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# Center point of arc

Posted on 2001-08-17
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There is an arc having 11 x,y points. How to calculate coordinates of center of this arc?

Thanks.

0
Question by:mansan

LVL 6

Accepted Solution

kotan earned 35 total points

centerX = sum(x1,x2,...,x11)/11;
centerY = sum(y1,y2,...,y11)/11;

centerpoint is (centerX, centerY)
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Expert Comment

Suppose (x,y) are the co-ordinates of the centre of arc.
Let (x1,y1) and (x2,y2) be two of the points on arc.
Then :
(x-x1)^2+(y-y1)^2=r^2 where r is the radius.
(x-x2)^2+(y-y2)^2=r^2
So equate these two equations to get the centre of circle which (x,y)
With regards,
V.Kartik
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LVL 7

Expert Comment

..and you shouldmake sure all pairs result in the same centerpoint
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LVL 1

Expert Comment

Sorry, that ain't right.

Given any two points, there are an infinite number of different arcs that pass through both.

You can see this because if you do what kartik suggested, you get:

(x-x1)^2+(y-y1)^2=(x-x2)^2+(y-y2)^2

1 equation with 2 unknowns (x and y) has an infinite number of solutions.

So you need *three* points, from which you can get *two* equations:

(x-x1)^2+(y-y1)^2=(x-x2)^2+(y-y2)^2
and
(x-x1)^2+(y-y1)^2=(x-x3)^2+(y-y3)^2

and now you really can solve for x and y.

kotan answered the question `how do I find the center of mass of the arc' rather than `how do I find the center of the circle of which the arc belongs to' .. if that was what you intended, then his answer is correct.
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Author Comment

Thanks you all for kind help.
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