Mathematica - extracting upper bound envelope of of listplot

Question

I have an unstructured dataset "nm", excel file in the link below.

https://www.dropbox.com/s/k7sdblxg4txjvj8/nm.xls?dl=0

it looks like that in a Mathematica list plot 1.

Could You please help me extracting upper bound envelope of this dataset, similar to the red line marked in picture 2? By extracting an envelope I mean to make another list "nm2" that for a given n produces a maximum m? I need another list "nm2" because then i need to work with it in excel.

Best Regards, BG

Answer 1

Using a technique found here : obtain all boundary points on a convex hull

data = Import["nm.xls"];
chr = ConvexHullRegion[data];
sr = SignedRegionDistance[chr];
dist = sr /@ data;
points = Extract[data, Position[dist, 0.]];
{maxx, maxy} = Max /@ Transpose[data];
minx = First[FirstCase[points, {_, maxy}]];
miny = Last[FirstCase[points, {maxx, _}]];
arc = Select[points, First[#] >= minx && Last[#] >= miny &];
f = Interpolation[arc];
Show[ListPlot[data], Plot[f[x], {x, minx, maxx},
  PlotStyle -> {Thick, Red}]]