Area under the curve ignoring axis values (Absolute area)

Hi all, I am computing area under the curve using "Trapz" function where it takes x and y co-ordinates into consideration. For example, if you consider the attached figure, I am getting the value of shaded area as 296 where it takes into x and y axis values. But I would like to compute only the absolute area ignoring x and y axis values. In this example y axis height is around 7 (-84 to -91) and x axis distance is around 0.1 hence the absolute area would be very small. Any help in this would be highly appreciated.

Answer 1

[Scott MacKenzie]

The trapz function uses integration so the result is the area under the curve. That's not what you want. I suggest you first create a polygon of points encompassing the area of interest. Then use the area function to get the area. Here's and example using some test data similar to your data.

% test data
x = -0.8:0.1:1;
y = [-75 -76 -77 -78 -78 -79 -80 -81 -86 -87 -88.3 -92 -91 ...
    -88 -86 -85 -84 -84 -83];

% x range for area of interest
x1 = 0;
x2 = 0.6;

% find x indices for range of interest
idx1 = find(x >= x1, 1);
idx2 = find(x >= x2, 1);

% create polyshape for area of interest
x1 = x(idx1:idx2);
y1 = y(idx1:idx2);
ps = polyshape(x1, y1);

% compute and output area
a3 = polyarea(x1,y1);
fprintf('Area: %f\n', a3);

Area: 1.630000

% plot it
plot(x,y);
set(gca,'ylim', [-95 -70]);
hold on;
plot(ps);

[Ganesh Naik]

Hi Scott, thanks for your answer. Currently for my work I am using "ginput" to select two points and computing the area. Would this work for ginput? Please let me know your opinion. I will try it my end and let you know.

[Scott MacKenzie]

Hmmm, in that case, I guess you'd need to first decide on what area you are interested in. It's unlikely a mouse click will be exactly on a data point; so, what do you want to happen in the various possibilities there?

[Ganesh Naik]

Hi Scott I have managed to get the precise points using modified "ginput" function. Everytime, I select (click) two points and generate (x1,y1) and (x2,y2) points. The figure above is the result of using modified ginput. After that I compute the area and shade them. I think I can modifiy your solution to achieve the result. I will try it and let you know. Any opinion or suggestion from your end is highly appreciated.

[Scott MacKenzie]

I just posted an new answer that uses ginput.

Answer 2

[Scott MacKenzie]

@Ganesh Naik Here's a new answer that uses ginput to "select" data points along the line for definiing the area of interest. You'll need to run this yourself to get a feel for the interaction with a mouse. Select two points along the data line and the area will be computed, sent to the command window, and plotted.

% test data (similar pattern to data in question)
xx = -0.8:0.1:1;
yy = [-75 -76 -77 -78 -78 -79 -80 -81 -86 -87 -88.3 -92 -91 ...
    -88 -86 -85 -84 -84 -83];

% interpolate to get more points and better "closest" point to mouse click
x = linspace(min(xx), max(xx), 250);
y = interp1(xx, yy, x);

% plot data and set axes
plot(x,y);
hold on;
axis([-1, 1.2, -95, -70]);

% get two mouse button clicks
[gx, gy] = ginput(2);

% get indices of "closest" data points along x-axis
idx1 = find(x >= gx(1), 1);
idx2 = find(x >= gx(2), 1);

% create polyshape for area of interest
x1 = x(idx1:idx2);
y1 = y(idx1:idx2);
ps = polyshape(x1, y1);

% compute, output, and plot area
a = polyarea(x1,y1);
fprintf('Area: %f\n', a);
plot(ps);

[Ganesh Naik]

Hi Scott, thanks for your help with the ginput part. Although I am using modifed ginput function but interpolating part that you mentioned would help me to select the precise points. Thanks again for your help, much appreciated. I am going to accept this answer.