Calculating the radius of a circle from measurements.

I am trying to calculate the radius of a circle from a data set of coordinates on the circumference.

To do this I have written a function which takes three data points from the entire set at random (15 data points) and calculates the radius from these then takes three more and so on. It builds a matrix with all the calculated radii and the average and SD are calculated from this.

I do this around 500 times as I feel that this would likely consider all possible combinations; however, this is rather unscientific and alters the statistical analysis I will need to perform to see the variation and whether the measurements are valid.

I want to produce a matrix which will be (n,3) where n is the total number of possible combinations of 3 coordinates from the set of 15 without any repeating 3 coordinates in the same row.

For example:

x = [0; 2; 5; 7; 9]

y = [0; 3; 6; 8; 9]

So we have 5 coordinates but only need 3, so the possible combinations are:

c = [ 1 2 3

1 3 4

1 4 5

1 2 4

1 2 5

1 3 5

and so on...

That way I can make the code calculate every possible radius form the data available with no repeats.

Sorry if this is unclear, I can provide more information if required.

Thanks in advance,

Alex.

[Torsten]

You should take all points at once and calculate the circle that best fits the complete set of points:

http://www.spaceroots.org/documents/circle/circle-fitting.pdf

[Guillaume]

@Torsten, I totally agree. Your comment should be an answer.

[darova]

♥ ♥ ♥

[Alex Boote]

Thanks for your response @Torsten. Unfortunately this method does not give a way of calculating the standard deviation of the points from the circle. I guess I could use the equation created to calculate the corresponding y value for a measure x value and use this difference to calculate the margin of error. Thank you!

[Torsten]

The first sentence of your question was

I am trying to calculate the radius of a circle from a data set of coordinates on the circumference.

To do this, you should include all data points in your calculation.

I don't know why you think it's impossible to calculate the standard deviation of the distance of the points from the circle if you proceed as suggested: the distance of a point from the circle is equal to the absolute value of the distance of the point from the midpoint of the circle minus the radius of the circle.