Selecting points on either side of a curve

I have the following array of data. Suppose I want only to keep data within the two lines. I can achieve my result using the following code:

data = Table[i, RandomReal[-10, 10], i, 0, 100];
line1[x_] := 0.1 x - 10;
line2[x_] := -0.1 x + 10;


rf = RegionMember[Polygon[0, line1[0], 0, line2[0], 100,line1[100]]];
bool1 = rf[data];
notbool1 = Not[#] & /@ bool1
datain = Pick[data, bool1];
dataout = Pick[data, notbool1];


This has the desired effect.

Now suppose I only have one line, since I can't make a closed region what would be the best way to select points either above or below a line? What if the curve is not a straight line? Any ideas?

Pick[data, RegionMember[HalfPlane[line1[0], line1[1], 0, -1], data]]

2 Answers
2

Some knowledge about (planar) analytic geometry facilitates this problem. Suppose now you only have line1, this

line1

Select[data, line1[ #[[1]] ] < #[[2]] &]


selects out the points above line1; the key lies in the inequality. If it is connected by >, then the points below line1 you will get.

line1

>

line1

in, out = GeneralUtilities`SelectDiscard[data, line1[#[[1]]]<=#[[2]]<=line2[#[[1]]]&];

Show[ListPlot[in, out, PlotStyle -> Green, Red],
Plot[line1@x, line2@x, x, 0, 100,
Filling -> 1 -> 2, Opacity[.5, LightBlue], None]]


above1, below1 = GeneralUtilities`SelectDiscard[data, line1[#[[1]]] <= #[[2]] &];
above2, below2 = GeneralUtilities`SelectDiscard[data, line2[#[[1]]] <= #[[2]] &];

plt1, plt2 = Show[ListPlot[#, PlotStyle -> Green, Red],
Plot[line1@x, line2@x, x, 0, 100,
Filling -> 1 -> 2, Opacity[.5, LightBlue], None]] & /@
above1,below1, above2, below2 ;
Row[plt1, plt2, Spacer[5]]


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