finding the slope of each segement in a fitted curve

having the following plot,

Is there a method that would allow me to find the slope of each segment in this plot or at least, how I cann retrieve the x , y coordinates for the points on the plot so I can use them to find the slope?

attached is the data I am fitting, the x coordinate is GDALT variable and the y coordinate is the NE variabel. I used the curve fitting toolbox to generate this plot.

[Matt J]

You speak as if the plot is to be viewed as piecewise linear. It doesn't look like it is.

[Akira Agata]

It might be better to smoothen your data before calculating slope for each point, like:

T = readtable('https://jp.mathworks.com/matlabcentral/answers/uploaded_files/963595/t1.txt');

idx = isnan(T.NE);
T(idx, :) = [];

x = linspace(T.GDALT(1), T.GDALT(end));
y = interp1(T.GDALT, T.NE, x, 'spline');

figure
plot(T.GDALT, T.NE, 'o-')
hold on
plot(x, y)
legend({'Original', 'Smoothed'})

[Salma fathi]

Thank you for your reply, I believe I can do that also by using interpolating via 'cubic spline' instead of 'linear' in the curve fitting toolbox and it would give the same result right?

But I am still not sure how this will help me in finding the slope at the indicated points in the plot...

Answer 1

[Chunru]

T = readtable('https://jp.mathworks.com/matlabcentral/answers/uploaded_files/963595/t1.txt');
idx = isnan(T.NE);
T(idx, :) = [];
x = T.GDALT;
y = T.NE;

plot(x, y, 'o-')

% The slope for each segment
slope = diff(y)./diff(x)

slope = 15×1

1.0e+10 * 0.1733 0.4733 1.0267 1.1600 0.8067 0.3600 -0.1067 -0.3467 -0.4267 -0.4267

[Salma fathi]

Thank you for the help.

Answer 2

[Akira Agata]

By applying interpolation, you can decrease and, as a result, the deviation will be more accurate.

The following is an example.

BTW, you don't need to use Curve Fitting Toolbox for interpolation. The function interp1 is in the basic MATLAB.

T = readtable('https://jp.mathworks.com/matlabcentral/answers/uploaded_files/963595/t1.txt');

idx = isnan(T.NE);
T(idx, :) = [];

x = linspace(T.GDALT(1), T.GDALT(end));
y = interp1(T.GDALT, T.NE, x, 'spline');

dy = diff(y)/uniquetol(diff(x));

figure
yyaxis left
plot(T.GDALT, T.NE, 'bo')
hold on
plot(x, y, 'b-')
xlabel('NE')
ylabel('GDALT')
yyaxis right
plot(x(1:end-1),dy)
ylabel('\Delta GDALT / \Delta NE')
legend({'Original', 'Smoothed', 'Slope'})

[Salma fathi]

Thank you for the great explanation, I have a better understanding now. Much appreciated.