# Keeping points the same distance apart in ArcMap

10 replies to this topic

### #1 Brock Posted 30 September 2008 - 11:49 AM

Brock

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Hello all. Nice to be on the asking end, since I answer more questions online (typically musical instrument related) than I ask.

I have a cluster of GPS coordinates that I want to move in ArcMap from around the equator to over North America. I want the distances to be the same between points. Currently when this is done, they aren't maintaining their original relative placements from each other. This is obvious when measuring between points, but is more obvious when looking at the data.

Here's an example of the sort of thing I'm currently getting:
INPUT (x,y)
-130, 0
-120, 0
-110, 0
-100, 0
-90, 0

OUTPUT (x,y) (I'm also shifting x)
-120, 45
-110, 45
-100, 45
-90, 45
-80, 45

The coordinates in the output set above are no longer spaced the same distance as the original set, thanks to the earth not being flat and the values receiving a simple shift. Here's the sort of data I'm hoping to get (these numbers are not correct):
DESIRED OUTPUT (x,y) (with x shift)
-128.16, 45
-114.09, 45.6
-100.12, 46.6
-85.93, 45.6
-71.84, 45

Basically, the latitude points "bend" (but not really) for an "as the crow flies" path and the overall length "streches" (but again, not really) due to lines of longitude being closer to each other at 45 degrees. The coordinates above (if they were calculated correctly) would be in the same positions relative with each other over North America (and the Pacific) as they were at the equator.

Is there a way or option in ArcMap (or other software) to move a set of coordinates to another part of the world while maintaining original distances between the coordinates? I am dealing with thousands of coordinates that need to maintain their positions relative to one another. (Also worth noting, all points are at the same altitude in both sets, so I don't have any terrain or altitude concerns.)

-Brock

### #2 Hans van der Maarel Posted 30 September 2008 - 01:09 PM

Hans van der Maarel

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Hi Brock,

Interesting question. I think the best thing to do is transform them to an equidistant, conformal coordinate system and then shift them. UTM (Universal Transverse Mercator) could be a good choice.
Hans van der Maarel - Cartotalk Editor
Red Geographics

### #3 Brock Posted 01 October 2008 - 11:17 AM

Brock

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UTM (Universal Transverse Mercator) could be a good choice.

Interesting suggestion. From what I'm reading, UTM won't work too well in my instance because my points cover too great of an area.

This is my first dive into 3D earth (I've done some flat earth work before) and it is interesting to see the problems created by our 3 dimensional world. My goal should be reasonable obtainable, but even then it won't be perfect due to:
1. Altitude differences in actual earth.
2. That whole ellipsoidal earth factor.

Thanks for your response. At some point I think I might be looking at XYZ coordinate systems. Oh my.

-Brock

### #4 Hans van der Maarel Posted 01 October 2008 - 12:24 PM

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Interesting suggestion. From what I'm reading, UTM won't work too well in my instance because my points cover too great of an area.

How great exactly?
Hans van der Maarel - Cartotalk Editor
Red Geographics

### #5 Rob Posted 01 October 2008 - 02:17 PM

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I want the distances to be the same between points.

Brock, by distance, do you mean in Lat/Long, or in something like miles/km?

### #6 Brock Posted 02 October 2008 - 06:02 AM

Brock

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I want the distances to be the same between points.

Brock, by distance, do you mean in Lat/Long, or in something like miles/km?

By distance, I mean miles. The lat/lon I'm getting is "correct" from a lat/lon perspective but is not by physical distance between coordinates.

-Brock

### #7 Kalai Selvan Posted 02 October 2008 - 06:16 AM

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Your ? seems to look very simple, if my understanding is correct.
You have a set of points, and you want those set of points to be moved in an equidistance correct.
I did exactly the same in the past, but i did that in Autocad and imported back to Arcmap. Simple
To do that we use something called Array, its mutiple copying command it does exactly what your are looking for.

Hope this puts some light.

Thanks
GISGURU

Thanks and Regards
Kalai Selvan

### #8 David T Posted 03 October 2008 - 09:11 AM

David T

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Well, you've figured out where the problem is - using lat/long, longitude lines are closer together as you move further away from the Equator.

Have you tried converting the points to a project that will maintain distance? It doesn't have to be UTM, but any projection that maintains distance is what you're looking for. Then you should be able to move them around without problem.
David Toney, GISP
GIS Manager
United States Marine Corps
West Coast Installations

### #9 Hans van der Maarel Posted 03 October 2008 - 09:56 AM

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Well, you've figured out where the problem is - using lat/long, longitude lines are closer together as you move further away from the Equator.

Have you tried converting the points to a project that will maintain distance? It doesn't have to be UTM, but any projection that maintains distance is what you're looking for. Then you should be able to move them around without problem.

I guess the projection has to be conformal (maintaining shape) as well.
Hans van der Maarel - Cartotalk Editor
Red Geographics

### #10 paul Posted 03 October 2008 - 12:31 PM

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Try World Mercator.

### #11 Brock Posted 03 October 2008 - 03:49 PM

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Well, you've figured out where the problem is - using lat/long, longitude lines are closer together as you move further away from the Equator.

That's one of four problems. I can ignore problems #3 and #4 below since they are tiny percentages, but the others are notable:
1. As mentioned: "lat/long, longitude lines are closer together as you move further away from the Equator"
2. Latitude lines curve downward compared to the relocated equator.
3. Altitude differences between where dots were and where they are moved to (no big deal for me).
4. Earth's curvature is different being ellipsoid rather than a pure sphere (again, no big deal for me).

I just photoshopped an example together showing the lat line difference. The white lat/lon lines are actual. The orange lat are where the lines are relative to my data when shifted.

I didn't realize this was a challenge. I figured software would just magically handle this. By magic, I mean "do lots of math".

I looked at Mercator but it appears to introduce new problems, especially given the size of area (North America) being covered.

-Brock

Edited by Brock, 03 October 2008 - 03:51 PM.

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