Curve fitting of data points

I have a series of repeated data points that i am trying to fit with a skewed curve. In the graph I am showing one set of the data points which are in blue. The black hand drawn line is the kind of fit i want for my data. I want my fit to be a curve like the one drawn, not a combination of two linear functions or a sawtooth. I have included the data points in text files. Thank you.

[Walter Roberson]

Your fit has multiple y values for the same x. Is that desired, or should it instead be unique y values for each x (just possibly steep) ?

[Angela]

Although in the plot it looks like there are multiple values for the same x, in reality they are unique. For example for X=4172,Y=55.31 the next point is X=4173,Y=56.71. The plot is just very steep on the left side. Thank you.

[Walter Roberson]

That may be true for the input data, but the black line you show us as the desired fit distinctly wobbles back and forth on the x axis, and since that is presented as your desired outcome, the implication could be that you want the output function to have multiple y values for some of the x.

Anyhow... so if a sharp corner is not desired, then what turn radius should be used?

Do you have a model for what you want the function to be like?

[Angela]

The wobble is because i am not very good at drawing a straight line but the intent was for that line to be straight. You are right, the model that i want should be almost a straight line on the left side, unfortunately i do not have a model function, i am trying to built a model based on this data so i do not have the form, I am just trying to fit the data. Thank you.

Answer 1

[Matt J]

My suggestion would be a hyperbola, but rotated.

[Angela]

The problem with the rotated hyperbola is that it has a form of f(x,y), the y is because of the rotation. I am familiar with fitting a f(x) but i am not sure how to fit a f(x,y) function.

[Matt J]

You are only interested in the positive portion of the hyperbola, so you can write that portion as,

y=a*sqrt(1+(x/b)^2);

which will be like the green curve in the image below. You can also rotate your input x,y data about 135 degrees counter-clockwise so that it will also have a corresponding profile like the red lines in the image below.

Now everything is oriented in a familiar way.

[Angela]

Thank you, it worked well!

Answer 2

[Walter Roberson]

Have you considered smoothing splines? https://www.mathworks.com/help/curvefit/smoothing-splines.html

[Angela]

Thank you for the suggestion. I did try that but unfortunately it does not give me the curved shape i want, it looks more like a combination of 2 linear fits (one for the sloped line on the right and another one that is almost straight for the left side).