[math-fun] Re: n-D median?

From: "Fred lunnon" <fred.lunnon@gmail.com>

Using the term "median" suggests to me that you intend the result to be a member of the original point set. Is that what you meant?

No more than that's true of the 1-D median, which sometimes averages two points. With the sum-of-directions-approaches-zero definition, original points would be more likely candidates at least, because the direction function has a step as you pass through a point, making it a zero-crossing magnet. I guess if there are zero-crossing curves in the areas between original points, they have to lead to original points. --Steve