x-intersection of part of extended line from curve

Hello There.

I have plot which looks below. Part of curve which behave like straight line such as red highlighted part. I want extend this red line and find time when it intersects with horizonal axis (Time).

The initial code is provided with redline part. I will be using this method to analyses many other similar types of graphs.

Answer 1

[Star Strider]

Add these lines to your code after the ‘m’ calculation and before figure(1):

B = [TC ones(size(TC))] \ IC;                                           % Fit Red Line (Estimate Parameters)
Slope = B(1);
YIntercept = B(2);
XIntercept = -YIntercept / Slope                                        % Calculate X-Intercept
ExtLine = [[TC(1); XIntercept] ones(size(TC))] * B                      % Y-Coordinates

and after the first hold call:

plot([TC(1); XIntercept], ExtLine, '-g')                                % Plot Line

The x-intercept is 1.4494 microseconds.

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[Akhtar Rind]

Thank you Star. I checked this in other data, this is working. This bags me one related question which will help me to analyse curve.

Can we find angle of this extedned line (Red or Green) w.r.t horizontal/vertical? I am looking for optimal angle from many data plots.

[Alan Stevens]

The angle with respect to the horizontal is given by the arctangent of the slope. i..e.

theta = atan( max(y_redline_value) / ( max(x_redline_value) - x_desired ) )

using the same notation as my previous reply.

[Star Strider]

Akhtar Rind —

My pleasure.

The angle is the arctangent of the ‘Slope’ variable, ‘B(2)’ in my code, 1.338295858640334 radians, or 76.678704439927756 degrees.

If my Answer helped you solve your problem, please Accept it!

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[Akhtar Rind]

Star Strider

You mean B(1) as that is the slope. B(2) is YIntercept

Thanks

[Star Strider]

Correct. That was a typo on my part. (Still too early for me here!) They are labeled correctly in my code. The angles were calculated from the ‘Slope’ variable, so they are correct.

Answer 2

[Alan Stevens]

You can use the following relation:

( max(y_redline_value) - min(y_redline_value) ) / ( max(x_redline_value) - min(x_redline_value) )=

( max(y_redline_value) - 0 ) / ( max(x_redline_value) - x_desired )

Rearrange to get x_desired (i.e. the value of the straight line intercept on the x-axis).

[Akhtar Rind]

Thank you very much for explaination. This code worked as well.