MATLAB: How to calculate area between curve and horizontal line

areaarea between curvesyline

Apologies if this has already been answered in another form elsewhere on the forums, however I couldn't find any answers that helped me directly with my code. I currently have code that maps the profile and area of a channel. I wish to have a horizontal y value across my channel width to simulate the fluctuating water level, the example line is shown in the image as the green line. So for example I would want to calculate and shade the area underneath the greenline only.
With the function would I be able to loop the same function for a range of values for the horizontal values, to provide an output I could then plot? A vector form would be ideal if possible.
I've already tried to use the area and fill commands unsuccesfully, or maybe I was not using the correct format for them.
I've also attached the relevant code below, any help would be much appreciated.
x = [ 0 1 2 3 4 5 6 7 8 9 10 11 12];
y = -[0 -0.5 -0.8 -0.8 -1 -1.1 -1.2 -1.2 -1.4 -1.2 -1.1 -1 0]; % y values in image were produced by rand function
subplot(2, 1, 1);
area(x,-y)
grid on;
hold on;
for k = 1 : length(x)
	xline(x(k), 'Color', 'k');
end
yt = yticks;
for k = 1 : length(yt)
	yline(yt(k), 'Color', 'k');
end
plot (x, -y, 'r.-', 'LineWidth', 3, 'MarkerSize', 30)
hold on
yline(-0.5,'g',11);
xlabel('Chainage (m)', 'FontSize', 11);
ylabel('Depth (m)', 'FontSize', 11);
An = (trapz(x,y)); % Overall area.
% Compute areas within each pair of x locations.
midpoints = (y(1:end-1) + y(2:end))/2;
deltax = diff(x);
Ani = deltax .* midpoints;
subplot(2, 1, 2);
bar(x(1:end-1)-x(1)+ 0.5, Ani);
title('Areas of Slices', 'FontSize', 14);
xlabel('x', 'FontSize', 11);
ylabel('Area (m^2)', 'FontSize', 11);
grid on;

Best Answer

clc;clear;
x = [ 0 1 2 3 4 5 6 7 8 9 10 11 12];
y = [0 -0.5 -0.8 -0.8 -1 -1.1 -1.2 -1.2 -1.4 -1.2 -1.1 -1 0];
h0= -0.5; %the axis in the graph
h=ones(size(x))*h0;
Int=pchip(x,y);
xx=linspace(x(1),x(end),500);
yy=y-h0;
yyy=pchip(x,yy,xx);
gt=yyy<0;
theArea =-trapz(xx(gt), (yyy(gt)))
hold off
area(xx, min(ppval(Int,xx), h(1)), h(1), 'EdgeColor', 'none', 'FaceColor', 'b'),grid,
hold on
plot(xx,ppval(Int,xx),'k',xx,h0,'Linewidth',2)
set(gca, 'XLim', [x(1) x(end)], 'YLim', [min(y) 0]);
title(strcat('BlueArea=', num2str(theArea)))
xlabel('Chainage (m)', 'FontSize', 11);
ylabel('Depth (m)', 'FontSize', 11);
You can change h0 which is horizontal line. when h0=-1
when h0=-0.5
when h0=0
I RESHAPED YOUR X AND Y DATAS 500 INTERVALS WITH PCHIP INTERPOLATION, IF NOT THE DATA IS NOT ENOUGH FOR GOOD SOLUTION.
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