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DukeOfURL01

Triangulate?

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The folks in this forum seem pretty knowledgeable about such things, so I'm trying to triangulate a position, but can't seem to find a good explanation of how.

 

I am given 3 distances from sets of coordinates, but I don't really know what to do next. I'm trying to find a final set of coordinates.

 

Would somebody tell me how to do this?

 

Thanks

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The folks in this forum seem pretty knowledgeable about such things, so I'm trying to triangulate a position, but can't seem to find a good explanation of how.

 

I am given 3 distances from sets of coordinates, but I don't really know what to do next. I'm trying to find a final set of coordinates.

 

Would somebody tell me how to do this?

 

Just to make sure we understand the problem, are you saying that you know the locations (a,B), (c,d), (e,f), and the distances R, S, and T in the diagram below, and you are trying to find the coordinates (x,y)? Technically, that problem is called trilateralization.

 

Next, are you looking for mathematical formulas so you can calculate it yourself, or are you looking for some web site or program that does all the calculations for you?

 

trilaterization.png

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The folks in this forum seem pretty knowledgeable about such things, so I'm trying to triangulate a position, but can't seem to find a good explanation of how.

 

I am given 3 distances from sets of coordinates, but I don't really know what to do next. I'm trying to find a final set of coordinates.

 

Would somebody tell me how to do this?

 

Just to make sure we understand the problem, are you saying that you know the locations (a,:yikes:, (c,d), (e,f), and the distances R, S, and T in the diagram below, and you are trying to find the coordinates (x,y)? Technically, that problem is called trilateralization.

 

Next, are you looking for mathematical formulas so you can calculate it yourself, or are you looking for some web site or program that does all the calculations for you?

 

 

The information I am given is as follows:

 

At 0.11 miles from N 39 46.459 W 121 46.994

At 0.14 miles from N 39 46.451 W 121 46.870

At 0.28 miles from N 39 46.351 W 121 47.124

 

I am looking for information on how to calculate it myself. If there is a website or program that will do the calculations for me, that is good too, but I want to know how to do it myself also.

 

In addition, I am looking for information on how to do the reverse; knowing coordinates of a center point, and knowing a constant distance, I need to find 3 sets of coordinates for the corners.

 

I would like to create a puzzle where you have to calculate the orthocenter of a triangle created by 3 points, but I don't know how to do it myself.

 

Basically, I'd like to implement this: http://blog.expertgps.com/blog/2009/03/geo...ight=geocaching

 

Thanks

Edited by DukeOfURL01

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Since you'd like to solve it yourself, here's a nudge and a hint:

 

Nudge: you are trying to find the intersection of three circles.

 

Hint: converting to state plane coordinates will make the math a wee bit easier.

 

Cheers,

Bobby

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State Plane Coordinates (which can be converted from lat-lon using the free program CORPSCON) will get you a correct answer. This answer can be checked by using the program from the NGS toolkit called INVERSE or other geodetic calculation utilities.

 

However, if this is a geocaching puzzle it is unlikely the person who set it up expects finders to be that sophistocated about geodetics. A majority of such geocaching puzzles assume a rectangular grid of lat-lon values, ignore the difference in length of a minute of latitude versus longitude, and disregard the pretty bad distortion this creates in the map. Thus my first attempt would be to solve it purely as a math problem with X-Y coordinated obtained by subtracting off a base value of N 39 46 W 121 46 and working in units of arc minutes.

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personally, i'd convert the coords to UTM and calculate with that. that's pretty common in the geocaching world.

 

intersecting two circles will give you two possible answers, the third one will tell you which one of the two answers is the correct one.

Edited by dfx

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If you remember some algebra, you can write equations involving (X-X1)^2+(Y-Y1)^2 etc to set equal to the radii you are given. After some manipulation you have 3 quadratic equations in the 2 unknowns X and Y. You may be able to find substitutions to eliminate Y and use the quadratic formula to find X, then substitute it back and find Y.

 

Your answer with UTM or SPC should be close enough to the same.

 

And if your answer doesn't check all 3 distances, then try the lat-lon minutes grid to see if that checks, showing what they assumed.

Edited by Bill93

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Ok, I think I know what I am going to do, I am going to use the Buffer tool in ArcGIS. That will at least help me solve the first problem. But I'm still thinking on the second.

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The second problem you mention is much easier, because you can use the "Forward" program at this link to compute coordinates at a given radius and direction from another point. Simply choose three directions from your central point, and you get three points.

 

For the original problem, in virtually all the practical cases, you need to convert the lat/lon coordinates into x/y map coordinates of some kind, UTM or State Plane being the most obvious, since your GPS can do the calculation for you.

 

The simplest method involves some graph paper, pencil, and compass. You can use that method on the USGS quad map sheets. If you have GIS software, you can create a map containing the three points, add circles centered on the points, and then get the coordinates of their intersection.

 

Different mathematical methods will vary in their tolerance to errors, which is important because the distances given to you are approximate, which means that the three circles won't perfectly intersect, which means that mathematically speaking, there won't be an exact solution to the system of three equations.

 

In the example you gave, you can see that there is no exact solution, because the three circles don't intersect. This is an especially bad example, because the circles from points A and C don't actually meet anywhere, the circle around A is entirely contained within the circle around C. It is hard to see, but you can compute the distance from A to C using the "Inverse" program, which gives you 0.1695 miles. Since circle C is 0.28 miles, that means that it is 0.1105 miles from point A at its closest. Since the circle around point A is only 0.11 miles, that means that there is a gap of 0.0005 miles (2.6 feet) between circle A and circle C.

 

Most likely, the puzzle author expected you to enter the three waypoints, and use your GPS to guide you to based on the ranges from the waypoints. That may be how they created the puzzle in the first place -- standing at the cache location and using the GPS to compute the ranges to three waypoints, not realizing how bad the configuration was mathematically.

 

trilaterization_2.png

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