center of 3 points

[+gwbbh]

I am working on a GPS problem involving Longitude and Latitude. I have 3 waypoints making a triangle and I need to find the center and the cooresponding coordinates to that center.

 

A= N 44.18.642

w 76.33.807

 

B= N 44.18.362

w 76.34.163

 

C= N 44.18.313

w 76.33.383

 

I know you draw a circle that touches on each point, but how can I derive a set of GPS ccordinates to find the location?

[+JSWilson64]

I am working on a GPS problem involving Longitude and Latitude. I have 3 waypoints making a triangle and I need to find the center and the cooresponding coordinates to that center.

 

A= N 44.18.642

w 76.33.807

 

B= N 44.18.362

w 76.34.163

 

C= N 44.18.313

w 76.33.383

 

I know you draw a circle that touches on each point, but how can I derive a set of GPS ccordinates to find the location?

 

I think you can simply convert to decimal degrees and average the Latitudes together, and the Longitudes together. I get 44.30731667 N and 76.56307222 W

Edited September 3, 2009 by JSWilson64

[+JSWilson64]

Try pasting this text into the form at this page:

http://www.gpsvisualizer.com/map_input?form=google

 

name,desc,latitude,longitude

A,A ,44.3107,76.56345

B,B ,44.3060333333333,76.569383

C,C ,44.3052166666667,76.556383

D,D ,44.3073166666667,76.563072

 

You'll see your 3 points (I hope) and the 4th averaged point in the middle.

[+fizzymagic]

I am working on a GPS problem involving Longitude and Latitude. I have 3 waypoints making a triangle and I need to find the center and the cooresponding coordinates to that center.

 

...

 

I know you draw a circle that touches on each point, but how can I derive a set of GPS ccordinates to find the location?

 

I think you can simply convert to decimal degrees and average the Latitudes together, and the Longitudes together. I get 44.30731667 N and 76.56307222 W

 

Unfortunately, this answer is incorrect. To see why, imagine that all 3 points are in the same half of the circle. Averaging the points does not work.

 

There are a couple ways to solve the problem, but if the points are not too far apart you can convert them to UTM and use the formula easily found online to find a circle given three (x, y) points. Then convert back from the UTM center to Lat/Lon.

 

I've written a program that does this and related problems iteratively, but it is not yet ready for release to the public. []

[+JSWilson64]

OK, maybe I didn't understand the problem. Is the question,

"Find the center of the circle that goes through these points."

or is it

"Find the center of the triangle described by these 3 points. " ???

Edited September 3, 2009 by JSWilson64

[+Red90]

Averaging does work.... It is not exact if you use lat/lon as the lines of longitude are not parallel, but for most cases it is very close. For the coordinates above the error will be way below the accuracy of a GPS.

 

Convert to UTM and average those. That will be the center, or more precisely the centroid of the triangle. A centroid is only one type of center....

 

http://www.jimloy.com/geometry/centers.htm

Edited September 3, 2009 by Red90

[+fizzymagic]

I'm pretty sure he wants the point equidistant from the three points he gives.

 

Hmm... he did mention a triangle. I might be wrong, then. In that case, the simple averaging of UTM works fine and averaging lats and lons works pretty well, too.

Edited September 4, 2009 by fizzymagic

[+user13371]

I read the problem entirely different from how it was presented.

 

For any triangle drawn on the surface of a sphere, there are two really two centers. If it's a relatively small triangle, your mind's eye naturally places the center "inside" the triangle. The other center would be at the antipodes, even though it might look like that's "outside." It's more evident when the triangle gets larger. Imagine three points on the equator at 0, -120 and +120 longitude. Staying on the surface -- is the North Pole or South Pole the "center?"

 

This is also true of ANY simple closed curve drawn on the surface of a sphere - although some analytical part of my brain is waving from the back of the room, trying to draw attention away from the intuitive part. Something about not having a rigorous proof that the two centers are always at the antipodes from each other. Anybody want to take a shot at that one?

 

Maybe I just had too much coffee this morning.

Edited September 4, 2009 by lee_rimar

[+EScout]

which center, centroid?

Triangle centers

[+julianh]

which center, centroid?

Triangle centres

Oww! My brain hurts!

 

More than 3,000 different "centres" for any given triangle ..... surely ONE of those should satisfy the OP!

 

(And that's only for plane geometry, before we even start considering spherical geometry, let alone geometry of a triangle on the geoid ..... )

[+coggins]

I am working on a GPS problem involving Longitude and Latitude.

Does this involve solving a puzzle cache? If so, what's the GC# in case there is any additional info included on the cache page. Edited September 4, 2009 by coggins