Finding by Algorithm the smallest circle that will encompass a group of shots

[Vic Thompson]

Note : this post is also listed in the BBS "General Airgun Section" : I'm after a quick and easy way of taking Excel data in the form of x and y columns of position of individual shot placement on a Target and coming up with the diameter of the smallest circle that will encompass them all. Is there anything that can be done directly using Excel, or if not, any free Software that is easy to download and use that I can put the coordinates into and get the right answer.

Thanks in advance for any helpful suggestions.

Vic Thompson.

[majex45]

Hi
I have seen an App for the Iphone that will do this from photographs. Unfortunately, I don't know what it was called.
The guy using it took a photo of each of his score cards and the program superimposed them one on each other (correcting for the different centres) and worked out score and group centre. I believe it can do other things as well.
Nothing short of miraculous, as far as I'm concerned.

Skynet is coming.

[Daryll]

You can get something similar for the PC, called "On Target PC"

You take a photo of your group, with a scale of some sort in the photo ( i used a tape measure), then you can enter the calibre and put the relevant circle over your shot holes.... it works out the group size..

You get a 15 day free trial, then its $12 for the basic version

https://ontargetshooting.com/

[Vic Thompson]

thanks for the replies to date but I don't have any shot targets to scan, only a list of numbers on a Spreadsheet. At a pinch I could reproduce the target using Power point but I'd prefer something that took the Excel data and produced a scaled shot spread image, but I can't even find anything suitable to do this at the moment.

Vic Thompson.

[PhatMan]

Vic,

Please have a peek here :

http://ballistipedia.com/index.php?t...ring_Precision

Have fun & a good Bank Holiday

Best regards

Russ

[Adam77K]

I don’t think there’s going to be a solution you can express in a single excel formula. It will have to be some quite heavy coding which you could do in VBA (is that still a thing these days?)

Some discussion on stack overflow.
https://stackoverflow.com/questions/...-other-circles

I like programming puzzles. Maths ones, not so much. This is both.

It would be quite straightforward to find the smallest circle centred on the origin that would encompass the centres (points). Then as all circles are the same diameter just add this to the total. But this doesn’t find your solution if the group is offset.

Interesting puzzle though, good luck.

[Turnup]

Presume you have x,y values for each shot from an arbitrary origin

1) calculate the straight line distance between each shot and all of the others (that's 9 + 8 + 7....) values. Probably easiest using rectangular notation by simply subtracting x from x and y from y and then converting each value into polar notation.

2) Find the three largest values of magnitude (disregard the angle)

3) these three shots form the vertices of a triangle

4) The centre of the triangle is the centre of the shot group (classical geometry)

5) Calculate the circle which will circumscribe the triangle (classical geometry)

6) correct the circle size to allow for the diameter of each shot hole. (I think in practice it is only necessary to consider the shot which is furthest from the circle centre - any circle that encloses the outside edge of this shot must also enclose the outside edge of the others.....I think)

You now have the centre and size of the smallest circle which will encompass all shots.