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

[Turnup]

Erk! It seems that this problem has been exercising mathematicians and so for no linear solution has been found. All present methods use iterative algorithms (using a guess to find a better guess until no further improvement can be made). There are algorithms of varying complexity and which take more or less time to find the solution but I don't think any of these can be implemented in a straight spreadsheet - needs programming.

Take a look here

http://www.delphiforfun.org/programs...ing_points.htm

[Vic Thompson]

thanks for the further reply Turnup, I more or less came to the same conclusion as yourself at aroundabouts the time of your latest posting.

I spent hours today working through your suggestions, checking several times that I was using the right aproach (mathematically speaking), but always ending up with the same result, it's a covering circle but not the guaranteed minimum one (then I rushed off to Tesco for an infrequent shopping trip in an attempt to beat the Bank Holiday Monday "last minute closing rush").

I have seen various discussions on the matter, all allude to a complex solution (in my simpleton view : think of an answer, see how good it is, rely on history, think of a better answer, ditto, ad infinitum). Not easy to do in Excel without a sophisticated Macro (one discussion of the problem suggested that 400 to 500 lines of code would be needed in a routine to establish a viable solution to the problem).

Based on my working through your suggested approach, I wondered if I had calculated the "wrong centre" of the triangle as even this "simple definition" is manifold (as it seems to be an open ended definition with multiple answers).

I'm always hopefull and appreciate yours and other informative suggestions as to which way to proceed Excelwise.

Vic Thompson.

[Turnup]

I should have been more precise - the centre I was thinking of is the intersection of the perpendicular bisectors for each side. This finds the point which is the centre of a circumscribing circle. As you say there are other centres, and anyway it is certainly not the correct solution <sigh>.

Coming back to my other idea, take the average of all points. I feels like at least it would be an easy way to make a first guess for an iterative algorithm. In fact without trying it, it feels like the centre of the group would lie on a line passing through the furthest outlying point and the average point.

WRT macros - could be done but don't think this is the most appropriate tool for the job - hard work - embedded VB would be fine.

[BigEars]

This is one of the most interesting thread ever. When I think about it, my head hurts.

[zooma]

This is one of the most interesting thread ever. When I think about it, my head hurts.

Absolutely!

[Turnup]

Me too. The thing about hard mathematical problems is that there is often a simple and elegant solution waiting to be found. When a thing is mathematically true there are many ways to get to the answer.

[angrybear]

Go old school, get a sheet of Perspex & scribe circles of increasing size around a common centre

[Norfolkngood]

I use TargetScan on an iPad. All you do is photograph the target and it gives mean radius etc and superimposes the group diameter over the holes.

[Turnup]

Go old school, get a sheet of Perspex & scribe circles of increasing size around a common centre

Yes, and I find it surprising that this task is something we can perform to a good degree of accuracy almost without thinking about it.