximates those measured points in some
sense.

There are many ellipsoids in use for mapping the earth because (a)
historically measurements have gotten better, (b) the earth's surface is

constantly changing shape, (c) criteria to compare the ellipsoid with
the
measured locations can vary, and--most importantly--(d) many different
sets
of measurements have focused on relatively small patches of the earth's
surface. An ellipsoid that fits one patch well does not necessarily fit

the rest of the earth's surface well. That's why an ellipsoid suitable
for
the UK is unlikely to be used for distant South Africa, for instance.

> To refine it even more, we use the term geoid to explain the bumps
and
> hollows of the ocean depths and mountain peaks.

No, this is incorrect. There is a unique geoid defined as a particular
a
gravitational equipotential surface. As such, it depends on the
distribution of mass within a planet, not on the form its surface
takes. On the earth, the geoid varies only a little from any decent
ellipsoid; the variation rarely exceeds 100 meters. That obviously does

not "explain" ocean depths or mountain peaks, which are local variations

two orders of magnitude greater. Moreover, the geoid's undulations do
not
exactly follow all mountain ranges or ocean floors, although there is a
close correlation.

Of the many possible such equipotential surfaces for the earth
(differing
only in height), the geoid is the one along which the surface of the
oceans
would lie were there no winds, waves, currents, or tides. (See the
Wikipedia article at http://en.wikipedia.org/wiki/Geoid .)
Equipotential
surfaces of gravity are of interest in geodesy primarily because at any
point within the influence of earth's gravitation, "up" is always
perpendicular to the equipotential surface at that point. Because the
"up"
direction is used to measure things like geodetic latitude and
longitude,
which by definition are determined by the direction perpendicular to the

*ellipsoid*, any deviations between the geoid and whatever ellipsoid is
being used will oblige us to make corrections in geodetic measurements.

BTW, the mechanism we use to represent the ocean floor and mountain
peaks,
as well as everything in between, is called a digital elevation model
(or
digital terrain model).

>Again, this must be at a fairly coarse resolution because your computer

>would be crunching numbers for days if we wanted to be extremely
accurate.

There's nothing the matter with this statement, but it reflects a
philosophy that IMHO reverses priorities, although I'm sure that's not
what
was intended. It seems to suggest that the accuracy we accept in our
work
should be determined by the computer's capabilities. Yes, compromises
must
be made, but especially with today's power, it should work the other
way:
you, as the user of the data, should begin by determining the accuracy
you
need. Then you set up a system capable of delivering that accuracy. If

you need the submicron-level accuracy that would be delivered by using a

geoid instead of an ellipsoid, then you should compute with the geoid.
It
wouldn't cost you days: the calculations aren't that much more involved
(but it's a real pain to program and simply not worth the effort). The
real point is that imprecision in all the other data we have is vastly
greater than the imprecision created by using an ellipsoid instead of
the
geoid.

>Then we get to the datum. This is the mathematical surface that fits
>closely to the mean sea level of the earth and to which ground control
>point are referenced. Here in North America our maps used to use NAD27

>(North American Datum 1927) as a final refinement.

These statements actually are contradictory, because NAD27 is neither a
mathematical surface nor a refinement at all: it's actually a gross,
unintended distortion of a datum.

A datum, in its broadest sense, is a system set up to let us find (via
measurement) the point on an ellipsoid (and elevation relative to that
point) corresponding to any physical point on or near the earth's
surface. This can be done in many ways. For NAD27 it consists of a
network of thousands of points laid across the US. To each point was
associated, once and for all (although with great inaccuracy for today's

needs) a point on the Clarke 1866 ellipsoid. To locate any point in
North
America, a surveyor finds one or more nearby points in this network and
makes measurements relative to them. With the capabilities afforded by
modern instruments (e.g., GPS), to define a datum it now suffices to
provide an ellipsoid and a single reference location, reference
direction,
and reference height on the earth's surface. The example of NAD27
reminds
us that this is not the only way to establish a datum, though.

The fact that NAD27 is not a mathematical surface, nor even a refinement
of
one, is made apparent by NADCON and VERTCON, the apparatus needed to
relate
NAD27 to other datums. These algorithms require a database that
essentially records the errors (usually at quarter degree intervals)
made
within the NAD27 geodetic reference network across North America. The
errors often reach hundreds of meters, especially in northwestern US and

outside the conterminous US. Older datums in Canada and Australia
require
similar methods of correction.

>In 83, a new datum (NAD 83) used our new knowledge, based on satellite
>measurements, to more accurately pinpoint the centre of the earth as
the
>reference point, which helped to remove the error as you moved across
the
>continent. Again, this is just a mathematical refinement to the
projection
>when used at a more local level.

The new datum was needed in part because of the large errors introduced
in
the network of NAD 27 reference points, not to "pinpoint the center of
the
earth." Indeed, even today many datums use ellipsoids whose centers do
*not* coincide with that of the earth, and this is on purpose: it's not
an
error. The reason is that these datums attempt to approximate one small

patch of the earth, such as a single country, as well as possible, and
in
so doing it just turns out that the ellipsoid is not concentric with the

geoid. This is why we need those seven-parameter datum transformations:

three parameters to shift the ellipsoids, three to rotate them, and one
to
rescale their size.

None of this has anything to do with projections. We're talking about
establishing ways to identify points on the earth with points on an
ellipsoid, period. The projection comes only when you decide to make a
map. You make a map in two steps: the datum supplies you with a point
on
the ellipsoid, then a mathematical formula--the projection
itself--derives
Cartesian coordinates (x,y) from that point.

>A Mercator projection uses the cylinder as its developable surface. If
you
>picture wrapping a tube around the globe with its open ends at the
poles,
>and "projecting" a light from the centre of the globe outwards onto the

>tube, you sort of get the image.

Yes, but the "sort of" hides some important details. The Mercator
projection also includes an exponential distortion of the north-south
distances, even after this geometric projection operation is carried
out:
it is _not_ the same as the light-and-shadow process described. This is

true of many projections: although in some loose intuitive sense they
are
"based" on geometric projections onto a developable surface, that's not
really how they work. That's why we need the more general mathematical
idea of projection introduced earlier.

>Because the tube touches only at the equator, that is the point where
the
>distortion will be the least. Hence the world maps we used to always
see
>had the lands at the top and bottom greatly stretched because they used
a
>Mercator projection (Greenland isn't really as big as Brazil).

Again, sort of. The distortion in the Mercator projection has little to
do
with tubes or "touching" the equator. It is inherent in the mathematics
of
the projection. The distortion is a phenomenon better understood by
considering the map scale in two directions at every point: east-west
and
north-south. The Mercator has the special property of being conformal,
which implies those two scales are always equal. Up and down the map,
from
north to south, the common scale will increase with increasing distance
from the equator. It becomes unbounded as the poles are approached.

>To make a "transverse" Mercator, we simply rotate the cylinder or tube
to
>run crosswise to the globe.

A minor point: that method works when using a perfect sphere for the
datum;
mathematically it's more complicated for an ellipsoid, because a
meridian
then has the shape of an ellipse, not of a circle.

>Now the area of least distortion follows a meridian from north to
south.
>We then decide (well, somebody decided) that a 6 degree swath is as
wide
>as we need for one zone in order to minimize distortion.

This does not by any means "minimize" distortion. You can make
distortion
smaller still in many ways, such as by using narrower zones. This point

goes back to the philosophical issue raised earlier: the design of UTM
began with a target for scale accuracy. In turns out this target is met
by
using reference circles approximately 500 km apart and limiting the
projection to a swath approximately 800 km wide (seven degrees at the
equator). Successive swaths in the UTM system overlap at the equator by

one degree apiece, whence 60 swaths are needed to cover the lower
latitudes
of the globe. (A different projection altogether is used for the polar
regions in UTM.)

BTW, there's more to UTM than this. It also includes a hierarchical,
tree-like organization of regions within each UTM zone. However, this
additional structure is rarely used within GIS. It can become important

for interpreting certain military coordinates.

>As for a coordinate system, that is merely a method of identifying a
>location (x,y and perhaps z) on your globe or map. We use degrees,
minutes
>and seconds for the 3D globe because that has been the tradition.

Thus, fundamentally, a 3D coordinate function consists of the following:

(1) A set of points, "M", in 3D Euclidean space endowed with its
Cartesian coordinates (x,y,z).

(2) A mechanism to associate a unique point near the earth's surface

with each (x,y,z) in M.

(3) Units of measurement, such as feet, meters, or degrees, for x,
y,
and z.

Typically, the mechanism in (2) is "adapted" to the ellipsoid in the
sense
that the ellipsoid itself is a level surface of the z coordinate and, to
a
good approximation, 'z' can be interpreted as height relative to the
ellipsoid. Consequently, (x,y) can be taken as coordinates for the
ellipsoid itself and 'z' can be taken as elevation.

If this sounds like a "projection," you're hearing right: there's a
projection lurking here. Remember that a projection assigns coordinates
to
physical points. A coordinate function as just defined does the
opposite:
it assigns physical points to coordinates. But in most cases you can go
in
reverse: each physical point usually has only one set of
coordinates. Assigning those coordinates to the point and forgetting
about
the 'z' part constitutes a projection. It's a subtle difference, but it

affords ample opportunity for confusion.

BTW, in mathematics a coordinate function is usually defined in the same

way a "projection" is defined here. This is not the place to unravel
differences in terminology. The important thing is to understand the
distinction being made between assigning coordinates to points and
assigning points to coordinates. Both mechanisms are important and
useful;
both are very closely related; but they are distinct things.

The idea of "coordinate system" generalizes this: it can comprise more
than
one coordinate function. UTM is the archetypical example: it includes
more
than 60 coordinate functions. To designate a point on the earth in UTM,

then, you have to specify one of its coordinate function (which amounts
to
naming the UTM zone) along with the (x, y) or (x, y, z) coordinates that

will be interpreted in terms of that coordinate function. The State
Plane
systems in the U.S. provide another example of a coordinate system that
is
not merely one coordinate function.

Best,

Bill Huber
Quantitative Decisions

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Re: Projections, co-ordinate systems, datums, spheroids, geoids etc.

2009-11-19T07:43:41Z

At 10:21 AM 11/19/2009 +0200, a respondent wrote:
>The ellipsoid can be measured ...

As a point of clarification concerning the implications of "the": no
planetary body has a uniquely determined ellipsoid. No single ellipsoid
will be a perfect fit to the body's geoid or land surface and different
ellipsoids will fit it better in some places than others. When we remember
that an ellipsoid is a mathematical construct, the impossibility of
actually measuring it becomes clear.

> ... the flattening ratio (the difference between the semi-major and the
> semi minor axis.

The flattening, as usually defined, is the ratio between the difference
between the semi-axis lengths and the length of the semi-major axis. This
makes it unitless, which is essential for any property of a figure intended
to be independent of its size.

> Since we are using the WGSâ84 (world geodetic survey 1984) ellipsoid
> as it is a more accurate determination of the shape of the earth.

It is "more accurate" only in a global sense. For use at particular
locations, it can actually be *less* accurate than other ellipsoids.

>Three types of projections are used: Conical, cylindrical and asimuthal [sic]

These would more properly be termed "aspects," not types. Related to any
projection is a whole family of projections that can be obtained by first
rotating the earth to a new position and re-applying the projection;
members of this family differ according to "aspect" but otherwise obviously
have much in common, such as being conformal or equal area or whatever.

> In these three types you would find hundreds of adaptations to limit
> distortion on paper maps.

The sense of "adaptation" used here corresponds to the usual meaning of
"projection."

> In SA we use the Gauss Conformal (conformal = true shape)

Although this equation is commonly seen, "conformal" does not really mean
or even imply "true shape." Very few shapes on the earth's surface can be
rendered truly correctly on a map. By definition, a projection is
conformal when it preserves all *relative angles.* For example, all
Mercator projections are conformal but as Rick Gray pointed out yesterday,
it introduces huge distortions of both shape and size.

This might seem like a quibble but when we consider how confusing the
subject is, and when we contemplate the possibility that somebody reading
"conformal = true shape" could easily mistake it to mean there is
absolutely *no* distortion of shape, it becomes evident that getting these
small details right can be crucial for helping people develop a correct
understanding of the concepts.

>However, if you need to calculate distances and areas it can be quite a
>hassle and we then use a Cartesian coordinate system with which you can
>calculate distances and areas using metric units (eg meter).

Some ambiguities make this potentially confusing. There is a Cartesian
coordinate system available for the Euclidean 3D space within which the
earth sits, but using it to compute distances would ignore the earth's
surface; for example, the distance calculated between the north and south
pole would be the distance of a straight tube bored through the earth
between the two. There is also a Cartesian coordinate system available for
the Euclidean 2D space in which a map is drawn, but then (necessarily, by
Gauss's Theorema Egregium) distances calculated with it will not be (quite)
correct, except for some exceptional pairs of points. (If the map is drawn
with an equal area projection, though, the areas will be correct. This is
kind of amazing.)

> Cartesian coordinate systems are referenced to a local geographic
> coordinate system.

If "referenced" and "local" and "geographic" were given precise
definitions, one might be able to make sense of this statement and it might
actually be correct. Because I'm aware of multiple valid definitions of
all three of these terms, which result in myriad possible meanings when
taken in combination, I'm at a loss to provide any disambiguating comments.

> To summarise: The shape of the earth determines the ellipsoid
> determines the datum determines the location of an object (coordinates)
> and the projection is used to draw all this on a flat piece of paper with
> the least distortion possible.

I can see where this statement would come from, because it draws a nice
picture of the process of producing a map, but as far as the definitions go
it strikes me as being systematically backwards. *An* ellipsoid is
controlled by the earth's shape but ultimately is chosen by the
surveyor. The datum is established by people so they can reference points
on the earth to the ellipsoid by means of measurement. The location of an
object is given (not "determined" by a datum!): it determines itself; by
means of the datum it also determines a point on the ellipsoid. The
projection, which is purely a mathematical transformation, assigns (x,y)
coordinates to this point. Among the many uses of those coordinates is
making a map, which occurs when we establish Cartesian coordinates on the
map and interpret (x,y) as those coordinates. Finally, although the idea
of minimizing distortion is modern and sophisticated, in practice the
distortion that occurs rarely is the least possible. (Otherwise we would
use a unique projection and datum for each map.) For example, navigators
accept enormous distortion on Mercator maps in return for the ease of
navigation afforded by their loxodromic property: a straight course on the
earth is represented by a straight line on the map. As another example,
people often accept infinite distortion by interrupting global
maps--literally cutting the image apart along curves, usually in the middle
of oceans or in polar regions--because that can produce less distortion in
areas of interest, such as land masses and middle latitudes.

Best,

Bill Huber
Quantitative Decisions

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Re: Projections, co-ordinate systems, datums, spheroids, geoids etc.

2009-11-19T00:21:59Z

Gillian,

I’ll try to explain in the way I do to my students starting from the
shape of the earth, the ellipsoid, the datum, coordinates and
projections.

Your definitions are largely correct:

The shape of the earth can be described as an ellipsoid (an ellipse
rotated on its shorter axis). The geoid will be a more accurate
description as it incorporates local variations in gravity but is rarely
used by us mortals.

The ellipsoid can be measured and is normally expressed with the
flattening ratio (the difference between the semi-major and the semi
minor axis. Clarke 1880 is the ellipsoid which was used in South Africa
until 1994. Since we are using the WGS’84 (world geodetic survey 1984)
ellipsoid as it is a more accurate determination of the shape of the
earth. There has been a lot of these things measured.

The datum forms the basis for mapping from a predetermined point,
usually in a specific country or region and is based on the ellipsoid.
The Cape datum (older SA maps) was based on the Clarke 1880 ellipsoid
and the origin was a trigonometrical beacon near Port Elizabeth. The
“new” Hartebeesthoek ’94 datum is based on the WGS 84 ellipsoid with
its origin at the Hartebeesthoek Radio Observatory near Pretoria. There
is a nice (albeit a bit technical) explanation on the Chief Director;
Surveys and Mapping’s website http://www.cdsm.gov.za/ click on WGS84

A projection is the transformation of the 3D shape of the earth to a
plane (2D). Three types of projections are used: Conical, cylindrical
and asimuthal depending on the needs of the cartographer and what part
of the earth the map is about. In these three types you would find
hundreds of adaptations to limit distortion on paper maps. In SA we use
the Gauss Conformal (conformal = true shape) for the large scale maps
(1:50 000) and Albers’s equal area projection for the smaller scale maps
(1:1 000 000). The Gauss conformal projection is based on the
Transverse Mercator (and is not the same as the Gauss-Kruger as you
mention in your e-mail)

A coordinate system is one of various ways to determine the location of
an object on the surface of the earth (generally referred to as
georeferencing). Geographic coordinates (latitude and longitude) are
the most commonly used and is recognisable throughout the world. It
therefore works well if you are working only with the location of
objects. However, if you need to calculate distances and areas it can
be quite a hassle and we then use a Cartesian coordinate system with
which you can calculate distances and areas using metric units (eg
meter). Cartesian coordinate systems are referenced to a local
geographic coordinate system. The SA Lo system which you refer to are
based on every odd meridian (from 17 degrees east to 31 degrees east)
and on the equator. The blue numbers on your topographical maps gives
the x and y values in meters from the equator and the Longitude of
Origin (Lo). Just be careful when using these in your GIS. The axis
system is different from what we as geographers are used to (as a rule
of thumb y-values on the map should be x and vice versa, you also have
to change the sign of the value).

E.g. The coordinates for the UFS campus (on 2926AA) on the map is +3
220 000 x and +80 000 y but if you would use this in a GIS it should be
-3 220 000 (m south of the equator) and -80 000 (m west of 27 degrees
east). According to Iliffe and Lott the latter is because of the south
orientated Tranverse Mercator parameter values. I’m still looking for a
surveyor who can explain this in plain English

To summarise: The shape of the earth determines the ellipsoid
determines the datum determines the location of an object (coordinates)
and the projection is used to draw all this on a flat piece of paper
with the least distortion possible.

I hope it helps

Regards

Charles

Dr CH Barker
Senior Lecturer (GIS)
Dept of Geography (53)
University of the Free State
PO Box 339
Bloemfontein, 9300
South Africa
Tel: +27 (0)51 401 2554
+27 (0)83 282 8040
Fax +27 (0)51 401 3816

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Please refer to http://www.ufs.ac.za/disclaimer for full details.

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Hierdie boodskap en sy inhoud is aan 'n vrywaringsklousule onderhewig.
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Thanks - Projections, co-ordinate systems, datums, spheroids, geoids etc.

2009-11-18T21:33:31Z

Thanks to all of you for a very interesting and informative set of
responses. Although I am still trying to digest a lot of it (!), the
discussion has clarified many of my somewhat fuzzy ideas and given me plenty
of new info.

Cheers

Gillian McGregor
Lecturer
Dept. of Geography
Rhodes University
Grahamstown
6140

Tel: 046-603 8322 (w)

Fax: 046-636 1199

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Question on Opensource s/w for Logistics

2009-11-18T16:16:31Z

Hello to everyone,

I was wondering if anyone knows or has used in the past any opensource
GIS sw package for Logistics (Supply Chain Management, ERPS, Fleet
Management, etc.).
The main target is to use such sw for advanced, educational courses
and practicing, showing to the students the capabilities of opensource
sw against expensive packages from the market.
Any advice or recomendation would be appreciated.
Thank you in advance.

Dr. Abraham Mavridis

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Dr. ABRAHAM P. MAVRIDIS

Ph.D. in GIS of CIVIL ENGINEERING, AUTh
Lab. of Geodesy and Geomatics
SCHOOL OF ENGINEERING
Aristotle University of Thessaloniki
URL: http://gserver.civil.auth.gr/
Lecturer in GIS in ATEITh
www.teithe.gr
www.logistics.teithe.gr

e-mails: lmac7@...
& mavaby7@...
& amavridi@...

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Re: Projections, co-ordinate systems, datums, spheroids, geoids etc.

2009-11-18T13:09:11Z

I really appreciate this conversation. It has educated me on several terms
that are often used but apparently not well defined in the first couple
dozen hits of web searches and other references...

This might be a good time to introduce a social database project I started
called MapCentral: http://mapcentral.freebase.com/

There are likely other similar sources of information out there but I really
like the graph-based approach that Freebase uses to link topics via
community built schema. I created MapCentral to help me keep track of links
and metadata for some of the maps that I use. I modeled the schema around
the online image map of the FGDC standard:
http://www.fgdc.gov/csdgmgraphical/index.html

You can view these Freebase schema by clicking on the "Schema" tab on the
right and then clicking one of the links.

Here is an example of a map that I described in some detail using these
schema:
http://www.freebase.com/edit/topic/en/2001_national_land_cover_data_metadata?domain=%2Fbase%2Fmapcentral
Note that all the blue text on this page contains hyperlinks to those
topic's pages. Also note that you sometimes must click the "Edit this topic"
button on the top right to see all the user contributed details (login not
required). Freebase is still in alpha stage development and this is one of
the user interface issues I hope they change soon...

One reason that MapCentral is relevant to this conversation is that it
contains community-edited descriptions of map topics. For example, Freebase
has already imported Wikipedia topics. I used this information and other
sources to group and view "similar" topics using the MapCentral schema. For
example, see reference ellipsoids:
http://www.freebase.com/view/base/mapcentral/views/ellipsoid_type

Topic descriptions can be edited in Wikipedia, which will update the
Freebase description, or the Wikipedia description can be removed in
Freebase and replaced by a new one written by members of the community (the
Wikipedia link will still be maintained Freebase on the page).

It would be great if some of the really useful information from this thread
made its way into the structured metadata of Freebase and MapCentral, which
is neither perfect nor complete. I'm certainly not as knowledgeable of GIS
as many others on this list, so encourage those who are interested to join
me in developing MapCentral schema as well as adding and describing map
topics. I'm happy to provide more information here or by personal email, but
encourage you to ask questions there where others outside this list can
learn and contribute.

-Ed

Edward J. Laurent <http://www.freebase.com/view/en/edward_j_laurent>

American Bird Conservancy <http://www.abcbirds.org/>

On Wed, Nov 18, 2009 at 3:21 PM, RICK GRAY <rgray@...>wrote:

> Hi Bill,
>
> I was pretty sure that if you were still watching this list that you would
> weigh in (at least I had hoped so). In fact I held off for a while to see if
> you would respond before I weighed in because I knew my "intuitive" approach
> to the subject would be no match to your "technical" approach.
>
> I answered Gillian with the kind of answers I use for my first year,
> non-GIS students to whom I teach an introductory GIS course. If I got into
> the mathematics as you have done, their eyes would glaze over in an instant.
> Hell, I had to re-read many of your points to be sure I understood them and
> I've still got some work to do on that front. Math-phobia can provide
> challenges - both for my students and me - though I find they usually get a
> good picture of the general concepts through the intuitive interpretation.
>
> Every year I search on-line to upgrade my lectures, and the Projections
> lecture has always created the most grief for me for the very reasons
> Gillian mentioned. A lot of what's out there, both in texts and online, is
> confusing and sometimes seems contradictory. That's why I left the
> invitation at the bottom of my response for anyone to correct me if I was
> leading Gillian astray. Hopefully by the time I have chewed through your
> email and digested all this, I will be able to do a much better job of
> explaining these concepts to my students.
>
> Thanks for the lesson.
>
> Cheers,
> Rick
>
>
> >>> Quantitative Decisions <whuber@...> 11/18/09 2:55 PM >>>
> This morning Gilllian McGregor asked,
> >I would like to clarify the use and definition of a range of terms ... I
> >would like to understand better, with regard to ... a better definition,
> >when they are used and why they are used and how they relate to one
> another.
>
> The terms include
>
> Geoid
> Ellipsoid
> Datum
> Coordinate system
> Projection.
>
>
> A helpful respondent wrote:
>
> >A projection is the systematic mathematical transformation of the "round"
> >surface so that it will lay flat. Different projections try to minimize
> >what gets distorted and by how much and which you utilize will be
> >partially dependent on what you want to display in your final map (is
> >preserving area more important than direction, etc).
>
> This is excellent. Although everything that followed it was helpful for
> the intuition and consistent with what is taught and "known" among GIS
> professionals, it nevertheless bears closer examination in the
> details. Let's look.
>
>
> >There are 3 "developable surfaces" that projections are based on - the
> >cylinder, the cone and the plane.
>
> This is true for some projections but not all. Many modern projections,
> such as many of those developed by the late John Snyder at the USGS, are
> not "based" on any developable surface in any fundamental or important way.
>
> An equivalent way to think of a "projection" of any surface is that it
> assigns a pair of real numbers to each point on the surface. When you
> interpret those numbers as Cartesian coordinates in the plane, you have
> drawn a map. That's all there is to map projection.
>
> (BTW, there are many more developable surfaces than these three. By
> definition these are surfaces that can be "unrolled": they have everywhere
> zero Gaussian curvature but are not necessarily planar. One example is the
> elliptical cylinder related to a transverse Mercator projection from an
> ellipsoid. For more fanciful examples, take any sheet of paper and roll
> its corners and edges into any shape you can without creating folds.)
>
>
> >Different people (Clarke, etc.) have defined the spheroid or ellipsoid
> >mathematically and this goes into the projection formula.
>
> This is less a matter of mathematics than of measurement. A spheroid is an
> imaginary surface coincident with the earth (and rotating and moving
> through the universe with it). At any given time, the spheroid provides a
> way of identifying all points in the universe by means of two things: a
> point on the spheroid itself and a distance up or down, perpendicular to
> the spheroid, from that point.
>
> What makes a spheroid useful is that it has a simple mathematical
> description, unlike the actual surface of a planet. Thus, ellipsoids of
> revolution (or sometimes triaxial ellipsoids) are used as references for
> the spheroids of planets and planetoids because of their mathematical
> simplicity. Having elected to use, say, an ellipsoid of revolution, one
> then makes measurements of selected points on the planet's surface and
> finds an ellipsoid that best approximates those measured points in some
> sense.
>
> There are many ellipsoids in use for mapping the earth because (a)
> historically measurements have gotten better, (b) the earth's surface is
> constantly changing shape, (c) criteria to compare the ellipsoid with the
> measured locations can vary, and--most importantly--(d) many different sets
> of measurements have focused on relatively small patches of the earth's
> surface. An ellipsoid that fits one patch well does not necessarily fit
> the rest of the earth's surface well. That's why an ellipsoid suitable for
> the UK is unlikely to be used for distant South Africa, for instance.
>
>
> > To refine it even more, we use the term geoid to explain the bumps and
> > hollows of the ocean depths and mountain peaks.
>
> No, this is incorrect. There is a unique geoid defined as a particular a
> gravitational equipotential surface. As such, it depends on the
> distribution of mass within a planet, not on the form its surface
> takes. On the earth, the geoid varies only a little from any decent
> ellipsoid; the variation rarely exceeds 100 meters. That obviously does
> not "explain" ocean depths or mountain peaks, which are local variations
> two orders of magnitude greater. Moreover, the geoid's undulations do not
> exactly follow all mountain ranges or ocean floors, although there is a
> close correlation.
>
> Of the many possible such equipotential surfaces for the earth (differing
> only in height), the geoid is the one along which the surface of the oceans
> would lie were there no winds, waves, currents, or tides. (See the
> Wikipedia article at http://en.wikipedia.org/wiki/Geoid .) Equipotential
> surfaces of gravity are of interest in geodesy primarily because at any
> point within the influence of earth's gravitation, "up" is always
> perpendicular to the equipotential surface at that point. Because the "up"
> direction is used to measure things like geodetic latitude and longitude,
> which by definition are determined by the direction perpendicular to the
> *ellipsoid*, any deviations between the geoid and whatever ellipsoid is
> being used will oblige us to make corrections in geodetic measurements.
>
> BTW, the mechanism we use to represent the ocean floor and mountain peaks,
> as well as everything in between, is called a digital elevation model (or
> digital terrain model).
>
>
> >Again, this must be at a fairly coarse resolution because your computer
> >would be crunching numbers for days if we wanted to be extremely accurate.
>
> There's nothing the matter with this statement, but it reflects a
> philosophy that IMHO reverses priorities, although I'm sure that's not what
> was intended. It seems to suggest that the accuracy we accept in our work
> should be determined by the computer's capabilities. Yes, compromises must
> be made, but especially with today's power, it should work the other way:
> you, as the user of the data, should begin by determining the accuracy you
> need. Then you set up a system capable of delivering that accuracy. If
> you need the submicron-level accuracy that would be delivered by using a
> geoid instead of an ellipsoid, then you should compute with the geoid. It
> wouldn't cost you days: the calculations aren't that much more involved
> (but it's a real pain to program and simply not worth the effort). The
> real point is that imprecision in all the other data we have is vastly
> greater than the imprecision created by using an ellipsoid instead of the
> geoid.
>
>
> >Then we get to the datum. This is the mathematical surface that fits
> >closely to the mean sea level of the earth and to which ground control
> >point are referenced. Here in North America our maps used to use NAD27
> >(North American Datum 1927) as a final refinement.
>
> These statements actually are contradictory, because NAD27 is neither a
> mathematical surface nor a refinement at all: it's actually a gross,
> unintended distortion of a datum.
>
> A datum, in its broadest sense, is a system set up to let us find (via
> measurement) the point on an ellipsoid (and elevation relative to that
> point) corresponding to any physical point on or near the earth's
> surface. This can be done in many ways. For NAD27 it consists of a
> network of thousands of points laid across the US. To each point was
> associated, once and for all (although with great inaccuracy for today's
> needs) a point on the Clarke 1866 ellipsoid. To locate any point in North
> America, a surveyor finds one or more nearby points in this network and
> makes measurements relative to them. With the capabilities afforded by
> modern instruments (e.g., GPS), to define a datum it now suffices to
> provide an ellipsoid and a single reference location, reference direction,
> and reference height on the earth's surface. The example of NAD27 reminds
> us that this is not the only way to establish a datum, though.
>
> The fact that NAD27 is not a mathematical surface, nor even a refinement of
> one, is made apparent by NADCON and VERTCON, the apparatus needed to relate
> NAD27 to other datums. These algorithms require a database that
> essentially records the errors (usually at quarter degree intervals) made
> within the NAD27 geodetic reference network across North America. The
> errors often reach hundreds of meters, especially in northwestern US and
> outside the conterminous US. Older datums in Canada and Australia require
> similar methods of correction.
>
>
> >In 83, a new datum (NAD 83) used our new knowledge, based on satellite
> >measurements, to more accurately pinpoint the centre of the earth as the
> >reference point, which helped to remove the error as you moved across the
> >continent. Again, this is just a mathematical refinement to the projection
> >when used at a more local level.
>
> The new datum was needed in part because of the large errors introduced in
> the network of NAD 27 reference points, not to "pinpoint the center of the
> earth." Indeed, even today many datums use ellipsoids whose centers do
> *not* coincide with that of the earth, and this is on purpose: it's not an
> error. The reason is that these datums attempt to approximate one small
> patch of the earth, such as a single country, as well as possible, and in
> so doing it just turns out that the ellipsoid is not concentric with the
> geoid. This is why we need those seven-parameter datum transformations:
> three parameters to shift the ellipsoids, three to rotate them, and one to
> rescale their size.
>
> None of this has anything to do with projections. We're talking about
> establishing ways to identify points on the earth with points on an
> ellipsoid, period. The projection comes only when you decide to make a
> map. You make a map in two steps: the datum supplies you with a point on
> the ellipsoid, then a mathematical formula--the projection itself--derives
> Cartesian coordinates (x,y) from that point.
>
>
> >A Mercator projection uses the cylinder as its developable surface. If you
> >picture wrapping a tube around the globe with its open ends at the poles,
> >and "projecting" a light from the centre of the globe outwards onto the
> >tube, you sort of get the image.
>
> Yes, but the "sort of" hides some important details. The Mercator
> projection also includes an exponential distortion of the north-south
> distances, even after this geometric projection operation is carried out:
> it is _not_ the same as the light-and-shadow process described. This is
> true of many projections: although in some loose intuitive sense they are
> "based" on geometric projections onto a developable surface, that's not
> really how they work. That's why we need the more general mathematical
> idea of projection introduced earlier.
>
>
> >Because the tube touches only at the equator, that is the point where the
> >distortion will be the least. Hence the world maps we used to always see
> >had the lands at the top and bottom greatly stretched because they used a
> >Mercator projection (Greenland isn't really as big as Brazil).
>
> Again, sort of. The distortion in the Mercator projection has little to do
> with tubes or "touching" the equator. It is inherent in the mathematics of
> the projection. The distortion is a phenomenon better understood by
> considering the map scale in two directions at every point: east-west and
> north-south. The Mercator has the special property of being conformal,
> which implies those two scales are always equal. Up and down the map, from
> north to south, the common scale will increase with increasing distance
> from the equator. It becomes unbounded as the poles are approached.
>
>
> >To make a "transverse" Mercator, we simply rotate the cylinder or tube to
> >run crosswise to the globe.
>
> A minor point: that method works when using a perfect sphere for the datum;
> mathematically it's more complicated for an ellipsoid, because a meridian
> then has the shape of an ellipse, not of a circle.
>
>
> >Now the area of least distortion follows a meridian from north to south.
> >We then decide (well, somebody decided) that a 6 degree swath is as wide
> >as we need for one zone in order to minimize distortion.
>
> This does not by any means "minimize" distortion. You can make distortion
> smaller still in many ways, such as by using narrower zones. This point
> goes back to the philosophical issue raised earlier: the design of UTM
> began with a target for scale accuracy. In turns out this target is met by
> using reference circles approximately 500 km apart and limiting the
> projection to a swath approximately 800 km wide (seven degrees at the
> equator). Successive swaths in the UTM system overlap at the equator by
> one degree apiece, whence 60 swaths are needed to cover the lower latitudes
> of the globe. (A different projection altogether is used for the polar
> regions in UTM.)
>
> BTW, there's more to UTM than this. It also includes a hierarchical,
> tree-like organization of regions within each UTM zone. However, this
> additional structure is rarely used within GIS. It can become important
> for interpreting certain military coordinates.
>
>
> >As for a coordinate system, that is merely a method of identifying a
> >location (x,y and perhaps z) on your globe or map. We use degrees, minutes
> >and seconds for the 3D globe because that has been the tradition.
>
> Thus, fundamentally, a 3D coordinate function consists of the following:
>
> (1) A set of points, "M", in 3D Euclidean space endowed with its
> Cartesian coordinates (x,y,z).
>
> (2) A mechanism to associate a unique point near the earth's surface
> with each (x,y,z) in M.
>
> (3) Units of measurement, such as feet, meters, or degrees, for x, y,
> and z.
>
> Typically, the mechanism in (2) is "adapted" to the ellipsoid in the sense
> that the ellipsoid itself is a level surface of the z coordinate and, to a
> good approximation, 'z' can be interpreted as height relative to the
> ellipsoid. Consequently, (x,y) can be taken as coordinates for the
> ellipsoid itself and 'z' can be taken as elevation.
>
> If this sounds like a "projection," you're hearing right: there's a
> projection lurking here. Remember that a projection assigns coordinates to
> physical points. A coordinate function as just defined does the opposite:
> it assigns physical points to coordinates. But in most cases you can go in
> reverse: each physical point usually has only one set of
> coordinates. Assigning those coordinates to the point and forgetting about
> the 'z' part constitutes a projection. It's a subtle difference, but it
> affords ample opportunity for confusion.
>
> BTW, in mathematics a coordinate function is usually defined in the same
> way a "projection" is defined here. This is not the place to unravel
> differences in terminology. The important thing is to understand the
> distinction being made between assigning coordinates to points and
> assigning points to coordinates. Both mechanisms are important and useful;
> both are very closely related; but they are distinct things.
>
> The idea of "coordinate system" generalizes this: it can comprise more than
> one coordinate function. UTM is the archetypical example: it includes more
> than 60 coordinate functions. To designate a point on the earth in UTM,
> then, you have to specify one of its coordinate function (which amounts to
> naming the UTM zone) along with the (x, y) or (x, y, z) coordinates that
> will be interpreted in terms of that coordinate function. The State Plane
> systems in the U.S. provide another example of a coordinate system that is
> not merely one coordinate function.
>
> Best,
>
> Bill Huber
> Quantitative Decisions
>
> _______________________________________________
> gislist mailing list
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> http://lists.geocomm.com/mailman/listinfo/gislist
>
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> http://www.geocomm.com/
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Re: Projections, co-ordinate systems, datums, spheroids, geoids etc.

2009-11-18T13:08:05Z

I am so glad to read that I'm not the only one having problems
explaining these concepts to students. Thanks for the answers, I also
learned more on the topic.

Gillian, if you need more info on the Hartbeeshoek 94 Datum for South
Africa, let me know as I have an article dealing with it.

Thea Schoeman
University of Johannesburg
South Africa

RICK GRAY wrote:

> Hi Bill,
>
> I was pretty sure that if you were still watching this list that you would weigh in (at least I had hoped so). In fact I held off for a while to see if you would respond before I weighed in because I knew my "intuitive" approach to the subject would be no match to your "technical" approach.
>
> I answered Gillian with the kind of answers I use for my first year, non-GIS students to whom I teach an introductory GIS course. If I got into the mathematics as you have done, their eyes would glaze over in an instant. Hell, I had to re-read many of your points to be sure I understood them and I've still got some work to do on that front. Math-phobia can provide challenges - both for my students and me - though I find they usually get a good picture of the general concepts through the intuitive interpretation.
>
> Every year I search on-line to upgrade my lectures, and the Projections lecture has always created the most grief for me for the very reasons Gillian mentioned. A lot of what's out there, both in texts and online, is confusing and sometimes seems contradictory. That's why I left the invitation at the bottom of my response for anyone to correct me if I was leading Gillian astray. Hopefully by the time I have chewed through your email and digested all this, I will be able to do a much better job of explaining these concepts to my students.
>
> Thanks for the lesson.
>
> Cheers,
> Rick
>
>
>
>>>> Quantitative Decisions <whuber@...> 11/18/09 2:55 PM >>>
>>>>
> This morning Gilllian McGregor asked,
>
>> I would like to clarify the use and definition of a range of terms ... I
>> would like to understand better, with regard to ... a better definition,
>> when they are used and why they are used and how they relate to one another.
>>
>
> The terms include
>
> Geoid
> Ellipsoid
> Datum
> Coordinate system
> Projection.
>
>
> A helpful respondent wrote:
>
>
>> A projection is the systematic mathematical transformation of the "round"
>> surface so that it will lay flat. Different projections try to minimize
>> what gets distorted and by how much and which you utilize will be
>> partially dependent on what you want to display in your final map (is
>> preserving area more important than direction, etc).
>>
>
> This is excellent. Although everything that followed it was helpful for
> the intuition and consistent with what is taught and "known" among GIS
> professionals, it nevertheless bears closer examination in the
> details. Let's look.
>
>
>
>> There are 3 "developable surfaces" that projections are based on - the
>> cylinder, the cone and the plane.
>>
>
> This is true for some projections but not all. Many modern projections,
> such as many of those developed by the late John Snyder at the USGS, are
> not "based" on any developable surface in any fundamental or important way.
>
> An equivalent way to think of a "projection" of any surface is that it
> assigns a pair of real numbers to each point on the surface. When you
> interpret those numbers as Cartesian coordinates in the plane, you have
> drawn a map. That's all there is to map projection.
>
> (BTW, there are many more developable surfaces than these three. By
> definition these are surfaces that can be "unrolled": they have everywhere
> zero Gaussian curvature but are not necessarily planar. One example is the
> elliptical cylinder related to a transverse Mercator projection from an
> ellipsoid. For more fanciful examples, take any sheet of paper and roll
> its corners and edges into any shape you can without creating folds.)
>
>
>
>> Different people (Clarke, etc.) have defined the spheroid or ellipsoid
>> mathematically and this goes into the projection formula.
>>
>
> This is less a matter of mathematics than of measurement. A spheroid is an
> imaginary surface coincident with the earth (and rotating and moving
> through the universe with it). At any given time, the spheroid provides a
> way of identifying all points in the universe by means of two things: a
> point on the spheroid itself and a distance up or down, perpendicular to
> the spheroid, from that point.
>
> What makes a spheroid useful is that it has a simple mathematical
> description, unlike the actual surface of a planet. Thus, ellipsoids of
> revolution (or sometimes triaxial ellipsoids) are used as references for
> the spheroids of planets and planetoids because of their mathematical
> simplicity. Having elected to use, say, an ellipsoid of revolution, one
> then makes measurements of selected points on the planet's surface and
> finds an ellipsoid that best approximates those measured points in some sense.
>
> There are many ellipsoids in use for mapping the earth because (a)
> historically measurements have gotten better, (b) the earth's surface is
> constantly changing shape, (c) criteria to compare the ellipsoid with the
> measured locations can vary, and--most importantly--(d) many different sets
> of measurements have focused on relatively small patches of the earth's
> surface. An ellipsoid that fits one patch well does not necessarily fit
> the rest of the earth's surface well. That's why an ellipsoid suitable for
> the UK is unlikely to be used for distant South Africa, for instance.
>
>
>
>> To refine it even more, we use the term geoid to explain the bumps and
>> hollows of the ocean depths and mountain peaks.
>>
>
> No, this is incorrect. There is a unique geoid defined as a particular a
> gravitational equipotential surface. As such, it depends on the
> distribution of mass within a planet, not on the form its surface
> takes. On the earth, the geoid varies only a little from any decent
> ellipsoid; the variation rarely exceeds 100 meters. That obviously does
> not "explain" ocean depths or mountain peaks, which are local variations
> two orders of magnitude greater. Moreover, the geoid's undulations do not
> exactly follow all mountain ranges or ocean floors, although there is a
> close correlation.
>
> Of the many possible such equipotential surfaces for the earth (differing
> only in height), the geoid is the one along which the surface of the oceans
> would lie were there no winds, waves, currents, or tides. (See the
> Wikipedia article at http://en.wikipedia.org/wiki/Geoid .) Equipotential
> surfaces of gravity are of interest in geodesy primarily because at any
> point within the influence of earth's gravitation, "up" is always
> perpendicular to the equipotential surface at that point. Because the "up"
> direction is used to measure things like geodetic latitude and longitude,
> which by definition are determined by the direction perpendicular to the
> *ellipsoid*, any deviations between the geoid and whatever ellipsoid is
> being used will oblige us to make corrections in geodetic measurements.
>
> BTW, the mechanism we use to represent the ocean floor and mountain peaks,
> as well as everything in between, is called a digital elevation model (or
> digital terrain model).
>
>
>
>> Again, this must be at a fairly coarse resolution because your computer
>> would be crunching numbers for days if we wanted to be extremely accurate.
>>
>
> There's nothing the matter with this statement, but it reflects a
> philosophy that IMHO reverses priorities, although I'm sure that's not what
> was intended. It seems to suggest that the accuracy we accept in our work
> should be determined by the computer's capabilities. Yes, compromises must
> be made, but especially with today's power, it should work the other way:
> you, as the user of the data, should begin by determining the accuracy you
> need. Then you set up a system capable of delivering that accuracy. If
> you need the submicron-level accuracy that would be delivered by using a
> geoid instead of an ellipsoid, then you should compute with the geoid. It
> wouldn't cost you days: the calculations aren't that much more involved
> (but it's a real pain to program and simply not worth the effort). The
> real point is that imprecision in all the other data we have is vastly
> greater than the imprecision created by using an ellipsoid instead of the
> geoid.
>
>
>
>> Then we get to the datum. This is the mathematical surface that fits
>> closely to the mean sea level of the earth and to which ground control
>> point are referenced. Here in North America our maps used to use NAD27
>> (North American Datum 1927) as a final refinement.
>>
>
> These statements actually are contradictory, because NAD27 is neither a
> mathematical surface nor a refinement at all: it's actually a gross,
> unintended distortion of a datum.
>
> A datum, in its broadest sense, is a system set up to let us find (via
> measurement) the point on an ellipsoid (and elevation relative to that
> point) corresponding to any physical point on or near the earth's
> surface. This can be done in many ways. For NAD27 it consists of a
> network of thousands of points laid across the US. To each point was
> associated, once and for all (although with great inaccuracy for today's
> needs) a point on the Clarke 1866 ellipsoid. To locate any point in North
> America, a surveyor finds one or more nearby points in this network and
> makes measurements relative to them. With the capabilities afforded by
> modern instruments (e.g., GPS), to define a datum it now suffices to
> provide an ellipsoid and a single reference location, reference direction,
> and reference height on the earth's surface. The example of NAD27 reminds
> us that this is not the only way to establish a datum, though.
>
> The fact that NAD27 is not a mathematical surface, nor even a refinement of
> one, is made apparent by NADCON and VERTCON, the apparatus needed to relate
> NAD27 to other datums. These algorithms require a database that
> essentially records the errors (usually at quarter degree intervals) made
> within the NAD27 geodetic reference network across North America. The
> errors often reach hundreds of meters, especially in northwestern US and
> outside the conterminous US. Older datums in Canada and Australia require
> similar methods of correction.
>
>
>
>> In 83, a new datum (NAD 83) used our new knowledge, based on satellite
>> measurements, to more accurately pinpoint the centre of the earth as the
>> reference point, which helped to remove the error as you moved across the
>> continent. Again, this is just a mathematical refinement to the projection
>> when used at a more local level.
>>
>
> The new datum was needed in part because of the large errors introduced in
> the network of NAD 27 reference points, not to "pinpoint the center of the
> earth." Indeed, even today many datums use ellipsoids whose centers do
> *not* coincide with that of the earth, and this is on purpose: it's not an
> error. The reason is that these datums attempt to approximate one small
> patch of the earth, such as a single country, as well as possible, and in
> so doing it just turns out that the ellipsoid is not concentric with the
> geoid. This is why we need those seven-parameter datum transformations:
> three parameters to shift the ellipsoids, three to rotate them, and one to
> rescale their size.
>
> None of this has anything to do with projections. We're talking about
> establishing ways to identify points on the earth with points on an
> ellipsoid, period. The projection comes only when you decide to make a
> map. You make a map in two steps: the datum supplies you with a point on
> the ellipsoid, then a mathematical formula--the projection itself--derives
> Cartesian coordinates (x,y) from that point.
>
>
>
>> A Mercator projection uses the cylinder as its developable surface. If you
>> picture wrapping a tube around the globe with its open ends at the poles,
>> and "projecting" a light from the centre of the globe outwards onto the
>> tube, you sort of get the image.
>>
>
> Yes, but the "sort of" hides some important details. The Mercator
> projection also includes an exponential distortion of the north-south
> distances, even after this geometric projection operation is carried out:
> it is _not_ the same as the light-and-shadow process described. This is
> true of many projections: although in some loose intuitive sense they are
> "based" on geometric projections onto a developable surface, that's not
> really how they work. That's why we need the more general mathematical
> idea of projection introduced earlier.
>
>
>
>> Because the tube touches only at the equator, that is the point where the
>> distortion will be the least. Hence the world maps we used to always see
>> had the lands at the top and bottom greatly stretched because they used a
>> Mercator projection (Greenland isn't really as big as Brazil).
>>
>
> Again, sort of. The distortion in the Mercator projection has little to do
> with tubes or "touching" the equator. It is inherent in the mathematics of
> the projection. The distortion is a phenomenon better understood by
> considering the map scale in two directions at every point: east-west and
> north-south. The Mercator has the special property of being conformal,
> which implies those two scales are always equal. Up and down the map, from
> north to south, the common scale will increase with increasing distance
> from the equator. It becomes unbounded as the poles are approached.
>
>
>
>> To make a "transverse" Mercator, we simply rotate the cylinder or tube to
>> run crosswise to the globe.
>>
>
> A minor point: that method works when using a perfect sphere for the datum;
> mathematically it's more complicated for an ellipsoid, because a meridian
> then has the shape of an ellipse, not of a circle.
>
>
>
>> Now the area of least distortion follows a meridian from north to south.
>> We then decide (well, somebody decided) that a 6 degree swath is as wide
>> as we need for one zone in order to minimize distortion.
>>
>
> This does not by any means "minimize" distortion. You can make distortion
> smaller still in many ways, such as by using narrower zones. This point
> goes back to the philosophical issue raised earlier: the design of UTM
> began with a target for scale accuracy. In turns out this target is met by
> using reference circles approximately 500 km apart and limiting the
> projection to a swath approximately 800 km wide (seven degrees at the
> equator). Successive swaths in the UTM system overlap at the equator by
> one degree apiece, whence 60 swaths are needed to cover the lower latitudes
> of the globe. (A different projection altogether is used for the polar
> regions in UTM.)
>
> BTW, there's more to UTM than this. It also includes a hierarchical,
> tree-like organization of regions within each UTM zone. However, this
> additional structure is rarely used within GIS. It can become important
> for interpreting certain military coordinates.
>
>
>
>> As for a coordinate system, that is merely a method of identifying a
>> location (x,y and perhaps z) on your globe or map. We use degrees, minutes
>> and seconds for the 3D globe because that has been the tradition.
>>
>
> Thus, fundamentally, a 3D coordinate function consists of the following:
>
> (1) A set of points, "M", in 3D Euclidean space endowed with its
> Cartesian coordinates (x,y,z).
>
> (2) A mechanism to associate a unique point near the earth's surface
> with each (x,y,z) in M.
>
> (3) Units of measurement, such as feet, meters, or degrees, for x, y,
> and z.
>
> Typically, the mechanism in (2) is "adapted" to the ellipsoid in the sense
> that the ellipsoid itself is a level surface of the z coordinate and, to a
> good approximation, 'z' can be interpreted as height relative to the
> ellipsoid. Consequently, (x,y) can be taken as coordinates for the
> ellipsoid itself and 'z' can be taken as elevation.
>
> If this sounds like a "projection," you're hearing right: there's a
> projection lurking here. Remember that a projection assigns coordinates to
> physical points. A coordinate function as just defined does the opposite:
> it assigns physical points to coordinates. But in most cases you can go in
> reverse: each physical point usually has only one set of
> coordinates. Assigning those coordinates to the point and forgetting about
> the 'z' part constitutes a projection. It's a subtle difference, but it
> affords ample opportunity for confusion.
>
> BTW, in mathematics a coordinate function is usually defined in the same
> way a "projection" is defined here. This is not the place to unravel
> differences in terminology. The important thing is to understand the
> distinction being made between assigning coordinates to points and
> assigning points to coordinates. Both mechanisms are important and useful;
> both are very closely related; but they are distinct things.
>
> The idea of "coordinate system" generalizes this: it can comprise more than
> one coordinate function. UTM is the archetypical example: it includes more
> than 60 coordinate functions. To designate a point on the earth in UTM,
> then, you have to specify one of its coordinate function (which amounts to
> naming the UTM zone) along with the (x, y) or (x, y, z) coordinates that
> will be interpreted in terms of that coordinate function. The State Plane
> systems in the U.S. provide another example of a coordinate system that is
> not merely one coordinate function.
>
> Best,
>
> Bill Huber
> Quantitative Decisions
>
> _______________________________________________
> gislist mailing list
> gislist@...
> http://lists.geocomm.com/mailman/listinfo/gislist
>
> _________________________________
> This list is brought to you by
> The GeoCommunity
> http://www.geocomm.com/
>
> _______________________________________________
> gislist mailing list
> gislist@...
> http://lists.geocomm.com/mailman/listinfo/gislist
>
> _________________________________
> This list is brought to you by
> The GeoCommunity
> http://www.geocomm.com/
>

Re: Projections, co-ordinate systems, datums, spheroids, geoids etc.

2009-11-18T12:21:40Z

Hi Bill,

I was pretty sure that if you were still watching this list that you would weigh in (at least I had hoped so). In fact I held off for a while to see if you would respond before I weighed in because I knew my "intuitive" approach to the subject would be no match to your "technical" approach.

I answered Gillian with the kind of answers I use for my first year, non-GIS students to whom I teach an introductory GIS course. If I got into the mathematics as you have done, their eyes would glaze over in an instant. Hell, I had to re-read many of your points to be sure I understood them and I've still got some work to do on that front. Math-phobia can provide challenges - both for my students and me - though I find they usually get a good picture of the general concepts through the intuitive interpretation.

Every year I search on-line to upgrade my lectures, and the Projections lecture has always created the most grief for me for the very reasons Gillian mentioned. A lot of what's out there, both in texts and online, is confusing and sometimes seems contradictory. That's why I left the invitation at the bottom of my response for anyone to correct me if I was leading Gillian astray. Hopefully by the time I have chewed through your email and digested all this, I will be able to do a much better job of explaining these concepts to my students.

Thanks for the lesson.

Cheers,
Rick

>>> Quantitative Decisions <whuber@...> 11/18/09 2:55 PM >>>
This morning Gilllian McGregor asked,
>I would like to clarify the use and definition of a range of terms ... I
>would like to understand better, with regard to ... a better definition,
>when they are used and why they are used and how they relate to one another.

The terms include

Geoid
Ellipsoid
Datum
Coordinate system
Projection.

A helpful respondent wrote:

>A projection is the systematic mathematical transformation of the "round"
>surface so that it will lay flat. Different projections try to minimize
>what gets distorted and by how much and which you utilize will be
>partially dependent on what you want to display in your final map (is
>preserving area more important than direction, etc).

This is excellent. Although everything that followed it was helpful for
the intuition and consistent with what is taught and "known" among GIS
professionals, it nevertheless bears closer examination in the
details. Let's look.

>There are 3 "developable surfaces" that projections are based on - the
>cylinder, the cone and the plane.

This is true for some projections but not all. Many modern projections,
such as many of those developed by the late John Snyder at the USGS, are
not "based" on any developable surface in any fundamental or important way.

An equivalent way to think of a "projection" of any surface is that it
assigns a pair of real numbers to each point on the surface. When you
interpret those numbers as Cartesian coordinates in the plane, you have
drawn a map. That's all there is to map projection.

(BTW, there are many more developable surfaces than these three. By
definition these are surfaces that can be "unrolled": they have everywhere
zero Gaussian curvature but are not necessarily planar. One example is the
elliptical cylinder related to a transverse Mercator projection from an
ellipsoid. For more fanciful examples, take any sheet of paper and roll
its corners and edges into any shape you can without creating folds.)

>Different people (Clarke, etc.) have defined the spheroid or ellipsoid
>mathematically and this goes into the projection formula.

This is less a matter of mathematics than of measurement. A spheroid is an
imaginary surface coincident with the earth (and rotating and moving
through the universe with it). At any given time, the spheroid provides a
way of identifying all points in the universe by means of two things: a
point on the spheroid itself and a distance up or down, perpendicular to
the spheroid, from that point.

What makes a spheroid useful is that it has a simple mathematical
description, unlike the actual surface of a planet. Thus, ellipsoids of
revolution (or sometimes triaxial ellipsoids) are used as references for
the spheroids of planets and planetoids because of their mathematical
simplicity. Having elected to use, say, an ellipsoid of revolution, one
then makes measurements of selected points on the planet's surface and
finds an ellipsoid that best approximates those measured points in some sense.

There are many ellipsoids in use for mapping the earth because (a)
historically measurements have gotten better, (b) the earth's surface is
constantly changing shape, (c) criteria to compare the ellipsoid with the
measured locations can vary, and--most importantly--(d) many different sets
of measurements have focused on relatively small patches of the earth's
surface. An ellipsoid that fits one patch well does not necessarily fit
the rest of the earth's surface well. That's why an ellipsoid suitable for
the UK is unlikely to be used for distant South Africa, for instance.

> To refine it even more, we use the term geoid to explain the bumps and
> hollows of the ocean depths and mountain peaks.

No, this is incorrect. There is a unique geoid defined as a particular a
gravitational equipotential surface. As such, it depends on the
distribution of mass within a planet, not on the form its surface
takes. On the earth, the geoid varies only a little from any decent
ellipsoid; the variation rarely exceeds 100 meters. That obviously does
not "explain" ocean depths or mountain peaks, which are local variations
two orders of magnitude greater. Moreover, the geoid's undulations do not
exactly follow all mountain ranges or ocean floors, although there is a
close correlation.

Of the many possible such equipotential surfaces for the earth (differing
only in height), the geoid is the one along which the surface of the oceans
would lie were there no winds, waves, currents, or tides. (See the
Wikipedia article at http://en.wikipedia.org/wiki/Geoid .) Equipotential
surfaces of gravity are of interest in geodesy primarily because at any
point within the influence of earth's gravitation, "up" is always
perpendicular to the equipotential surface at that point. Because the "up"
direction is used to measure things like geodetic latitude and longitude,
which by definition are determined by the direction perpendicular to the
*ellipsoid*, any deviations between the geoid and whatever ellipsoid is
being used will oblige us to make corrections in geodetic measurements.

BTW, the mechanism we use to represent the ocean floor and mountain peaks,
as well as everything in between, is called a digital elevation model (or
digital terrain model).

>Again, this must be at a fairly coarse resolution because your computer
>would be crunching numbers for days if we wanted to be extremely accurate.

There's nothing the matter with this statement, but it reflects a
philosophy that IMHO reverses priorities, although I'm sure that's not what
was intended. It seems to suggest that the accuracy we accept in our work
should be determined by the computer's capabilities. Yes, compromises must
be made, but especially with today's power, it should work the other way:
you, as the user of the data, should begin by determining the accuracy you
need. Then you set up a system capable of delivering that accuracy. If
you need the submicron-level accuracy that would be delivered by using a
geoid instead of an ellipsoid, then you should compute with the geoid. It
wouldn't cost you days: the calculations aren't that much more involved
(but it's a real pain to program and simply not worth the effort). The
real point is that imprecision in all the other data we have is vastly
greater than the imprecision created by using an ellipsoid instead of the
geoid.

>Then we get to the datum. This is the mathematical surface that fits
>closely to the mean sea level of the earth and to which ground control
>point are referenced. Here in North America our maps used to use NAD27
>(North American Datum 1927) as a final refinement.

These statements actually are contradictory, because NAD27 is neither a
mathematical surface nor a refinement at all: it's actually a gross,
unintended distortion of a datum.

A datum, in its broadest sense, is a system set up to let us find (via
measurement) the point on an ellipsoid (and elevation relative to that
point) corresponding to any physical point on or near the earth's
surface. This can be done in many ways. For NAD27 it consists of a
network of thousands of points laid across the US. To each point was
associated, once and for all (although with great inaccuracy for today's
needs) a point on the Clarke 1866 ellipsoid. To locate any point in North
America, a surveyor finds one or more nearby points in this network and
makes measurements relative to them. With the capabilities afforded by
modern instruments (e.g., GPS), to define a datum it now suffices to
provide an ellipsoid and a single reference location, reference direction,
and reference height on the earth's surface. The example of NAD27 reminds
us that this is not the only way to establish a datum, though.

The fact that NAD27 is not a mathematical surface, nor even a refinement of
one, is made apparent by NADCON and VERTCON, the apparatus needed to relate
NAD27 to other datums. These algorithms require a database that
essentially records the errors (usually at quarter degree intervals) made
within the NAD27 geodetic reference network across North America. The
errors often reach hundreds of meters, especially in northwestern US and
outside the conterminous US. Older datums in Canada and Australia require
similar methods of correction.

>In 83, a new datum (NAD 83) used our new knowledge, based on satellite
>measurements, to more accurately pinpoint the centre of the earth as the
>reference point, which helped to remove the error as you moved across the
>continent. Again, this is just a mathematical refinement to the projection
>when used at a more local level.

The new datum was needed in part because of the large errors introduced in
the network of NAD 27 reference points, not to "pinpoint the center of the
earth." Indeed, even today many datums use ellipsoids whose centers do
*not* coincide with that of the earth, and this is on purpose: it's not an
error. The reason is that these datums attempt to approximate one small
patch of the earth, such as a single country, as well as possible, and in
so doing it just turns out that the ellipsoid is not concentric with the
geoid. This is why we need those seven-parameter datum transformations:
three parameters to shift the ellipsoids, three to rotate them, and one to
rescale their size.

None of this has anything to do with projections. We're talking about
establishing ways to identify points on the earth with points on an
ellipsoid, period. The projection comes only when you decide to make a
map. You make a map in two steps: the datum supplies you with a point on
the ellipsoid, then a mathematical formula--the projection itself--derives
Cartesian coordinates (x,y) from that point.

>A Mercator projection uses the cylinder as its developable surface. If you
>picture wrapping a tube around the globe with its open ends at the poles,
>and "projecting" a light from the centre of the globe outwards onto the
>tube, you sort of get the image.

Yes, but the "sort of" hides some important details. The Mercator
projection also includes an exponential distortion of the north-south
distances, even after this geometric projection operation is carried out:
it is _not_ the same as the light-and-shadow process described. This is
true of many projections: although in some loose intuitive sense they are
"based" on geometric projections onto a developable surface, that's not
really how they work. That's why we need the more general mathematical
idea of projection introduced earlier.

>Because the tube touches only at the equator, that is the point where the
>distortion will be the least. Hence the world maps we used to always see
>had the lands at the top and bottom greatly stretched because they used a
>Mercator projection (Greenland isn't really as big as Brazil).

Again, sort of. The distortion in the Mercator projection has little to do
with tubes or "touching" the equator. It is inherent in the mathematics of
the projection. The distortion is a phenomenon better understood by
considering the map scale in two directions at every point: east-west and
north-south. The Mercator has the special property of being conformal,
which implies those two scales are always equal. Up and down the map, from
north to south, the common scale will increase with increasing distance
from the equator. It becomes unbounded as the poles are approached.

>To make a "transverse" Mercator, we simply rotate the cylinder or tube to
>run crosswise to the globe.

A minor point: that method works when using a perfect sphere for the datum;
mathematically it's more complicated for an ellipsoid, because a meridian
then has the shape of an ellipse, not of a circle.

>Now the area of least distortion follows a meridian from north to south.
>We then decide (well, somebody decided) that a 6 degree swath is as wide
>as we need for one zone in order to minimize distortion.

This does not by any means "minimize" distortion. You can make distortion
smaller still in many ways, such as by using narrower zones. This point
goes back to the philosophical issue raised earlier: the design of UTM
began with a target for scale accuracy. In turns out this target is met by
using reference circles approximately 500 km apart and limiting the
projection to a swath approximately 800 km wide (seven degrees at the
equator). Successive swaths in the UTM system overlap at the equator by
one degree apiece, whence 60 swaths are needed to cover the lower latitudes
of the globe. (A different projection altogether is used for the polar
regions in UTM.)

BTW, there's more to UTM than this. It also includes a hierarchical,
tree-like organization of regions within each UTM zone. However, this
additional structure is rarely used within GIS. It can become important
for interpreting certain military coordinates.

>As for a coordinate system, that is merely a method of identifying a
>location (x,y and perhaps z) on your globe or map. We use degrees, minutes
>and seconds for the 3D globe because that has been the tradition.

Thus, fundamentally, a 3D coordinate function consists of the following:

(1) A set of points, "M", in 3D Euclidean space endowed with its
Cartesian coordinates (x,y,z).

(2) A mechanism to associate a unique point near the earth's surface
with each (x,y,z) in M.

(3) Units of measurement, such as feet, meters, or degrees, for x, y,
and z.

Typically, the mechanism in (2) is "adapted" to the ellipsoid in the sense
that the ellipsoid itself is a level surface of the z coordinate and, to a
good approximation, 'z' can be interpreted as height relative to the
ellipsoid. Consequently, (x,y) can be taken as coordinates for the
ellipsoid itself and 'z' can be taken as elevation.

If this sounds like a "projection," you're hearing right: there's a
projection lurking here. Remember that a projection assigns coordinates to
physical points. A coordinate function as just defined does the opposite:
it assigns physical points to coordinates. But in most cases you can go in
reverse: each physical point usually has only one set of
coordinates. Assigning those coordinates to the point and forgetting about
the 'z' part constitutes a projection. It's a subtle difference, but it
affords ample opportunity for confusion.

BTW, in mathematics a coordinate function is usually defined in the same
way a "projection" is defined here. This is not the place to unravel
differences in terminology. The important thing is to understand the
distinction being made between assigning coordinates to points and
assigning points to coordinates. Both mechanisms are important and useful;
both are very closely related; but they are distinct things.

The idea of "coordinate system" generalizes this: it can comprise more than
one coordinate function. UTM is the archetypical example: it includes more
than 60 coordinate functions. To designate a point on the earth in UTM,
then, you have to specify one of its coordinate function (which amounts to
naming the UTM zone) along with the (x, y) or (x, y, z) coordinates that
will be interpreted in terms of that coordinate function. The State Plane
systems in the U.S. provide another example of a coordinate system that is
not merely one coordinate function.

Best,

Bill Huber
Quantitative Decisions

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Re: Projections, co-ordinate systems, datums, spheroids, geoids etc.

2009-11-18T11:54:09Z

This morning Gilllian McGregor asked,
>I would like to clarify the use and definition of a range of terms ... I
>would like to understand better, with regard to ... a better definition,
>when they are used and why they are used and how they relate to one another.

The terms include

Geoid
Ellipsoid
Datum
Coordinate system
Projection.

A helpful respondent wrote:

>A projection is the systematic mathematical transformation of the "round"
>surface so that it will lay flat. Different projections try to minimize
>what gets distorted and by how much and which you utilize will be
>partially dependent on what you want to display in your final map (is
>preserving area more important than direction, etc).

This is excellent. Although everything that followed it was helpful for
the intuition and consistent with what is taught and "known" among GIS
professionals, it nevertheless bears closer examination in the
details. Let's look.

>There are 3 "developable surfaces" that projections are based on - the
>cylinder, the cone and the plane.

This is true for some projections but not all. Many modern projections,
such as many of those developed by the late John Snyder at the USGS, are
not "based" on any developable surface in any fundamental or important way.

An equivalent way to think of a "projection" of any surface is that it
assigns a pair of real numbers to each point on the surface. When you
interpret those numbers as Cartesian coordinates in the plane, you have
drawn a map. That's all there is to map projection.

(BTW, there are many more developable surfaces than these three. By
definition these are surfaces that can be "unrolled": they have everywhere
zero Gaussian curvature but are not necessarily planar. One example is the
elliptical cylinder related to a transverse Mercator projection from an
ellipsoid. For more fanciful examples, take any sheet of paper and roll
its corners and edges into any shape you can without creating folds.)

>Different people (Clarke, etc.) have defined the spheroid or ellipsoid
>mathematically and this goes into the projection formula.

This is less a matter of mathematics than of measurement. A spheroid is an
imaginary surface coincident with the earth (and rotating and moving
through the universe with it). At any given time, the spheroid provides a
way of identifying all points in the universe by means of two things: a
point on the spheroid itself and a distance up or down, perpendicular to
the spheroid, from that point.

What makes a spheroid useful is that it has a simple mathematical
description, unlike the actual surface of a planet. Thus, ellipsoids of
revolution (or sometimes triaxial ellipsoids) are used as references for
the spheroids of planets and planetoids because of their mathematical
simplicity. Having elected to use, say, an ellipsoid of revolution, one
then makes measurements of selected points on the planet's surface and
finds an ellipsoid that best approximates those measured points in some sense.

There are many ellipsoids in use for mapping the earth because (a)
historically measurements have gotten better, (b) the earth's surface is
constantly changing shape, (c) criteria to compare the ellipsoid with the
measured locations can vary, and--most importantly--(d) many different sets
of measurements have focused on relatively small patches of the earth's
surface. An ellipsoid that fits one patch well does not necessarily fit
the rest of the earth's surface well. That's why an ellipsoid suitable for
the UK is unlikely to be used for distant South Africa, for instance.

> To refine it even more, we use the term geoid to explain the bumps and
> hollows of the ocean depths and mountain peaks.

No, this is incorrect. There is a unique geoid defined as a particular a
gravitational equipotential surface. As such, it depends on the
distribution of mass within a planet, not on the form its surface
takes. On the earth, the geoid varies only a little from any decent
ellipsoid; the variation rarely exceeds 100 meters. That obviously does
not "explain" ocean depths or mountain peaks, which are local variations
two orders of magnitude greater. Moreover, the geoid's undulations do not
exactly follow all mountain ranges or ocean floors, although there is a
close correlation.

Of the many possible such equipotential surfaces for the earth (differing
only in height), the geoid is the one along which the surface of the oceans
would lie were there no winds, waves, currents, or tides. (See the
Wikipedia article at http://en.wikipedia.org/wiki/Geoid .) Equipotential
surfaces of gravity are of interest in geodesy primarily because at any
point within the influence of earth's gravitation, "up" is always
perpendicular to the equipotential surface at that point. Because the "up"
direction is used to measure things like geodetic latitude and longitude,
which by definition are determined by the direction perpendicular to the
*ellipsoid*, any deviations between the geoid and whatever ellipsoid is
being used will oblige us to make corrections in geodetic measurements.

BTW, the mechanism we use to represent the ocean floor and mountain peaks,
as well as everything in between, is called a digital elevation model (or
digital terrain model).

>Again, this must be at a fairly coarse resolution because your computer
>would be crunching numbers for days if we wanted to be extremely accurate.

There's nothing the matter with this statement, but it reflects a
philosophy that IMHO reverses priorities, although I'm sure that's not what
was intended. It seems to suggest that the accuracy we accept in our work
should be determined by the computer's capabilities. Yes, compromises must
be made, but especially with today's power, it should work the other way:
you, as the user of the data, should begin by determining the accuracy you
need. Then you set up a system capable of delivering that accuracy. If
you need the submicron-level accuracy that would be delivered by using a
geoid instead of an ellipsoid, then you should compute with the geoid. It
wouldn't cost you days: the calculations aren't that much more involved
(but it's a real pain to program and simply not worth the effort). The
real point is that imprecision in all the other data we have is vastly
greater than the imprecision created by using an ellipsoid instead of the
geoid.

>Then we get to the datum. This is the mathematical surface that fits
>closely to the mean sea level of the earth and to which ground control
>point are referenced. Here in North America our maps used to use NAD27
>(North American Datum 1927) as a final refinement.

These statements actually are contradictory, because NAD27 is neither a
mathematical surface nor a refinement at all: it's actually a gross,
unintended distortion of a datum.

A datum, in its broadest sense, is a system set up to let us find (via
measurement) the point on an ellipsoid (and elevation relative to that
point) corresponding to any physical point on or near the earth's
surface. This can be done in many ways. For NAD27 it consists of a
network of thousands of points laid across the US. To each point was
associated, once and for all (although with great inaccuracy for today's
needs) a point on the Clarke 1866 ellipsoid. To locate any point in North
America, a surveyor finds one or more nearby points in this network and
makes measurements relative to them. With the capabilities afforded by
modern instruments (e.g., GPS), to define a datum it now suffices to
provide an ellipsoid and a single reference location, reference direction,
and reference height on the earth's surface. The example of NAD27 reminds
us that this is not the only way to establish a datum, though.

The fact that NAD27 is not a mathematical surface, nor even a refinement of
one, is made apparent by NADCON and VERTCON, the apparatus needed to relate
NAD27 to other datums. These algorithms require a database that
essentially records the errors (usually at quarter degree intervals) made
within the NAD27 geodetic reference network across North America. The
errors often reach hundreds of meters, especially in northwestern US and
outside the conterminous US. Older datums in Canada and Australia require
similar methods of correction.

>In 83, a new datum (NAD 83) used our new knowledge, based on satellite
>measurements, to more accurately pinpoint the centre of the earth as the
>reference point, which helped to remove the error as you moved across the
>continent. Again, this is just a mathematical refinement to the projection
>when used at a more local level.

The new datum was needed in part because of the large errors introduced in
the network of NAD 27 reference points, not to "pinpoint the center of the
earth." Indeed, even today many datums use ellipsoids whose centers do
*not* coincide with that of the earth, and this is on purpose: it's not an
error. The reason is that these datums attempt to approximate one small
patch of the earth, such as a single country, as well as possible, and in
so doing it just turns out that the ellipsoid is not concentric with the
geoid. This is why we need those seven-parameter datum transformations:
three parameters to shift the ellipsoids, three to rotate them, and one to
rescale their size.

None of this has anything to do with projections. We're talking about
establishing ways to identify points on the earth with points on an
ellipsoid, period. The projection comes only when you decide to make a
map. You make a map in two steps: the datum supplies you with a point on
the ellipsoid, then a mathematical formula--the projection itself--derives
Cartesian coordinates (x,y) from that point.

>A Mercator projection uses the cylinder as its developable surface. If you
>picture wrapping a tube around the globe with its open ends at the poles,
>and "projecting" a light from the centre of the globe outwards onto the
>tube, you sort of get the image.

Yes, but the "sort of" hides some important details. The Mercator
projection also includes an exponential distortion of the north-south
distances, even after this geometric projection operation is carried out:
it is _not_ the same as the light-and-shadow process described. This is
true of many projections: although in some loose intuitive sense they are
"based" on geometric projections onto a developable surface, that's not
really how they work. That's why we need the more general mathematical
idea of projection introduced earlier.

>Because the tube touches only at the equator, that is the point where the
>distortion will be the least. Hence the world maps we used to always see
>had the lands at the top and bottom greatly stretched because they used a
>Mercator projection (Greenland isn't really as big as Brazil).

Again, sort of. The distortion in the Mercator projection has little to do
with tubes or "touching" the equator. It is inherent in the mathematics of
the projection. The distortion is a phenomenon better understood by
considering the map scale in two directions at every point: east-west and
north-south. The Mercator has the special property of being conformal,
which implies those two scales are always equal. Up and down the map, from
north to south, the common scale will increase with increasing distance
from the equator. It becomes unbounded as the poles are approached.

>To make a "transverse" Mercator, we simply rotate the cylinder or tube to
>run crosswise to the globe.

A minor point: that method works when using a perfect sphere for the datum;
mathematically it's more complicated for an ellipsoid, because a meridian
then has the shape of an ellipse, not of a circle.

>Now the area of least distortion follows a meridian from north to south.
>We then decide (well, somebody decided) that a 6 degree swath is as wide
>as we need for one zone in order to minimize distortion.

This does not by any means "minimize" distortion. You can make distortion
smaller still in many ways, such as by using narrower zones. This point
goes back to the philosophical issue raised earlier: the design of UTM
began with a target for scale accuracy. In turns out this target is met by
using reference circles approximately 500 km apart and limiting the
projection to a swath approximately 800 km wide (seven degrees at the
equator). Successive swaths in the UTM system overlap at the equator by
one degree apiece, whence 60 swaths are needed to cover the lower latitudes
of the globe. (A different projection altogether is used for the polar
regions in UTM.)

BTW, there's more to UTM than this. It also includes a hierarchical,
tree-like organization of regions within each UTM zone. However, this
additional structure is rarely used within GIS. It can become important
for interpreting certain military coordinates.

>As for a coordinate system, that is merely a method of identifying a
>location (x,y and perhaps z) on your globe or map. We use degrees, minutes
>and seconds for the 3D globe because that has been the tradition.

Thus, fundamentally, a 3D coordinate function consists of the following:

(1) A set of points, "M", in 3D Euclidean space endowed with its
Cartesian coordinates (x,y,z).

(2) A mechanism to associate a unique point near the earth's surface
with each (x,y,z) in M.

(3) Units of measurement, such as feet, meters, or degrees, for x, y,
and z.

Typically, the mechanism in (2) is "adapted" to the ellipsoid in the sense
that the ellipsoid itself is a level surface of the z coordinate and, to a
good approximation, 'z' can be interpreted as height relative to the
ellipsoid. Consequently, (x,y) can be taken as coordinates for the
ellipsoid itself and 'z' can be taken as elevation.

If this sounds like a "projection," you're hearing right: there's a
projection lurking here. Remember that a projection assigns coordinates to
physical points. A coordinate function as just defined does the opposite:
it assigns physical points to coordinates. But in most cases you can go in
reverse: each physical point usually has only one set of
coordinates. Assigning those coordinates to the point and forgetting about
the 'z' part constitutes a projection. It's a subtle difference, but it
affords ample opportunity for confusion.

BTW, in mathematics a coordinate function is usually defined in the same
way a "projection" is defined here. This is not the place to unravel
differences in terminology. The important thing is to understand the
distinction being made between assigning coordinates to points and
assigning points to coordinates. Both mechanisms are important and useful;
both are very closely related; but they are distinct things.

The idea of "coordinate system" generalizes this: it can comprise more than
one coordinate function. UTM is the archetypical example: it includes more
than 60 coordinate functions. To designate a point on the earth in UTM,
then, you have to specify one of its coordinate function (which amounts to
naming the UTM zone) along with the (x, y) or (x, y, z) coordinates that
will be interpreted in terms of that coordinate function. The State Plane
systems in the U.S. provide another example of a coordinate system that is
not merely one coordinate function.

Best,

Bill Huber
Quantitative Decisions

_______________________________________________
gislist mailing list
gislist@...
http://lists.geocomm.com/mailman/listinfo/gislist

_________________________________
This list is brought to you by
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http://www.geocomm.com/

Re: Projections, co-ordinate systems, datums, spheroids, geoids etc.

2009-11-18T11:13:41Z

Hi,

Just in passing, in my classes I talk about projection-based coordinate systems, since in GIS both are necessary (putting aside using lat/long). Both elements must be described if the data is to be used in a GIS, and associated with every projection must be a datum. Together, datum -> projection -> coordinate system identify a project-based coordinate system (PBCS).

UTM is an example of a PBCS, although the choice of datum is not fixed.

Cheers,

Brian

----- Original Message -----
From: "David Hockman-Wert" <dhockman-wert@...>
To: gislist@..., "RICK GRAY" <RGRAY@...>
Sent: Wednesday, 18 November, 2009 10:28:50 GMT -08:00 US/Canada Pacific
Subject: Re: [gislist] Projections, co-ordinate systems, datums, spheroids, geoids etc.

Rick's explanation is very thorough. I would simply add that in the way
that ESRI uses the term "coordinate system", it is slightly different from
what Rick says. For ESRI, each "coordinate system" is one possible way of
presenting spatial data, using a "datum" and possibly a "projection"
(already well-defined by Rick). I think they use this terminology rather
than "projection", because there are unprojected coordinate systems
(geographic).

Below I'll paste the section on coordinate systems from ESRI's help. I
think it gets at the interconnections between the various terms, at least
in the way that ESRI is using them.

"Coordinate systems, also known as map projections, are arbitrary
designations for spatial data. Their purpose is to provide a common basis
for communication about a particular place or area on the earth's surface.
The most critical issue in dealing with coordinate systems is knowing what
the projection is and having the correct coordinate system information
associated with a dataset. There are two types of coordinate
systems?geographic and projected.
A geographic coordinate system uses a three-dimensional spherical surface
to define locations on the earth. It includes an angular unit of measure,
a prime meridian, and a datum (based on a spheroid). In a geographic
coordinate system a point is referenced by its longitude and latitude
values. Longitude and latitude are angles measured from the earth's center
to a point on the earth's surface. The angles often are measured in
degrees (or in grads).
A projected coordinate system is defined on a flat, two-dimensional
surface. Unlike a geographic coordinate system, a projected coordinate
system has constant lengths, angles, and areas across the two dimensions.
A projected coordinate system is always based on a geographic coordinate
system that is based on a sphere or spheroid.
In a projected coordinate system, locations are identified by x,y
coordinates on a grid, with the origin at the center of the grid. Each
position has two values that reference it to that central location. One
specifies its horizontal position and the other its vertical position."

David Hockman-Wert
Biologist
USGS FRESC Corvallis Research Group
3200 SW Jefferson Way
Corvallis, OR 97331
Phone: 541-750-7281 Fax: 541-758-8806
dhockman-wert@...

From:
"RICK GRAY" <RGRAY@...>
To:
<gislist@...>, "Gillian McGregor" <g.k.mcgregor@...>
Date:
11/18/2009 05:58 AM
Subject:
Re: [gislist] Projections, co-ordinate systems, datums, spheroids, geoids
etc.
Sent by:
gislist-bounces+dhockman-wert=usgs.gov@...

Hi Gillian,

Here is my understanding of the terminology. I will actually start from
the bottom of your list.

A projection is the mathematics of taking the globe and flattening it onto
a piece of paper (or computer screen). Think of an orange peel. If you try
to flatten it out, you are going to get bulges and bumps and pieces that
just won't want to lay down flat. Therefore once you have it flattened,
there will be some distortion in the final image. A projection is the
systematic mathematical transformation of the "round" surface so that it
will lay flat. Different projections try to minimize what gets distorted
and by how much and which you utilize will be partially dependent on what
you want to display in your final map (is preserving area more important
than direction, etc). Some projections work better on a large scale,
others at a small scale. Some work better at the poles than others. And so
on.

There are 3 "developable surfaces" that projections are based on - the
cylinder, the cone and the plane. These, and variations on these - such as
whether it is transverse or tangent, etc. - help to refine your choice of
projection. (I'll come back to cylinders in a minute).

Part of the math behind your final projected map depends on some
assumptions. Since we know that the earth is not a perfect sphere, we have
to decide how much distortion there is, and where that distortion is. In a
very broad sense, the earth is a spheroid or ellipsoid - a somewhat
flattened and fat around the middle globe. This is the starting point.
Different people (Clarke, etc.) have defined the spheroid or ellipsoid
mathematically and this goes into the projection formula. To refine it
even more, we use the term geoid to explain the bumps and hollows of the
ocean depths and mountain peaks. Again, this must be at a fairly coarse
resolution because your computer would be crunching numbers for days if we
wanted to be extremely accurate.

Then we get to the datum. This is the mathematical surface that fits
closely to the mean sea level of the earth and to which ground control
point are referenced. Here in North America our maps used to use NAD27
(North American Datum 1927) as a final refinement. This was developed with
a location in the midwestern US as its starting point and careful surveys
compared everything to that point. Unfortunately, it became a less
accurate model the further you got away from the centre but for fairly
small scale maps it seemed pretty good. In 83, a new datum (NAD 83) used
our new knowledge, based on satellite measurements, to more accurately
pinpoint the centre of the earth as the reference point, which helped to
remove the error as you moved across the continent. Again, this is just a
mathematical refinement to the projection when used at a more local level.

UTM (Universal Transverse Mercator) - my favourite. As I was taught it,
UTM is not a projection although it is sometimes called one (even on some
of our government maps here in Canada). It is a grid system imposed on a
Mercator projection.

A Mercator projection uses the cylinder as its developable surface. If you
picture wrapping a tube around the globe with its open ends at the poles,
and "projecting" a light from the centre of the globe outwards onto the
tube, you sort of get the image. Because the tube touches only at the
equator, that is the point where the distortion will be the least. Hence
the world maps we used to always see had the lands at the top and bottom
greatly stretched because they used a Mercator projection (Greenland isn't
really as big as Brazil).

To make a "transverse" Mercator, we simply rotate the cylinder or tube to
run crosswise to the globe. Now the area of least distortion follows a
meridian from north to south. We then decide (well, somebody decided) that
a 6 degree swath is as wide as we need for one zone in order to minimize
distortion. This system works very well at a very local level. A grid
imposed on the zone, with a central meridian artificially chosen to be
500,000 meters ensures that there will never be any negative coordinates
to deal with since even at the equator 6 degrees is less than a million
meters wide. And to minimize distortion even further, we use the cylinder
in its secant case where it actually touches the surface at 2 points in
the 6 degree zone rather than just the one. It now becomes universally
accepted and is called a Universal Transverse Mercator grid. (There are
local variations, but this is the basic system.)

As for a coordinate system, that is merely a method of identifying a
location (x,y and perhaps z) on your globe or map. We use degrees, minutes
and seconds for the 3D globe because that has been the tradition. Once we
project the globe onto a flat surface, those coordinates can still be
displayed but there is often a better way and so we use Eastings and
Northings, measured in meters, on our UTM maps, or decimal degrees on our
GIS system, etc. Your local SA maps probably use something developed
locally that makes sense based on the how the maps were built.

I hope this helps clarify some points.

This is my understanding of how it all works. If I have led Gillian
astray, I hope someone on the list can correct me.

Cheers,
Rick Gray

>>> "Gillian McGregor" <g.k.mcgregor@...> 11/18/2009 4:28 AM >>>
I would like to clarify the use and definition of a range of terms. While
I understand their meaning in isolation, it's sometimes difficult to work
out how the terms relate to each other, or how they are different to one
another. I would be grateful if someone out there with more experience is
able to correspond with me and provide some answers to these and other
related queries. I have read quite a few basic texts, but would also like
to know of more specific ones? (I am a South African and dealing with SA
examples).

Here are some of the terms I would like to understand better, with regard
to firstly, a better defintion, when they are used and why they are used
and how the relate to one another:

Geoid: most accurate measurement of earths axes, accounts for
irregularities at a local scale in terms of high and low points and
bulging caused by gravitational forces. A geodetic datum eg: the
Haartebeeshoek datum or the Cape datum is a 'local' version of an
ellipsoid which is much more accurate because it takes in to account local
variation in size, shape, gravitational bulges etc.

Datum: a set of measurements related to a spheroid, ellipsoid or geoid ?
And....

Ellipsoid: mathematical model defining the 'smoothed' earth sphere
according to equatorial and polar radii

Spheroid: more generalised and the simplest shape model of the earth.

Co-ordinate system: 2 or 3 D grid of some description? Typically I think
of Geographic co-ordinates as an example, but I know there are other
co-ordinate systems. I was once told that once a projection is employed
with customised parameters, it 'becomes' a co-ordinate system'? eg: in
South Africa we use the Gauss Kruger projection for local area (1:10 000
to 1: 250 000 scale) maps, referenced to the nearest uneven line of
longtitude. This is what we call the Lo co-ordinate system. UTM is a
co-ordinate system, but it is based on the Transverse mercator projection?
Then there are local co-ordinate systems like the UK ntaional grid, the
South African Lo co-ordinate system....

Projection: a mathematical algorithm used to transform the round earth
onto a 2D plane transformation
Every projection is related to a datum? Or an ellipsoid?

My perception is that various software packages use incorrect terms or use
them synonymously which causes confusion....

Thanks

Gillian McGregor
Lecturer
Dept. of Geography
Rhodes University
Grahamstown
6140

Tel: 046-603 8322 (w)
046-622 8482 (h)
Fax: 046-636 1199
_______________________________________________
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---------------------------------------------------
Brian Klinkenberg :: http://www.geog.ubc.ca/~brian
Visit E-Flora BC :: http://eflora.bc.ca
P: 604.822.3534 :: F: 604.822.6150
Department of Geography, UBC
1984 West Mall, Vancouver BC V6T 1Z2

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Re: Projections, co-ordinate systems, datums, spheroids, geoids etc.

2009-11-18T10:28:50Z

Rick's explanation is very thorough. I would simply add that in the way
that ESRI uses the term "coordinate system", it is slightly different from
what Rick says. For ESRI, each "coordinate system" is one possible way of
presenting spatial data, using a "datum" and possibly a "projection"
(already well-defined by Rick). I think they use this terminology rather
than "projection", because there are unprojected coordinate systems
(geographic).

Below I'll paste the section on coordinate systems from ESRI's help. I
think it gets at the interconnections between the various terms, at least
in the way that ESRI is using them.

"Coordinate systems, also known as map projections, are arbitrary
designations for spatial data. Their purpose is to provide a common basis
for communication about a particular place or area on the earth's surface.
The most critical issue in dealing with coordinate systems is knowing what
the projection is and having the correct coordinate system information
associated with a dataset. There are two types of coordinate
systems?geographic and projected.
A geographic coordinate system uses a three-dimensional spherical surface
to define locations on the earth. It includes an angular unit of measure,
a prime meridian, and a datum (based on a spheroid). In a geographic
coordinate system a point is referenced by its longitude and latitude
values. Longitude and latitude are angles measured from the earth's center
to a point on the earth's surface. The angles often are measured in
degrees (or in grads).
A projected coordinate system is defined on a flat, two-dimensional
surface. Unlike a geographic coordinate system, a projected coordinate
system has constant lengths, angles, and areas across the two dimensions.
A projected coordinate system is always based on a geographic coordinate
system that is based on a sphere or spheroid.
In a projected coordinate system, locations are identified by x,y
coordinates on a grid, with the origin at the center of the grid. Each
position has two values that reference it to that central location. One
specifies its horizontal position and the other its vertical position."

David Hockman-Wert
Biologist
USGS FRESC Corvallis Research Group
3200 SW Jefferson Way
Corvallis, OR 97331
Phone: 541-750-7281 Fax: 541-758-8806
dhockman-wert@...

From:
"RICK GRAY" <RGRAY@...>
To:
<gislist@...>, "Gillian McGregor" <g.k.mcgregor@...>
Date:
11/18/2009 05:58 AM
Subject:
Re: [gislist] Projections, co-ordinate systems, datums, spheroids, geoids
etc.
Sent by:
gislist-bounces+dhockman-wert=usgs.gov@...

Hi Gillian,

Here is my understanding of the terminology. I will actually start from
the bottom of your list.

A projection is the mathematics of taking the globe and flattening it onto
a piece of paper (or computer screen). Think of an orange peel. If you try
to flatten it out, you are going to get bulges and bumps and pieces that
just won't want to lay down flat. Therefore once you have it flattened,
there will be some distortion in the final image. A projection is the
systematic mathematical transformation of the "round" surface so that it
will lay flat. Different projections try to minimize what gets distorted
and by how much and which you utilize will be partially dependent on what
you want to display in your final map (is preserving area more important
than direction, etc). Some projections work better on a large scale,
others at a small scale. Some work better at the poles than others. And so
on.

There are 3 "developable surfaces" that projections are based on - the
cylinder, the cone and the plane. These, and variations on these - such as
whether it is transverse or tangent, etc. - help to refine your choice of
projection. (I'll come back to cylinders in a minute).

Part of the math behind your final projected map depends on some
assumptions. Since we know that the earth is not a perfect sphere, we have
to decide how much distortion there is, and where that distortion is. In a
very broad sense, the earth is a spheroid or ellipsoid - a somewhat
flattened and fat around the middle globe. This is the starting point.
Different people (Clarke, etc.) have defined the spheroid or ellipsoid
mathematically and this goes into the projection formula. To refine it
even more, we use the term geoid to explain the bumps and hollows of the
ocean depths and mountain peaks. Again, this must be at a fairly coarse
resolution because your computer would be crunching numbers for days if we
wanted to be extremely accurate.

Then we get to the datum. This is the mathematical surface that fits
closely to the mean sea level of the earth and to which ground control
point are referenced. Here in North America our maps used to use NAD27
(North American Datum 1927) as a final refinement. This was developed with
a location in the midwestern US as its starting point and careful surveys
compared everything to that point. Unfortunately, it became a less
accurate model the further you got away from the centre but for fairly
small scale maps it seemed pretty good. In 83, a new datum (NAD 83) used
our new knowledge, based on satellite measurements, to more accurately
pinpoint the centre of the earth as the reference point, which helped to
remove the error as you moved across the continent. Again, this is just a
mathematical refinement to the projection when used at a more local level.

UTM (Universal Transverse Mercator) - my favourite. As I was taught it,
UTM is not a projection although it is sometimes called one (even on some
of our government maps here in Canada). It is a grid system imposed on a
Mercator projection.

A Mercator projection uses the cylinder as its developable surface. If you
picture wrapping a tube around the globe with its open ends at the poles,
and "projecting" a light from the centre of the globe outwards onto the
tube, you sort of get the image. Because the tube touches only at the
equator, that is the point where the distortion will be the least. Hence
the world maps we used to always see had the lands at the top and bottom
greatly stretched because they used a Mercator projection (Greenland isn't
really as big as Brazil).

To make a "transverse" Mercator, we simply rotate the cylinder or tube to
run crosswise to the globe. Now the area of least distortion follows a
meridian from north to south. We then decide (well, somebody decided) that
a 6 degree swath is as wide as we need for one zone in order to minimize
distortion. This system works very well at a very local level. A grid
imposed on the zone, with a central meridian artificially chosen to be
500,000 meters ensures that there will never be any negative coordinates
to deal with since even at the equator 6 degrees is less than a million
meters wide. And to minimize distortion even further, we use the cylinder
in its secant case where it actually touches the surface at 2 points in
the 6 degree zone rather than just the one. It now becomes universally
accepted and is called a Universal Transverse Mercator grid. (There are
local variations, but this is the basic system.)

As for a coordinate system, that is merely a method of identifying a
location (x,y and perhaps z) on your globe or map. We use degrees, minutes
and seconds for the 3D globe because that has been the tradition. Once we
project the globe onto a flat surface, those coordinates can still be
displayed but there is often a better way and so we use Eastings and
Northings, measured in meters, on our UTM maps, or decimal degrees on our
GIS system, etc. Your local SA maps probably use something developed
locally that makes sense based on the how the maps were built.

I hope this helps clarify some points.

This is my understanding of how it all works. If I have led Gillian
astray, I hope someone on the list can correct me.

Cheers,
Rick Gray

>>> "Gillian McGregor" <g.k.mcgregor@...> 11/18/2009 4:28 AM >>>
I would like to clarify the use and definition of a range of terms. While
I understand their meaning in isolation, it's sometimes difficult to work
out how the terms relate to each other, or how they are different to one
another. I would be grateful if someone out there with more experience is
able to correspond with me and provide some answers to these and other
related queries. I have read quite a few basic texts, but would also like
to know of more specific ones? (I am a South African and dealing with SA
examples).

Here are some of the terms I would like to understand better, with regard
to firstly, a better defintion, when they are used and why they are used
and how the relate to one another:

Geoid: most accurate measurement of earths axes, accounts for
irregularities at a local scale in terms of high and low points and
bulging caused by gravitational forces. A geodetic datum eg: the
Haartebeeshoek datum or the Cape datum is a 'local' version of an
ellipsoid which is much more accurate because it takes in to account local
variation in size, shape, gravitational bulges etc.

Datum: a set of measurements related to a spheroid, ellipsoid or geoid ?
And....

Ellipsoid: mathematical model defining the 'smoothed' earth sphere
according to equatorial and polar radii

Spheroid: more generalised and the simplest shape model of the earth.

Co-ordinate system: 2 or 3 D grid of some description? Typically I think
of Geographic co-ordinates as an example, but I know there are other
co-ordinate systems. I was once told that once a projection is employed
with customised parameters, it 'becomes' a co-ordinate system'? eg: in
South Africa we use the Gauss Kruger projection for local area (1:10 000
to 1: 250 000 scale) maps, referenced to the nearest uneven line of
longtitude. This is what we call the Lo co-ordinate system. UTM is a
co-ordinate system, but it is based on the Transverse mercator projection?
Then there are local co-ordinate systems like the UK ntaional grid, the
South African Lo co-ordinate system....

Projection: a mathematical algorithm used to transform the round earth
onto a 2D plane transformation
Every projection is related to a datum? Or an ellipsoid?

My perception is that various software packages use incorrect terms or use
them synonymously which causes confusion....

Thanks

Gillian McGregor
Lecturer
Dept. of Geography
Rhodes University
Grahamstown
6140

Tel: 046-603 8322 (w)
046-622 8482 (h)
Fax: 046-636 1199
_______________________________________________
gislist mailing list
gislist@...
http://lists.geocomm.com/mailman/listinfo/gislist

_________________________________
This list is brought to you by
The GeoCommunity
http://www.geocomm.com/
_______________________________________________
gislist mailing list
gislist@...
http://lists.geocomm.com/mailman/listinfo/gislist

_________________________________
This list is brought to you by
The GeoCommunity
http://www.geocomm.com/

_______________________________________________
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_________________________________
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Re: Projections, co-ordinate systems, datums, spheroids, geoids etc.

2009-11-18T05:57:21Z

Hi Gillian,

Here is my understanding of the terminology. I will actually start from the bottom of your list.

A projection is the mathematics of taking the globe and flattening it onto a piece of paper (or computer screen). Think of an orange peel. If you try to flatten it out, you are going to get bulges and bumps and pieces that just won't want to lay down flat. Therefore once you have it flattened, there will be some distortion in the final image. A projection is the systematic mathematical transformation of the "round" surface so that it will lay flat. Different projections try to minimize what gets distorted and by how much and which you utilize will be partially dependent on what you want to display in your final map (is preserving area more important than direction, etc). Some projections work better on a large scale, others at a small scale. Some work better at the poles than others. And so on.

There are 3 "developable surfaces" that projections are based on - the cylinder, the cone and the plane. These, and variations on these - such as whether it is transverse or tangent, etc. - help to refine your choice of projection. (I'll come back to cylinders in a minute).

Part of the math behind your final projected map depends on some assumptions. Since we know that the earth is not a perfect sphere, we have to decide how much distortion there is, and where that distortion is. In a very broad sense, the earth is a spheroid or ellipsoid - a somewhat flattened and fat around the middle globe. This is the starting point. Different people (Clarke, etc.) have defined the spheroid or ellipsoid mathematically and this goes into the projection formula. To refine it even more, we use the term geoid to explain the bumps and hollows of the ocean depths and mountain peaks. Again, this must be at a fairly coarse resolution because your computer would be crunching numbers for days if we wanted to be extremely accurate.

Then we get to the datum. This is the mathematical surface that fits closely to the mean sea level of the earth and to which ground control point are referenced. Here in North America our maps used to use NAD27 (North American Datum 1927) as a final refinement. This was developed with a location in the midwestern US as its starting point and careful surveys compared everything to that point. Unfortunately, it became a less accurate model the further you got away from the centre but for fairly small scale maps it seemed pretty good. In 83, a new datum (NAD 83) used our new knowledge, based on satellite measurements, to more accurately pinpoint the centre of the earth as the reference point, which helped to remove the error as you moved across the continent. Again, this is just a mathematical refinement to the projection when used at a more local level.

UTM (Universal Transverse Mercator) - my favourite. As I was taught it, UTM is not a projection although it is sometimes called one (even on some of our government maps here in Canada). It is a grid system imposed on a Mercator projection.

A Mercator projection uses the cylinder as its developable surface. If you picture wrapping a tube around the globe with its open ends at the poles, and "projecting" a light from the centre of the globe outwards onto the tube, you sort of get the image. Because the tube touches only at the equator, that is the point where the distortion will be the least. Hence the world maps we used to always see had the lands at the top and bottom greatly stretched because they used a Mercator projection (Greenland isn't really as big as Brazil).

To make a "transverse" Mercator, we simply rotate the cylinder or tube to run crosswise to the globe. Now the area of least distortion follows a meridian from north to south. We then decide (well, somebody decided) that a 6 degree swath is as wide as we need for one zone in order to minimize distortion. This system works very well at a very local level. A grid imposed on the zone, with a central meridian artificially chosen to be 500,000 meters ensures that there will never be any negative coordinates to deal with since even at the equator 6 degrees is less than a million meters wide. And to minimize distortion even further, we use the cylinder in its secant case where it actually touches the surface at 2 points in the 6 degree zone rather than just the one. It now becomes universally accepted and is called a Universal Transverse Mercator grid. (There are local variations, but this is the basic system.)

As for a coordinate system, that is merely a method of identifying a location (x,y and perhaps z) on your globe or map. We use degrees, minutes and seconds for the 3D globe because that has been the tradition. Once we project the globe onto a flat surface, those coordinates can still be displayed but there is often a better way and so we use Eastings and Northings, measured in meters, on our UTM maps, or decimal degrees on our GIS system, etc. Your local SA maps probably use something developed locally that makes sense based on the how the maps were built.

I hope this helps clarify some points.

This is my understanding of how it all works. If I have led Gillian astray, I hope someone on the list can correct me.

Cheers,
Rick Gray

>>> "Gillian McGregor" <g.k.mcgregor@...> 11/18/2009 4:28 AM >>>
I would like to clarify the use and definition of a range of terms. While I understand their meaning in isolation, it's sometimes difficult to work out how the terms relate to each other, or how they are different to one another. I would be grateful if someone out there with more experience is able to correspond with me and provide some answers to these and other related queries. I have read quite a few basic texts, but would also like to know of more specific ones? (I am a South African and dealing with SA examples).

Here are some of the terms I would like to understand better, with regard to firstly, a better defintion, when they are used and why they are used and how the relate to one another:

Geoid: most accurate measurement of earths axes, accounts for irregularities at a local scale in terms of high and low points and bulging caused by gravitational forces. A geodetic datum eg: the Haartebeeshoek datum or the Cape datum is a 'local' version of an ellipsoid which is much more accurate because it takes in to account local variation in size, shape, gravitational bulges etc.

Datum: a set of measurements related to a spheroid, ellipsoid or geoid ? And....

Ellipsoid: mathematical model defining the 'smoothed' earth sphere according to equatorial and polar radii

Spheroid: more generalised and the simplest shape model of the earth.

Co-ordinate system: 2 or 3 D grid of some description? Typically I think of Geographic co-ordinates as an example, but I know there are other co-ordinate systems. I was once told that once a projection is employed with customised parameters, it 'becomes' a co-ordinate system'? eg: in South Africa we use the Gauss Kruger projection for local area (1:10 000 to 1: 250 000 scale) maps, referenced to the nearest uneven line of longtitude. This is what we call the Lo co-ordinate system. UTM is a co-ordinate system, but it is based on the Transverse mercator projection? Then there are local co-ordinate systems like the UK ntaional grid, the South African Lo co-ordinate system....

Projection: a mathematical algorithm used to transform the round earth onto a 2D plane transformation
Every projection is related to a datum? Or an ellipsoid?

My perception is that various software packages use incorrect terms or use them synonymously which causes confusion....

Thanks

Gillian McGregor
Lecturer
Dept. of Geography
Rhodes University
Grahamstown
6140

Tel: 046-603 8322 (w)
046-622 8482 (h)
Fax: 046-636 1199
_______________________________________________
gislist mailing list
gislist@...
http://lists.geocomm.com/mailman/listinfo/gislist

_________________________________
This list is brought to you by
The GeoCommunity
http://www.geocomm.com/
_______________________________________________
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gislist@...
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Projections, co-ordinate systems, datums, spheroids, geoids etc.

2009-11-18T01:28:41Z

I would like to clarify the use and definition of a range of terms. While I understand their meaning in isolation, it's sometimes difficult to work out how the terms relate to each other, or how they are different to one another. I would be grateful if someone out there with more experience is able to correspond with me and provide some answers to these and other related queries. I have read quite a few basic texts, but would also like to know of more specific ones? (I am a South African and dealing with SA examples).

Here are some of the terms I would like to understand better, with regard to firstly, a better defintion, when they are used and why they are used and how the relate to one another:

Geoid: most accurate measurement of earths axes, accounts for irregularities at a local scale in terms of high and low points and bulging caused by gravitational forces. A geodetic datum eg: the Haartebeeshoek datum or the Cape datum is a 'local' version of an ellipsoid which is much more accurate because it takes in to account local variation in size, shape, gravitational bulges etc.

Datum: a set of measurements related to a spheroid, ellipsoid or geoid ? And....

Ellipsoid: mathematical model defining the 'smoothed' earth sphere according to equatorial and polar radii

Spheroid: more generalised and the simplest shape model of the earth.

Co-ordinate system: 2 or 3 D grid of some description? Typically I think of Geographic co-ordinates as an example, but I know there are other co-ordinate systems. I was once told that once a projection is employed with customised parameters, it 'becomes' a co-ordinate system'? eg: in South Africa we use the Gauss Kruger projection for local area (1:10 000 to 1: 250 000 scale) maps, referenced to the nearest uneven line of longtitude. This is what we call the Lo co-ordinate system. UTM is a co-ordinate system, but it is based on the Transverse mercator projection? Then there are local co-ordinate systems like the UK ntaional grid, the South African Lo co-ordinate system....

Projection: a mathematical algorithm used to transform the round earth onto a 2D plane transformation
Every projection is related to a datum? Or an ellipsoid?

My perception is that various software packages use incorrect terms or use them synonymously which causes confusion....

Thanks

Gillian McGregor
Lecturer
Dept. of Geography
Rhodes University
Grahamstown
6140

Tel: 046-603 8322 (w)
046-622 8482 (h)
Fax: 046-636 1199
_______________________________________________
gislist mailing list
gislist@...
http://lists.geocomm.com/mailman/listinfo/gislist

_________________________________
This list is brought to you by
The GeoCommunity
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Free Midrange desktop GIS - release of stable version of gvSIG 1.9

2009-11-12T10:47:01Z

Much anticipated here is finally (after a long wait time) the brand new "stable" version of gvSIG 1.9
http://www.gvsig.gva.es/eng/gvsig-desktop/all-versions/download/gvsig-19/downloading-the-program/

An announcement in Spanish is here: http://geomaticblog.net/2009/11/12/habemvs-gvsig-1-9/

The list of new features almost knocks you over ;) http://www.gvsig.gva.es/eng/gvsig-desktop/all-versions/download/gvsig-19/version-notes/new-features/

Also there is an old summary about gvSIG and mid range GIS ("Resources regarding an (OS) "mid range desktop GIS") I wrote a while ago <http://waurisa.org/phpBB3/viewtopic.php?f=37&t=636> http://waurisa.org/phpBB3/viewtopic.php?f=37&t=636

Enjoy
Karsten

Karsten Vennemann
Principal

Terra GIS LTD
2119 Boyer Ave E
Seattle, WA 98112
USA
www.terragis.net <http://www.terragis.net/>

Phone 206 905 1711
Fax 925 905 1711

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New stable version of gvSIG Desktop available: gvSIG 1.9

2009-11-12T10:41:47Z

A new stable version of gvSIG Desktop has been released: gvSIG Desktop 1.9.

It's available on the Downloads section of the gvSIG website:
http://www.gvsig.gva.es/eng/gvsig-desktop/all-versions/download/gvsig-19/downloading-the-program/.

This new version has many new features which are listed next.

* Symbology:
o Density point legend.
o Symbol editor.
o Graduated symbol legend.
o Proportional symbol legend.
o Quantity category legend.
o Symbology levels.
o Load/Save SLD legend.
o Expressions legend.
o Basic default symbols.
o Two differents measure systems for symbols and labels (in
the paper / in the world).

* Labelling:
o Creation of individualized annotations.
o Overlaps labeling control.
o Priority position labeling.
o Range scale visualization of labeling.
o Orientation of labeling.
o Different location options for labeling.
o More kind of measure units for labeling.

* Raster and remote sensing:
o Clipping of bands and data
o Export layers
o Save from view to raster file
o Color table and gradient edition
o No data values management
o Pixel process (filters)
o Color interpretation management
o Overview creation
o Enhanced radiometric
o Histogram
o Geolocation
o Raster reprojection
o Georeferencing
o Automatic vectorization
o Region of Interest (ROI) definition

* Internationalitation:
o New languages: English (USA), Portuguesebrazilian,
Turkish, Russian, Greek, Swahili, Serbian.
o Translation management extension integrated.

* Editing:
o Matrix.
o Scale.
o Explode.
o New snappings.
o Polygon cutting.
o Polygon autocompletation
o Polygon joining.
o Previous editing selection.

* Geoprocessing:
o Geoprocessing tools can now work with line layers besides
with polygon layers.

* Tables:
o New wizard for joining tables.

* Layout:
o Add grid to the view into Layout.

* Project:
o Wizard for recovering layers which path has changed.
o Online help.

* Interface:
o Possibility of hiding toolbars.
o New icons.

* CRS:
o CRS management extension JCRS v.2 integrated.

* Other:
o Improvementes in the reading of format DWG 2004
o Improvements of the hyperlink operations.
o Record the symbology legend path.
o Add "GeoServeisPort" server in the Nomenclator.
o Independent units for distances and Areas.
o Open layer properties by double clicking.

Also the following tools of the extension made by the Consejería de
Medio Ambiente of the Junta de Castilla y León have been added:

* Selection tools:
o Selection by polyline
o Selection by circle
o Selection by buffer
o Select all

* Information tools:
o Fast information tool (informs about a geometry when the
mouse stays on it)
o Multicoordinates tool: allows to visualize the view
coordinates simultaneously in geographic and UTM coordinates, even for
a different Zone from the one selected for the current view.

* Hyperlink:
o Improvement of the current hyperlink.
o Link different actions to the same layer
o Link properly several actions within one view.
o Add raster or vector layers in one view.
o Link to PDF files
o Link to HTML files
o Add new hyperlink actions with the help of plugins

* Data transformation tools:
o Export of tables subsets to DBF and Excel format.
o Add geographical information to the layer (for instance,
add the Area,
o Perimeter, etc. fields to a table in a faster way).
o Import tables fields.
o Interactively transform points to lines or polygons, and
lines to polygons.
* Open/save projects:
o Automatic backup of the .GVP when the project is saved.

* Other:
o Print view using a template.
o Select the order for loading several layers (for example,
it allows specifying the loading of shapes on top of the the raster
data by defect).

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Enterprise GIS

2009-11-12T10:31:34Z

Dear Ayo Akinseye,

sure there are other ways. I don't know anything about what your system
needs to do but you can use
these free great and reliable OpenSource products:

Desktop: gvSIG http://www.gvsig.gva.es/eng/inicio-gvsig/
(or QGIS http://www.qgis.org/ or UDIG http://udig.refractions.net/)

WebGIS Engine: MapServer http://mapserver.org/ and GeoServer
http://geoserver.org
Web Framework: OpenLayers http://openlayers.org/ and Mapfish
http://mapfish.org/
Spatial Database: PostgreSQL http://www.postgresql.org/ plus PostGIS (does
what ArcSde does and more) http://postgis.refractions.net/

Also read this "Open Source Geospatial - Overview Documents and Links" as an
overview http://waurisa.org/phpBB3/viewtopic.php?f=37&t=630

And check out http://www.osgeo.org/
Let me now if you have any questions

Cheers
Karsten Vennemann

Principal

Terra GIS LTD
Seattle, USA

> Dear All,
> I am responding to a Request For Proposal for a client who
> wants to deploy an enterprise GIS.
> I had assumed the way to go was ArcEdito & Arcview licenses
> for desktop, ArcGIS Server and Oracle Spatial as server.
> I am having an EXTREMELY hard time getting
> response/information from the ESRI representation for this
> part of the world (West Africa/Nigeria).
> Can anyone suggest options/another route for me to go? My
> Request For Proposal closes next week.
>
> Thanks in advance
>
> Best Regards
>
> Ayo Akinseye
> Digital & Spatial Solutions