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Fit a curve to data points x = f(y)

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I have data points represented by red stars on a graph (Fig 1, attached), and I would like to fit a curve to them. The curve does not have to be accurate -- it just needs to serve as a visual guide. I have drawn a sketch below to show what I would like. The other curves on the graph are by-products from the code I pulled this image from, and are not relevant to this problem. How can I fit a curve to the red data points in MATLAB?
I have tried using polyfit, smoothingspline, pchip and other curve-fitting tools, but all of them connect the wrong data points together, since this graph is actually x = f(y). In MS Excel, if I switch the axes so the curve becomes a one-to-one function where y = f(x), I can easily fit a quadratic curve to the points.
I am currently plotting each point indivdually. I can plot the points with a line, but it is not very smooth (see Fig 2, attached). I guess I could just increase the number of data points, but that increases computation time too much. Any suggestions?
Please find below some things I have already tried. The red data points are saved in 1 x 11 doubles p_tn (x values) and p_Tn (y values).
Thank you so much! PLEASE let me know if you need more information, clarification, or data.
%Attempt 1 - Polyfit
[p,s,mu] = polyfit(p_Tn,p_tn,3);
[Y,delta] = polyval(p,p_Tn,s,mu)
X = linspace(0,0.05,length(Y));
%Attempt 2 - Non parametric fitting
xq = linspace(0,0.05,100);
p = pchip(p_tn',p_Tn',xq);
pp = ppval(p,xq);
%Attempt 3 - Smoothingspline
f = fit(p_tn',p_Tn','smoothingspline');
%Attempt 4 - Split upper and lower half of data points and use polyfit
for i = 1:length(p_tn)-1
if p_tn(i) > p_tn(i+1)
x1(i) = p_tn(i) ;
y1(i) = p_Tn(i) ;
elseif p_tn(i) < p_tn(i+1)
x2(i) = p_tn(i) ;
y2(i) = p_Tn(i) ;
p1 = polyfit(x1,y1,2);
p2 = polyfit(x2,y2,2);
xf1 = linspace(min(x1),0.05);
xf2 = linspace(min(x2),0.05);
f1 = polyval(p1,xf1);
f2 = polyval(p2,xf2);
Sarah Armstrong
Sarah Armstrong on 25 Sep 2019
Of course! I have p_tn (x values) and p_Tn (y values) attached in a .mat file. Thanks!

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Accepted Answer

darova on 25 Sep 2019
Look HERE and HERE
Sarah Armstrong
Sarah Armstrong on 30 Sep 2019
Awesome, I will play around with this instead of using a loop. I am also thinking about trying polar co-ordinates to see if that can refine it as well, but for now the curve is accurate enough as-is! Thank you for your help.

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More Answers (1)

Ted Shultz
Ted Shultz on 25 Sep 2019
Because you are looking to make a function of “y” rather than “x”, you would need to flip the X and Y when you solve the equation (this is equivalent to when you rotated in excel).
Try something like this:
p = polyfit(y,x,n)
y1 = linspace(0,4*pi);
x1 = polyval(p,y1);

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