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I have a dataset with several points in space within a given area. UTM coordinates (easting, northing in m) or geographic coordinates were recorded for a single point in the vicinity of these points. Then, locations of each of the other points was recorded based on the distance of a given point along the x- and y-axes (e.g. 5 m, 7 m) from the point where UTM or geographic coordinates were recorded.

Now, how can I determine the UTM coordinates or geographic coordinates of each of these points based on the x,y distances from the point where UTM or geographic coordinates were recorded?

Isn't it appropriate to simply just add the x and y distances to the utm coordinates of the known point to determine the unknown utm co-ordinates of the other points (then use a utm to lat-long converter for determining geographic coordinates)?

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  • You are correct in your thinking. Here is a little page with some reference about UTM you can use, but your logic is spot on. use trig/alg to calculate the new coordinate pair then convert to lat/lon – ed.hank Sep 3 '15 at 19:06
  • Thanks for responding. You mentioned a page, but I can't find the link in your message. – Kris Sep 3 '15 at 19:19
  • woops extension.iastate.edu/naturemapping/mapping/utm.htm this page is mainly some reference about utm. I looked for a page about how to do the math given an xy distance, but all i could find were calculating a new coordinate pair from bearing distance, which using trig can be convereted to an x,y pretty easily. – ed.hank Sep 3 '15 at 19:20
  • @user3338197, "use trig/alg to calculate the new coordinate pair then convert to lat/lon". I guess I am a bit confused. The coordinate pair is already in the data (x and y distances (xy coordinates) from a known UTM point). All that needs to be done is to add x, y distances to the corresponding easting and northing values. No need for any trig/alg as I understand it. – Kris Sep 3 '15 at 20:17
  • you are correct, i was thinking in terms of bearing and distance. but yeah just add/sub them from your control point – ed.hank Sep 3 '15 at 21:12
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If I understand the problem correctly, it sounds like you have control points in both UTM and geographic (Lat/Lon) coordinates, and you have offsets measured in meters from these control points, and you need to calculate the locations of those offset points in either UTM or Lat/Lon?

I would start by getting all of the control points in one system, and since your offsets are measured in meters, it would make most sense to convert the geographic coordinates of your control points so that all are in UTM, then add the offsets to the eastings (x) and northings (y) to get the coordinates of the offset points.

The UTM coordinate system was partly developed for these types of applications. Plotting everything on a grid of square meters made it easier to calculate distances and directions for artillery using tables of cosines and square roots than it was using nasty spherical coordinates.

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