Finding intersection of plotted dataset and line

I am working with a stress strain curve at the moment and want to find the yield stress at 0.2%. I basically wanna find where the plotted dataset and the plotted line cross each other.

I feel like there should be a really easy way to do this, that is not using graph tools. Help is much appreciated and more info can be given if needed

youngs_modulus = strain([900:1600])\sigma([900:1600]);
offset_line = youngs_modulus*strain - youngs_modulus*0.002;
plot(strain, sigma)
hold on
plot(strain, offset_line)

Answer 1

[Star Strider]

One approach:

x = 0:20;                                                   % Create Data
y1 = 15 - 3*x;                                              % Create Line
y2 = 2*x - 20;                                              % Create Line

yd = y1 - y2;                                               % Subtract
x_cross = interp1(yd, x, 0);                                % X-Coordinate
y_cross = 15 - 3*x_cross;                                   % Substitute Into One Equation To Get Y-Coordinate

figure
plot(x, y1,    x, y2,    x_cross, y_cross, '+r')
grid
text(x_cross, y_cross, sprintf('x = %.3f\ny = %.3f', x_cross, y_cross), 'VerticalAlignment','bottom')

This appears to be linear. This code just subtracts the data of one line from the other, interpolates to find the x-intersection, and uses one of the equations to calculate the y-intersection.

If you know the equations for both lines, you can use basic algebra to calculate the intersection from the slopes and intercepts.

[Johannes Brunsbück]

The problem is that I don't know the equations for both lines. One is just made up by 13000 data points. And the other one I do know

[Star Strider]

My code does not require that you know the equations for both lines (although if they are actually linear, you could easily estimate the parameters). You only need to the know the equation of one line to use my code (to calculate the y-coordinate of the intersection). My code does not otherwise use the equations to find the intersection, and uses only the data.

[Johannes Brunsbück]

I still don't get it to work. I have written this:

youngs_modulus = strain([900:1600])\sigma([900:1600]);
offset_line = youngs_modulus*strain - youngs_modulus*0.002;

yd = offset_line - sigma;
x_cross = interp1(yd, strain, 0);
y_cross = -youngs_modulus*0.002 + youngs_modulus*strain
figure
plot(strain, sigma,     strain, offset_line,    x_cross, y_cross, 'r')
grid

I get this errror

Error using griddedInterpolant
The grid vectors must contain unique points.

Error in interp1 (line 151)
        F = griddedInterpolant(X,V,method);

Error in Untitled5 (line 12)
x_cross = interp1(yd, strain, 0);

[Star Strider]

Unfortunately, I cannot solve that without your data.

[Johannes Brunsbück]

Here is the data I am using. I am converting force load to the pressure sigma.

[Star Strider]

The first column is obviously time and the third is obviously strain. What are the others? Is ‘Load’=‘sigma’?

Time;Extension;Strain 1;Load

(My background is biomedical engineering, emphasizing signal processing, control, parameter estimation and system identification.)

[Johannes Brunsbück]

Made an error the first column is strain and the second is force. Sigma is force divided by the area which is assumed to be constant

[Star Strider]

The lines do not appear to cross in any meaningful way. Testing for the cross using:

yd = sigma - offset_line;                                               % Subtract

produces an irregualr area (‘strain’ ranging from 0 to 0.260) where there appears to be much oscillation. However a low-degree polynomial fit of that region indicates that the fitted line to ‘yd’ never goes below 0, so there do not appear to be any actual zero-crossings:

My full code —

D = dlmread('data.txt',';',3,0);
t = D(:,1);
strain = D(:,2);
force = D(:,3);
load = D(:,4);
sigma = force;

youngs_modulus = strain([900:1600])\sigma([900:1600]);
offset_line = youngs_modulus*strain - youngs_modulus*0.002;

yd = sigma - offset_line;                                               % Subtract
zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);                    % Returns Approximate Zero-Crossing Indices Of Argument Vector
xcidx = zci(yd);                                                        % Zero-Crossing Indices
p = polyfit(strain(1:max(xcidx)), yd(1:max(xcidx)), 3);                 % Smoothing Function
fv = polyval(p, strain(1:max(xcidx)));                                  % Smoothing Function Evaluated

figure
plot(strain, sigma)
hold on
plot(strain, offset_line)
plot(strain, yd)
plot(strain(xcidx), yd(xcidx), '+r')
hold off
legend('Sigma', 'Offset Line', 'Location','NW')
xlabel('Strain')

figure
plot(strain, yd)
hold on
plot(strain(xcidx), yd(xcidx), '+r')
plot(strain(1:max(xcidx)), fv, '-g', 'Linewidth',1)
hold off
title('Intersection Region')
xlabel('Strain')
ylabel('Sigma - Offset Line')
legend('yd = sigma - offset_line', 'Zero-Crossings Detected', 'Smoothing Function', 'Location','N')
axis([0  0.3    -0.0001  0.0002])

Look through this to be certain I imported and calculated everything correctly. If I did, there is likely nothing further that I can offer.