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Smallest Circle Math


Hammbone

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Perhaps I'm over analyzing this:

I just shot up 6 targets doing accuracy tests with some experimental reloads. Once I was done, I drew a verticle and horizontal centerline through the bullseye. The I measured the distace from "x" and "y" axis for each hole and created a table of coordinate points in Excel...assigning quadrants by dictating (+,+) for quad 1, (-,+) for quad 2, (-,-) for quad 3, and (+,-) for quad 4...as we're taught with the unit circle in calculus.

Here's what I can't figure out; How do I mathematically calculate the diameter of the smallest fit circle for a given set of 2D coordinate points?

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Not sure I follow what you are trying to accomplish. The smallest circle is going to be the one that intersects the two holes that are furthest from each other. You could use the distance formula to find these two if it's not obvious.

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JereyShoots - You'd think that, but its not true. First of all, I'm looking at group sizes for now. Ignoring relation to center of bullseye. However, I did use the bullseye as coordinate (0, 0). Then I shifted the center to the average center of the group (turns out mathematicians have multiple methods for calculating this). I quickly saw the flaw with my method, but I'm sticking with it for now.

The biggest problem with measuring the two outermost holes is that you need 3 points to calculate a circle. You can do it with a center point and two circumference points, or 3 circumference points. The problem with using the center as one point is that there is error induced by assuming the center is the average of all points (especially if there is a "flier" or two). The problem with using 3 circumference points is that I don't know how to mathematically select the optimum 3 points.

SteveRA - Is this software free? I have experience writing programming code in Fortran, m-code in MatLab, Engineering Equation Solver, and of course Excel...so I'm not affraid to get my hands dirty per say. Just trying to figure out the math behind it.

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I found a few algorithms, but they gave me a headache. I'm just going to this:

-Delete the two farthest from the group (of 10 shots)

-Then shift the center point from the bullseye to the average of the remaining group

-Then calculate the standard deviate from the new centroid

-Then multiply stdev x 3

...that will give me a radius for 99.7% of the data points.

I am just doing this for my own personal record keeping for developing new loads.

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