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

[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.

[BigEars]

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.

I may have a method which I have yet to test. Find the smallest rectangle which will enclose all the points and calculate its centre. That will be the centre of the circle with a radius of half the length of the diagonal. Thinking about this really cocked up my pistol session this afternoon.

[Turnup]

I may have a method which I have yet to test. Find the smallest rectangle which will enclose all the points and calculate its centre. That will be the centre of the circle with a radius of half the length of the diagonal. Thinking about this really cocked up my pistol session this afternoon.

Easy to say but is no simpler to actually do. Simples if the rectangle is confined to one orientation, however this will not be the smallest rectangle of the many possible orientations of the rectangle. The problem is essentially the same for any enclosure with a form which can be mathematically defined. Lots of work been done on these kind of problems and no linear solution (one which follows a direct mathematical path to the solution, or in computing terms one which can produce a solution in a predictable time for an arbitrary number of points) has been found so far - all solutions found so far are iterative (progressively refine successive guesses).

But there just might be an elegant approach which does yield the smallest enclosure with no iterations

Also does "smallest rectangle" cover the smallest area or have the smallest perimeter?

[BigEars]

Easy to say but is no simpler to actually do. Simples if the rectangle is confined to one orientation, however this will not be the smallest rectangle of the many possible orientations of the rectangle. The problem is essentially the same for any enclosure with a form which can be mathematically defined. Lots of work been done on these kind of problems and no linear solution (one which follows a direct mathematical path to the solution, or in computing terms one which can produce a solution in a predictable time for an arbitrary number of points) has been found so far - all solutions found so far are iterative (progressively refine successive guesses).

But there just might be an elegant approach which does yield the smallest enclosure with no iterations

Also does "smallest rectangle" cover the smallest area or have the smallest perimeter?

All good questions.
I was working using the edges of the target as traditional x and y axes. The size of the rectangle seems to be the same regardless of orientation. My refinment, after finding the centre of the rectangle is not to use the 0.5 diagonal as the radius, but the distance to the furthest point from my rectangle's centre.
However, man that is born of woman etc..

I'm not even sure knowing what the smallest circle is would be of any practical help to someone who shoots really well, or really badly,come to that.

[Vic Thompson]

I think that I agree with turnup (sort of), as in the first instance I see the smallest rectangle and smallest covering circle as being equivalent, especially as no solution has been provided to date for either.

And as to what regard one holds either of the above answers in is the next problem for discussion, is a minimum covering circle/rectangle a good thing (as neither takes into account the statistics of shot distribution and absolute best score (etc)) : are there preferred ways of analysising shot placement. I didn't really define the completeness of my problem very well in the first instance.

Vic Thompson.

[BigEars]

I think that I agree with turnup (sort of), as in the first instance I see the smallest rectangle and smallest covering circle as being equivalent, especially as no solution has been provided to date for either.

And as to what regard one holds either answer in is the next problem for discussion, is a minimum covering circle a good thing (it doesn't take into account the statistics of shot distribution and absolute best score (etc)), or is there a better analysis of shot placement.

Vic Thompson.

I find adding the score up to be a good surrogate for analysis.

[Vic Thompson]

I find adding the score up to be a good surrogate for analysis.

So do I, but I don't have a score to add up, just x and y co ordinates for various uncorrelated shot sequences.

Vic Thompson

[BigEars]

I find adding the score up to be a good surrogate for analysis.

So do I, but I don't have a score to add up, just x and y co ordinates for various uncorrelated shot sequences.

Vic Thompson

You may be beyond help.

[Vic Thompson]

I am beyond help as the data is provided to me as a written down list in x, y format which I can't currently do anything with.

To date I can't even think of a way of plotting it and generating a Target Overlay in order to then carry out a manual assessment.

Vic Thompson.

[Turnup]

I am beyond help as the data is provided to me as a written down list in x, y format which I can't currently do anything with.

To date I can't even think of a way of plotting it and generating a Target Overlay in order to then carry out a manual assessment.

Vic Thompson.

You can plot the data points in 2D using the scattergram type graphical function (chart) in Excel.

Superimposing a circle of arbitrary size and origin is quite trivial. Calculate x,y co-ords of a circle at suitable intervals. Take circle size as a fill in box and add an x and y offset fill in box as inputs to the calculation. Plot the points on the same chart. in a different colour. Change circle size and offsets to move it about and tweak until you get the best visual fit.

[BigEars]

You can plot the data points in 2D using the scattergram type graphical function (chart) in Excel.

Superimposing a circle of arbitrary size and origin is quite trivial. Calculate x,y co-ords of a circle at suitable intervals. Take circle size as a fill in box and add an x and y offset fill in box as inputs to the calculation. Plot the points on the same chart. in a different colour. Change circle size and offsets to move it about and tweak until you get the best visual fit.

Does he not need some indication of how the axes are scaled to get the relative size of the target picture correct?

[Turnup]

Does he not need some indication of how the axes are scaled to get the relative size of the target picture correct?

Well maybe yes and maybe no.


If results are required in units of distance then it will be necessary to know the scaling applied to the axes.


A perfectly correct result could also be produced in units of the existing x, y scales. E,g, group centre is at x 23.985, y 79.12 and group size is 15.1

This all falls apart if the x and y scale units are not the same though, but the data would then need to be scaled into common units OR for the really dedicated the "circle" generated could be substituted with an ellipse of appropriate scaling.

[Vic Thompson]

on my version of Excel you don't have the option of scaling the x and y axes to the same value on the screen. You can put numbers in but on the axes on the screen display have arbitrary values. I've plotted them but have to "pull one of the axes" to get an approximate square grid pattern. I've tried plotting the numbers in Powerpoint but can't set my version up for "circle centre positioning" so that's tedious as well.

Vic Thompson.