Points inside multiple polygon for contour

I made the following contourplot.

Then, I plot discretized points over this plot.

I wanted to find the (x,y) coordinates of the discretized points within the region between the boundaries 40.94 and 43. This is the way how I approached it. With contourtable I acquired the (x,y) coordinates of the contourlines.

muSP = [0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9];
muRP = [0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9];
[X,Y] = meshgrid(muSP,muRP);
Z = cell2mat(reshape(AoR_mean,[9,9]));
[C,h] = contour(X,Y,Z,(40.9431:2.0538:42.9969));
hold on
title('Angle of Repose - Ledge Test 2D');
xlabel('\mu_s')
ylabel('\mu_r')
clabel(C,h,'LabelSpacing',500,'FontSize',8);
h.LevelList = round(h.LevelList,2);
set(gca,'XTick',0.1:0.1:0.9,'XTickLabel',0.1:0.1:0.9,'XTickLabelRotation',45);
set(gca,'YTick',0.1:0.1:0.9,'YTickLabel',0.1:0.1:0.9);
grid on
% Extract x- and y-coordinates of contour lines
contourTable = getContourLineCoordinates(h);
% Define grid for the variable space
N1 = 80;
muRP_grid = linspace(0.1,0.9,N1);
muSP_grid = linspace(0.1,0.9,N1);
[R,S] = meshgrid(muRP_grid,muSP_grid);
plot(R,S,'.r');
hold off

% x- and y-coordinates of polygon vertices, i.e. between AoR of 40.11 degrees 
% and AoR of 43.83 degrees
xv = table2array(contourTable(1:31,3));
yv = table2array(contourTable(1:31,4));
inside_variablespace = inpolygon(R,S,xv,yv);
% x- and y-coordinates corresponding to the discretized points in the
% variable spac
xcoord = R(inside_variablespace);
ycoord = S(inside_variablespace);

However, for some reason I don't get de discretized points within the boundaries 40.94 and 43.

Answer 1

[KSSV]

Read about inpolygon. If you have a polygon and a set of points, you cann extract the points lying inside this polygon using that.

[Tessa Kol]

I did read about inpolygon and tried the solution with NaN. Didn't work.

Also I used the (x,y) coordinates of the contourlines. I obtained these coordinates with the function getContourLineCoordinates.

Since that didn't work either, what can be the problem?

[Tessa Kol]

I think I know where is goes wrong.

Matlab connects two boundary lines that shouldn't be connected. Hence the problem.

[KSSV]

You remove the boundary line..

[Tessa Kol]

How can you do that?

[Adam Danz]

Tessa, the polygon is defined by the (x,y) values within level 40.94, only.

idx = contourTable.Level==40.94; % or contourTable.Group==1
inpolygon(x,y,contourTable.X(idx), contourTable.Y(idx))

[Tessa Kol]

But how does that work if I have the boundary 40.94 and 43, respectively?

[Adam Danz]

Check out the examples in the documentation

https://www.mathworks.com/help/matlab/ref/inpolygon.html#buanygl-3

You can call inpolygon on the outer polygon, then call inpolygon on the inner polygon, then remove selected points that are in both.

Example

A = inpolygon(...)
B = inpolygon(...)
A(B) = false;

Use these answers as a stepping stone rather than looking for full solutions.

[Tessa Kol]

It worked thank you! I adjusted the code as follow:

xv1 = [0.9;table2array(contourTable(1:15,3));0.9];
yv1 = [0.9;table2array(contourTable(1:15,4));0.9];
xv2 = table2array(contourTable(16:18,3));
yv2 = table2array(contourTable(16:18,4));
xv3 = table2array(contourTable(19:31,3));
yv3 = table2array(contourTable(19:31,4));
inside_variablespace1 = inpolygon(R,S,xv1,yv1);
inside_variablespace2 = inpolygon(R,S,xv2,yv2);
inside_variablespace3 = inpolygon(R,S,xv3,yv3);
% x- and y-coordinates corresponding to the discretized points in the
% variable spac
inside_variablespace1(inside_variablespace2) = false;
inside_variablespace1(inside_variablespace3) = false;
xcoord = R(inside_variablespace1);
ycoord = S(inside_variablespace1);

Resulting in:

Answer 2

[Ameer Hamza]

There is no need to use inpolygon here. You can directly create a mask from the Z matrix. Following shows an example, and find the x and y coordinates from the mesh between contour lines at 0.33 and 0.66

[X, Y] = meshgrid(linspace(-1, 1));
Z = X.^2 + Y.^2;

levels = [0 0.33 0.66 1]; % levels for contour plot

mask = Z < 0.66 & Z > 0.33;
x_coord = X(mask);
y_coord = Y(mask);

contour(X, Y, Z, levels)
hold on
plot(x_coord, y_coord, '+')

[Tessa Kol]

How do you propose to do this since the contourlines are 40.97 and 43, but the (x,y) coordinates of those contourlines are between 0.4 and 0.9?

[Ameer Hamza]

You will write it like this

mask = Z < 43 & Z > 40.97;
x_coord = X(mask);
y_coord = Y(mask);

The x-y coordinates will be extracted from corresponding locations in X and Y matrix.

[Tessa Kol]

But that doesn't work here.

[Ameer Hamza]

What is the error. In the data you shared, AoR_mean is undefined, so I cannot run your code to see the issue.