On Saturday 02 August 2008 02:41, Ed Tomlinson wrote: > On August 1, 2008, Michael Rogers wrote: > > Daniel Cheng wrote: > > > in a circular space, we can get infinite number of "average" by changing > > > point of reference. --- choose the point of reference with the smallest > > > standard deviation. > > > > From an infinite number of alternatives? Sounds like it might take a > > while. ;-) I think we can get away with just trying each location as the > > reference point, but that's still O(n^2) running time. > > > > How about this: the average of two locations is the location midway > > along the shortest line between them. So to estimate the average of a > > set of locations, choose two locations at random from the set and > > replace them with their average, and repeat until there's only one > > location in the set. > > > > It's alchemy but at least it runs in linear time. :-) > > Another idea that should run in linear time. Consider each key a point on the edge > of a circle (with a radius of 1). Convert each key (0=0 degress, 1=360) to an x, y cord and > average these numbers. Once all keys are averaged convert the (x, y) back into a key to > get the average. > > eg x = sin (key * 360), y = cos(key * 360) assuming the angle is in degrees not radians. > where a key is a number between 0 and 1
You miss the point. We already have what is effectively an angle, it's just in 0 to 1 instead of 0 to 360 deg / 2*pi rads. The problem is the circular keyspace. > > Ed -------------- next part -------------- A non-text attachment was scrubbed... Name: not available Type: application/pgp-signature Size: 189 bytes Desc: not available URL: <https://emu.freenetproject.org/pipermail/devl/attachments/20080802/27ac09d2/attachment.pgp>
