Curve family fitting question

Hello everyone,

I want to ask how could I do this kind of curve fitting in matlab? as you can see in the figure, there are a curving family. the difference between curves in this family is caused by a paramter "R"( shown in the legend) which i use in the simulation. if it is possible that I use the (x,y) of these three curves and their corresponding parameter "R"(1000,1200,1400 respectively) to fit the relationship between "R" and (x,y)? (here I do not need the relationship between x and y, but I want to fit the relationship between "R" and "(X,Y)".

[John D'Errico]

In order to do curve fitting, you need to have a model, or you need to use some generic, non-parametric model. You have shown no hint that you have any idea of a model.

The non-parametric models I mention might be of the form of splines, polynomials, Fourier series, etc. However, none of them would have any remote chance of fitting the curves you show. Sorry. Essentially, this is not the kind of problem you can easily solve with curve fitting. At most, you can use interpolation to try to "fit" those curves. But any interpolation method will not then have coefficients you could then happily model as a function of another parameter.

[Frank C]

hi thank you for your reply，I don't think the interpolation could solve this either. I am not experienced in “curve fitting" , but previously, I only do the fitting like finding out the relationship between x and y using a partiular model like y=f(x), there was a single dependable variable y a single independent variable x. but here,I want to ask if it possible to do the curve fitting between (x,y) and R ,using the model (x,y)=f(R). i am not sure what the model "f" here shoulld be( but we can see with the variation of "R" the resulting curves change in a regular way), so I post the figure,to show groups of (x,y) and R. so if it is possible to fitting the relationship between one independent variable "R" and two dependable variable(x,y)?