Extract data below a curve

I have a gridded data as given in the figure. I want to extract data below the given line(ABCDEFGHI). The co-ordinate of the corner point of the line is given. That means I want to keep only data below that line.

Answer 1

[Veronica Taurino]

Your input data is something like that:

% Hypotesis: black points do not overlay the grid (can lay in between blue points)
A =[1 4.5];
B = [2.5 5.3];
C = [3.5 5.1];
D = [6.2 6.1];
E = [6.8 6.1];
F = [7.2 6];
G = [9.5 4.8];
H = [11.2 5.5];
I = [13 5];
ALL= [A;B;C;D;E;F;G;H;I];
plot(ALL(:,1),ALL(:,2))

[X,Y] = meshgrid(1:12,1:7); %gridded point
hold on
plot(X,Y,'.k') % grid

If your black points (A,B,C,...) do not overlay the grid but can lay in between blue points, like this:

first you need to evaluate the red point I dotted in red in the image above with a linear interpolation:

xq = [1 2 3 4 5 6 7 8 9 10 11 12]; % X-grid coordinates at which evaluate the Y
vq = interpn(ALL(:,1)',ALL(:,2)',xq,'linear');

and then you can do a comparison like that:

for jj=1:size(Y,2) 
       YY(:,jj)=Y(:,jj)<=vq(jj)
end

% Plot only remaining points
plot(X(YY),Y(YY),'or')

[Adam Danz]

+1, nice approach

1 error and 1 inefficiency to improve,

1. D and E are the same coordinate in the current version of your answer and that causes an error in interpn due to duplicity.
2. The jj-loop can be replaced by,

YY = Y < vq;