MATLAB - Intersect between a surface and a plane - matlab

Question

I have a 3D mesh like in this picture.
Now what I want to do is create a plane that will intersect the surface at a certain Z value. I would then want to get the x and y coordinates of this intersection and have matlab output them.
What I'm planning on doing is that this picture is a model of a lake. This lake will have water evaporating that will be removing a certain z value of water. I would then like to see what the new shoreline would look like by obtaining the x and y coordinates of this intersection.
This is my code for plotting that picture.
function plot(x,y,z)
Contour = xlsread('C:\Users\Joel\Copy\Contour','A2:D4757');
x = Contour(:,1);
y = Contour(:, 2);
z = Contour(:,3);
F = TriScatteredInterp(x,y,z);
[X,Y]=meshgrid(linspace(-600,600,300));
Z=F(X,Y);
surf(X,Y,Z);
end

Answer 1

You can do this by simply thresholding the interpolated Z values
inside = Z < seaLevel; % binary mask of points inside water
shoreline = bwmorph( inside, 'remove' ); % a mask with only shoreline pixels eq to 1
figure;
surf( X, Y, Z, 'EdgeColor', 'none', 'FaceColor', [210,180,140]/255, 'FaceAlpha', .5 );
hold on;
ii = find( shoreline );
plot3( X(ii), Y(ii), seaLevel*ones(size(ii)), 'b', 'LineWidth', 2 );

Answer 2

The contour3 will give nicer boundaries:
[h,c]=contour3(X,Y,Z,[seaLevel seaLevel]);
seaLevel is given twice: otherwise contour3 thinks seaLevel is the number of levels to automatically calibrate. And to nicely annotate with the numeric height of your seaLevel:
clabel(h,c);
you may modify c to print "sea level" instead of num2str(seaLevel).

Answer 3

If you don't have the MATLAB toolbox for image processing you can't use the function "bwmorph". As a solution you can replace line 2 of Shai's code with the following code which reimplements the bwmorph function for parameter 'remove'. (The reimplementation is probably neither very perfomrant nor an exact reimplementatin (the borders of the matrix aren't used) - but the solution should work as a first step. Feel free to improve).
shoreline= zeros(size(inside));
for i_row = 2:size(inside,1)-1
for i_col = 2:size(inside,2)-1
if(inside(i_row,i_col))
if (~( inside(i_row+1,i_col) && ...
inside(i_row-1,i_col) && ...
inside(i_row,i_col+1) && ...
inside(i_row,i_col-1)))
inside2(i_row,i_col) = 1;
end
end
end
end