January 17, 2019, 07:32:44 PM

# Center of circle.

### Author Topic:  Center of circle.  (Read 4273 times)

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March 08, 2015, 11:27:42 PM

#### Pluto_Robot

##### Center of circle.
Hi guys. I have a chalenge to solve down here in Brazil. In ABB robot using an SeachL instruction with a laser sensor, I'll find two or three points in a circle. I know de radius and I need to determine the center of the circle. Center (x,y). Anyone knows the formula from two points and radius to find de center? Or even a formula to determine de center from three points?
Thank you guys!!!

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Today at 07:32:44 PM

Guest
##### Re:  Center of circle.

March 16, 2015, 05:18:38 PM

#### CrossConnect

##### Re: Center of circle.
I hope this works
let
x1,y1 -->point 1
x2,y2  --> point 2
x,y ----> center of circle
then distance of point 1 to center is the radius
(x1-x)^2+(y1-y)^2=r^2
and same for point 2
(x2-x)^2+ (Y2-y)^2=r^2
So you have  2 unknowns  x, y and 2 equations solve to get your result
•
You get what you want, Think big to get big

March 17, 2015, 04:21:19 AM

#### Postprocessor

##### Re: Center of circle.
Few month ago I solve a same problem, but for 3 3d-space points, with x, y, z coords.  I build small script, you can try it here - http://chigishev-yuri.livejournal.com/2275.html
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June 27, 2015, 07:54:54 PM

#### panic mode

Global Moderator
##### Re: Center of circle.
there is no unique solution for center of the circle based on just two points - even if you know the radius.

in 3D there is infinite number of solutions (sort of like fat donut).
even in 2D, there are still two solutions which are mirror images of each other.

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April 08, 2016, 03:02:42 AM

#### jstolaruk

##### Re: Center of circle.
In a plane, if two points are known and the radius is known, there are three conditions which could be true:

1) If the distance between the two points is less than 2*radius and greater than zero, then there will be two circles with radius R that will intersect those points.

2) if the distance between the two points is exactly equal to 2*radius then one circle with radius R intersects the two points.

3) if the distance between the two points is greater than 2*radius, then no circle with radius R will intersect both points.

In a plane, if three points are known, there either will be one circle that intersects those points OR there will be none (if the 3 points are co-linear).
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July 14, 2016, 10:24:50 AM

#### Bart0664

##### Re: Center of circle.
if you still need a solution for this i have one, You just need to find 3 points of the circle (ech X and Y) and you can calculate everything in 2Dimensions.

If you need it in 3Dimensions its not a circle its a sphere and you would need 4 points. - but i think you will not need this!!
•

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