The Energon Pub

[Insurgent]

Here's the deal:

I have a number of GPS point and their coordinates. They lie close together (we are talking centimeters here) and they all lie on the arc of a circle. I know the radius of said circle. Is there a formula I can use with these components to calculate the coordinates of the centre of the circle?


I ask as this is the situation I'm faced with on my Uni Dissertation, and if I can't work it out, it means I'll have to sit on a rooftop for about 5 hours. And the British winter is not roof sitting weather.


Thanks in advance.

EDIT: Jazzrules pointed me in the right direction, so this can get locked/deleted/ignored.

[City Commander]

Just as an aside, I woulda thought finding the tangent at each point and then finding the coordinate where they cross would be the best thing to do.

[AlienQuiksilver]

I have a CAD program that will get the answer in 2 seconds ... but hey, he got the answer already.

I would just have to convert GPS coordinates into feet, or meters. I know the conversion formula, so it's no biggie.

It's totally cheating, but hey ... I'm an engineer. I put my "math time" in.

[Insurgent]

Just as an aside, I woulda thought finding the tangent at each point and then finding the coordinate where they cross would be the best thing to do.

Don't have tangents. Just the location on the circle and the radius. But I have the formula, and I need to practise my maths skills.
Thanks for the interest guys.

[AlienQuiksilver]

Yeah, (he/she?) was just looking for the center point of the circle. Sounds like Insurgent was given at least 2 specific points that were to be connected into an arc of a specified radius.

1 entity, so there would be no points of tangency. There need to be 2 entities for that.

Just remember, there are always 2 possible center points in a problem like this.(unless you have more than 2 points) You may have to think "outside of the box" to figure out which one it is, in that case.

So, this does create a 2nd theoretical entity ... but they are not tangent. They intersect, though!

Me head hurts.

[Insurgent]

Yeah, (he/she?) was just looking for the center point of the circle. Sounds like Insurgent was given at least 2 specific points that were to be connected into an arc of a specified radius.

1 entity, so there would be no points of tangency. There need to be 2 entities for that.

Just remember, there are always 2 possible center points in a problem like this.(unless you have more than 2 points) You may have to think "outside of the box" to figure out which one it is, in that case.

So, this does create a 2nd theoretical entity ... but they are not tangent. They intersect, though!

Me head hurts.

He can easily find out which centre is the correct one, as it's the one in the centre of the GPS points I have going around in circles. The incorrect one would be in the point cloud of the circle. Appolagies if I'm not making a whole lotta sense, but it would take some time to explain it all. Let's just say, once I have two possible values, it's just a matter of whacking it into some software and seeing if it's in the right place. If not, I know it's the other one. It was finding the centre coordinates that was being problematic.

[AlienQuiksilver]

oh okay, you obviously have more information than I thought then. My idea is still good ... you just described it for me. Thanks!

No need to explain anything, i'm an engineer for pete's sake ... I do stuff like this on an hourly basis.

With that said ... I have my job so simplified it's not even funny. I have a program for everything. You could probably swim mathematical circles around me at this point. Even though it is my career.

All of the little details that I learned in school have become 2nd nature to me. Which is really not healthy if you think about it, but I get by with ease ... regardless.