How to create a smallest quadrilateral concave polygon around GPS points?

I have this GPS track in a metric grid (Symbology by elevation, if anyone wonders):

I need to define it's general area - for registrations and permits, with just 4 points. Therefore, I assume that the corners of a circumscribed quadrilateral polygon (4 lines) will do, as that will be the smallest possible polygon area-wise.

I don't know which Arcmap tools I can use to do it, though I imagine the result should look something like this:

With a polygon I can easily know the corners' coordinates, but if there's another way to extract them, I'm all ears.

Edit: This is the resulting convex hull tool:

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convex hull is something you are looking for? – Naresh Mar 6 '13 at 11:28
Because your illustration shows that this polygon need not fully enclose the points, the "smallest possible polygon area-wise" will have zero area--and there are many such polygons. Could you please more fully describe the criteria that should apply to identifying a polygon that meets your needs? All you really have told us is that it must have four corners and we can guess it must somehow approximate your GPS points, but we don't yet know exactly how. – whuber Mar 6 '13 at 16:30

As Naresh suggests, it sounds like what you want to do is calculate the Convex Hull of your points. You can accomplish this using the Minimum Bounding Geometry tool in ArcGIS or with the Convex Hull tool in Quantum GIS.

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As you suggested, I've used the tool. I added the result to my original post. The outline is similar to what I'm looking for, yet there is still an issue with the corners themselves. They are curved, and the convex hull retains that curved outline, which has several defining points, and not one. I've tried the other functions in the tool, like rectangle by area, but the resulting feature is a parallelogram, which is a bit too simplistic for my needs. I've edited the resulting convex hull by hand and got a good result that kind-of suits my needs. – HDunn Mar 10 '13 at 9:53

I don't know this software but probably this is what you are looking for.

In general terms this reminds me of the Douglas-Peucker algorithm .

this other 2 links could be handy

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Simplify lines basically cuts the corners, whereas I need to do the opposite, and add, if you will, more area to the corners. – HDunn Mar 10 '13 at 9:45